Field Oriented Control Autotuner

Automatically and sequentially tune multiple PID control loops in field-oriented control application

Since R2020a

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Libraries:
Motor Control Blockset / Controls / Controllers

Description

The Field Oriented Control Autotuner block allows you to automatically tune PID control loops in your field-oriented control (FOC) application in real time. For more information on field-oriented control, see Field-Oriented Control (FOC).

You can automatically tune PID controllers associated with the following loops:

• Direct-axis (d-axis) current loop

• Quadrature-axis (q-axis) current loop

• Speed loop

• Flux loop

For each loop the block tunes, the Field Oriented Control Autotuner block performs the autotuning experiment in closed-loop without a parametric model associated with that loop. The block allows you to specify the order in which the control loops are tuned. When the tuning experiment is running for one loop, the block has no effect on the other loops. During the experiment, the block:

1. Injects a test signal into the plant associated with that loop to collect plant input-output data and estimate frequency response in real time. The test signal is combination of sinusoidal perturbation signals added on top of the plant input.

2. At the end of the experiment, tunes PID controller parameters based on estimated plant frequency responses near the target bandwidth.

3. Writes updated PID gains at the block output, allowing you to transfer the new gains to existing controllers and validate the closed-loop performance.

You can use the Field Oriented Control Autotuner block to tune the existing PID controllers in your FOC structure. If you do not have the initial PID controllers, you can use the Estimate Control Gains and Use Utility Functions workflow to obtain them. You can then use the Field Oriented Control Autotuner block for refinement or retuning.

If you have a code-generation product such as Simulink^® Coder™, you can generate code that implements the tuning algorithm on hardware, letting you tune in real time, using or without using Simulink to manage the autotuning process.

If you have a machine modeled in Simulink with Motor Control Blockset™ and an initial FOC structure with PID controllers, you can perform closed-loop PID autotuning against the modeled machine. Doing so lets you preview the plant response and adjust the settings for PID autotuning before tuning the controller in real time.

The block supports code generation with Simulink Coder, Embedded Coder^®, and Simulink PLC Coder™. It does not support code generation with HDL Coder™. For real-time applications, deploy the generated code on a rapid prototyping hardware such as Speedgoat^® real-time target machine.

For more information about using the Field Oriented Control Autotuner block, see How to Use Field Oriented Control Autotuner Block.

This block requires Simulink Control Design™ software.

Examples

Tune PI Controllers Using Field Oriented Control Autotuner

Computes the gain values of PI controllers available in the speed and current control loops by using the Field Oriented Control Autotuner block. For details about this block, see Field Oriented Control Autotuner. For details about field-oriented control, see Field-Oriented Control (FOC).

• Open Model

Tune PI Controllers Using Field Oriented Control Autotuner Block on Real-Time Systems

Compute the gain values of PI controllers within the speed and current controllers by using the Field Oriented Control Autotuner block.

• Open Model

Limitations

• The block does not support inherited sample time (–1) when the Experiment Mode is set to PRBS.

Ports

Input

PIDout daxis — Signal from direct-axis current controller

scalar

This port accepts the output of the d-axis controller PID_daxis, which is the output of PID controller that regulates the d-axis current of the motor. The controller generates the d-axis voltage reference Vd_ref, while the FOC autotuner block generates perturbations used during the tuning experiment for the d-axis current loop.

Dependencies

To enable this port, select Tune D-axis current loop.

Data Types: single | double

measured feedback daxis — Measured direct-axis current

scalar

This port accepts the d-axis current obtained from the measured (sensed or estimated) motor currents.

Dependencies

To enable this port, select Tune D-axis current loop.

Data Types: single | double

PIDout qaxis — Signal from quadrature-axis current controller

scalar

This port accepts the output of the q-axis controller PID_qaxis, which is the output of PID controller that regulates the q-axis current of the motor. The controller generates the q-axis voltage reference Vq_ref, while the FOC autotuner block generates perturbations used during the tuning experiment for the q-axis current loop.

Dependencies

To enable this port, select Tune Q-axis current loop.

Data Types: single | double

measured feedback qaxis — Measured quadrature-axis current

scalar

This port accepts the q-axis current obtained from the measured (sensed or estimated) motor currents.

Dependencies

To enable this port, select Tune Q-axis current loop.

Data Types: single | double

PIDout spd — Signal from speed controller

scalar

This port accepts the output of the speed controller PID_speed, which is the output of PID controller that regulates the speed of the motor. The controller generates the q-axis current reference Iq_ref, while the FOC autotuner block generates perturbations used during the tuning experiment for the speed loop.

Dependencies

To enable this port, select Tune speed loop.

Data Types: single | double

measured feedback spd — Measured speed

scalar

This port accepts the measured (sensed or estimated) speed from the motor.

Dependencies

To enable this port, select Tune speed loop.

Data Types: single | double

PIDout flux — Signal from flux controller

scalar

This port accepts the output of the flux controller PID_flux, which is the output of PID controller that regulates the flux of the motor. The controller generates the d-axis current reference Id_ref, while the FOC autotuner block generates perturbations used during the tuning experiment for the flux loop.

For a permanent magnet synchronous motor (PMSM), there is no flux loop controller as the rotor flux is fixed and Id_ref is set to zero. In some applications you can provide a negative Id_ref value to implement field-weakening control and achieve higher rotor speeds at the cost of a higher current.

Dependencies

To enable this port, select Tune flux loop.

Data Types: single | double

measured feedback flux — Measured flux

scalar

This port accepts the measured (sensed or estimated) flux from the motor.

Dependencies

To enable this port, select Tune flux loop.

Data Types: single | double

start/stop — Start and stop autotuning experiment

scalar

To externally start and stop the autotuning process, provide a signal at the start/stop port and the ActiveLoop port.

• The experiment starts when the value of the signal changes from negative or zero to positive.

• The experiment stops when the value of the signal changes from positive to negative or zero.

For the duration of the experiment, for each loop, the block injects sinusoidal perturbations at the plant input associated with the loop, near the nominal operating point, to collect input-output data and estimate frequency response. When the experiment stops, the block computes PID gains based on the plant frequency responses estimated near the target bandwidth.

When the experiment is not running, the block does not inject any perturbations at the plant inputs. In this state, the block has no impact on plant or controller behavior.

Typically, you can use a signal that changes from 0 to 1 to start the experiment, and from 1 to 0 to stop it. Consider the following when you configure the start/stop signal.

• Start the experiment when the motor is at the desired equilibrium operating point. Use the initial controller to drive the motor to the operating point.

• Avoid any input or output disturbance on the motor during the experiment. If your existing closed-loop system has good disturbance rejection, then the experiment can handle small disturbances. Otherwise, large disturbances can distort the plant output and reduce the accuracy of the frequency-response estimation.

• Let the experiment run long enough for the algorithm to collect sufficient data for a good estimate at all frequencies it probes. There are two ways to determine when to stop the experiment:

  • Determine the experiment duration in advance. A conservative estimate for the experiment duration is 200/ω_c in superposition experiment mode or 550/ω_c in sinestream experiment mode, where ω_c is your target bandwidth.

  • Observe the signal at the convergence output, and stop the experiment when the signal stabilizes near 100%.

  For PRBS mode, based on the specified Target bandwidth and Controller sample time values, the block dialog displays the recommended experiment length in the Description section of the Experiment tab. Stopping experiment prematurely may lead to incorrect tuning results. (since R2024a)

• When you stop the experiment, the block computes tuned PID gains and updates the signal at the pid gains port.

You can configure any logic appropriate for your application to control the start and stop times of the experiment. The start/stop signal is specified along with ActiveLoop. ActiveLoop takes integer values 1 to 4 and specifies which loop to tune.

Alternatively, if you are tuning in simulation or external mode, you can specify the tuning experiment sequence, start time and duration in the block parameters.

Dependencies

To enable this port, on the Block tab under Parameters Source, select Use external source for start/stop of experiment.

Data Types: single | double

ActiveLoop — Specify active loop for autotuning experiment

scalar

Set the ActiveLoop value to specify which loop to tune when providing an external source for the start and stop times of the tuning experiment.

ActiveLoop Value	Loop to Tune
1	D-axis current loop
2	Q-axis current loop
3	Speed loop
4	Flux loop

You can configure any logic appropriate for your application along with the start/stop port to control the sequence and the time at which the loop tuning experiment runs. ActiveLoop takes integer values from 1 to 4 and specifies which loop to tune. Any other number will result in no tuning taking place regardless of the start/stop signal. For example, when you supply a constant value 2 at ActiveLoop and the signal at start/stop rises, the block starts the tuning experiment for the q-axis current loop.

Alternatively, you can specify the tuning experiment sequence, start time, and duration in the block parameters.

Dependencies

To enable this port, on the Block tab under Parameters Source, select Use external source for start/stop of experiment.

Data Types: single | double

bandwidth — Target bandwidth for tuning

scalar | vector | bus

Supply the values for the Target bandwidth (rad/sec) parameter for each loop to be tuned. If you are tuning multiple loops, you can specify the bandwidth as a vector or bus, entries of which correspond to the target bandwidth for the loops in this order:

• D-axis current loop

• Q-axis current loop

• Speed loop

• Flux loop

The vector signal must be specified as a N-by-1 or 1-by-N signal or if specified as a bus must have N elements, where N is the number of loops to be tuned. For instance, if you are tuning the q-axis current loop and the speed loop, and you specify a vector [5000, 200] at this port, the block tunes the q-axis current controller with the target bandwidth 5000 rad/sec and the speed loop controller with the target bandwidth 200 rad/sec.

If you are tuning multiple loops and specify a scalar value at this port, then the block uses the same target bandwidth to tune all the controllers. For effective cascade control, the inner control loops (d-axis and q-axis) must respond much faster than the outer control loops (flux and speed). Therefore, you must supply the target bandwidth as a vector or bus signal when tuning multiple loops.

Alternatively, you can specify target bandwidth for individual loops in block parameters. For more information on how to choose a bandwidth, see that parameter description.

Dependencies

To enable this port, on the Block tab under Parameters Source, select Use external source for bandwidth.

Data Types: single | double

target PM — Target phase margin for tuning

scalar | vector | bus

Supply a value for the Target phase margin (degrees) parameter for each loop to be tuned. If you are tuning multiple loops, you can specify target PM as a vector or bus, entries of which correspond to the target phase margin for the loops in this order:

• D-axis current loop

• Q-axis current loop

• Speed loop

• Flux loop

The vector signal must be specified as a N-by-1 or 1-by-N signal or if specified as a bus must have N elements, where N is the number of loops to be tuned. For instance, if you are tuning q-axis current loop and speed loop, and you specify a vector [60, 45] at this port, the block tunes q-axis current controller with target phase margin 60 degrees and speed loop controller with target phase margin 45 degrees.

If you are tuning multiple loops and specify a scalar value at this port, then the block uses the same target phase margin to tune all the controllers.

Alternatively, you can specify target phase margin for individual loops in block parameters. For more information on how to choose a target phase margin, see that parameter description.

Dependencies

To enable this port, on the Block tab under Parameters Source, select Use external source for target phase margin.

Data Types: single | double

sine Amp — Amplitudes of injected sinusoidal perturbation signals

vector | matrix

Supply a value for the Sine Amplitudes parameter for each loop to be tuned. Specify one of the following:

• Vector of length 5 to specify a different amplitude at each of [1/10, 1/3, 1, 3, 10]ω_c , where ω_c is the target bandwidth for tuning.

• N-by-5 matrix, where N is the number of loops to be tuned. Each row entry must be of length 5 to specify a different amplitude at each of [1/10, 1/3, 1, 3, 10]ω_c .

If you are tuning multiple loops and specify a vector of length 5 at this port, then the block uses the specified amplitude for all the loops at each of [1/10, 1/3, 1, 3, 10]ω_c corresponding to that loop.

Alternatively, you can specify the sinusoidal perturbation amplitude for individual loops in block parameters. For more information, see the parameter description.

Dependencies

To enable this port, on the Block tab under Parameters Source, select Use external source for sine amplitudes.

Data Types: single | double

Output

perturbation daxis — Direct-axis current input perturbation

scalar

Perturbation signal input used for estimating the frequency-response data model associated with the d-axis current control loop. Inject the perturbation signal from this port by using a sum block to the output of the PID controller that regulates the d-axis current.

• When the experiment is running, the block generates perturbation signals at this port.

• When the experiment is not running, the signal at this port is zero. In this state, the block has no effect on the plant.

Dependencies

To enable this port, select Tune D-axis current loop.

Data Types: single | double

perturbation qaxis — Quadrature-axis current input perturbation

scalar

Perturbation signal input used for estimating the frequency-response data model associated with the q-axis current control loop. Inject this perturbation signal from this port by using a sum block to the output of the PID controller that regulates the q-axis current.

• When the experiment is running, the block generates perturbation signals at this port.

• When the experiment is not running, the signal at this port is zero. In this state, the block has no effect on the plant.

Dependencies

To enable this port, select Tune Q-axis current loop.

Data Types: single | double

perturbation spd — Speed input perturbation

scalar

Perturbation signal input used for estimating the frequency-response data model associated with the motor speed control loop. Inject this perturbation signal from this port by using a sum block with the output of the PID controller that regulates the speed of the motor.

• When the experiment is running, the block generates perturbation signals at this port.

• When the experiment is not running, the signal at this port is zero. In this state, the block has no effect on the plant.

Dependencies

To enable this port, select Tune speed loop.

Data Types: single | double

perturbation flux — Flux input perturbation

scalar

Perturbation signal input used for estimating the frequency-response data model associated with the motor flux control loop. Inject this perturbation signal from this port by using a sum block to the output of the PID controller that regulates the flux linkage of the motor.

• When the experiment is running, the block generates perturbation signals at this port.

• When the experiment is not running, the signal at this port is zero. In this state, the block has no effect on the plant.

Dependencies

To enable this port, select Tune flux loop.

Data Types: single | double

pid gains — Tuned PID coefficients

bus

This 4-element bus signal contains the tuned PID gains P, I, D, and the filter coefficient N for each control loop the block tunes. These values correspond to the P, I, D, and N parameters in the expressions given in the Form parameter. Initially, the values are 0, 0, 0, and 100, respectively. The block updates the values when the experiment ends. The bus signal corresponding to each loop the block tunes always has four elements, even if you are not tuning a PIDF controller.

Data Types: single | double

convergence — Convergence of FRD estimation during experiment

scalar

The block uses perturbation signals to estimate the frequency response of the plant associated with each loop at several frequencies around the target bandwidth for tuning. convergence indicates how close to completion the estimation of the plant frequency response is. Typically, this value quickly rises to about 90% after the experiment begins, and then gradually converges to a higher value. Stop the experiment when it levels off near 100%.

For PRBS experiment mode, the signal at this port updates only after the estimation experiment has finished. (since R2024a)

Data Types: single | double

estimated PM — Estimated phase margin for most recently tuned loop

scalar

This port outputs the estimated phase margin achieved by the tuned controller for the most recently tuned loop, in degrees. The block updates this value when the tuning experiment ends for each loop. The estimated phase margin is calculated from the angle of G(jω_c)C(jω_c), where G is the estimated plant for that loop, C is the tuned controller, and ω_c is the crossover frequency (bandwidth). The estimated phase margin might differ from the target phase margin specified by the Target phase margin (degrees) parameter. It is an indicator of the robustness and stability achieved by the tuned system.

• Typically, the estimated phase margin is near the target phase margin. In general, the larger the value, the more robust is the tuned system, and the less overshoot there is.

• A negative phase margin indicates that the closed-loop system might be unstable.

Dependencies

To enable this port, on the Block tab, select Estimated phase margin achieved by tuned controllers.

Data Types: single | double

frd — Estimated frequency response for most recently tuned loop

vector

This port outputs the frequency-response data estimated by the experiment for most recently tuned loop. Initially, the value at frd is [0, 0, 0, 0, 0]. During the experiment, the block injects signals at frequencies [1/10, 1/3, 1, 3, 10]ω_c, where ω_c is the target bandwidth. At each sample time during the experiment, the block updates frd with a vector containing the complex frequency response at each of these frequencies. You can use the progress of the response as an alternative to convergence to examine the convergence of the estimation. When the experiment stops, the block updates frd with the final estimated frequency response used for computing the PID gains.

For PRBS experiment mode, the signal at this port updates only after the estimation experiment has finished. (since R2024a)

Dependencies

To enable this port, on the Block tab, select Plant frequency responses near bandwidth.

Data Types: single | double

nominal — Plant input and output at nominal operating point for most recently tuned loop

vector

This port outputs a vector containing the plant input and plant output for the most recently tuned loop or the loop currently being tuned. These values are the plant input and output at the nominal operating point at which the block performs the experiment.

Dependencies

To enable this port, on the Block tab, select Plant nominal input and output.

Data Types: single | double

loop startstops — Active loop

bus

This 4-element bus signal indicates whether the tuning experiment for each loop tuned by the block is active or not. For each signal in the bus, the port outputs the logical value 1 (true) for the loop when the tuning experiment is running. The value is logical 0 (false) when the experiment is over or has not yet started. You can use this port to trigger updates of PID gains for individual loops.

Dependencies

To enable this port, on the Block tab, disable Use external source for start/stop of experiment and select Start/stop of autotuning process.

Data Types: single | double

Parameters

Tune D-axis current loop — Enable d-axis current loop tuning

on (default) | off

Use this parameter to enable or disable d-axis current loop autotuning.

Programmatic Use

Block Parameter: TuneDaxisLoop

Type: character vector

Values: 'on' | 'off'

Default: 'on'

Tune Q-axis current loop — Enable q-axis current loop tuning

on (default) | off

Use this parameter to enable or disable q-axis current loop autotuning.

Programmatic Use

Block Parameter: TuneQaxisLoop

Type: character vector

Values: 'on' | 'off'

Default: 'on'

Tune speed loop — Enable speed loop tuning

on (default) | off

Use this parameter to enable or disable speed loop autotuning.

Programmatic Use

Block Parameter: TuneSpeedLoop

Type: character vector

Values: 'on' | 'off'

Default: 'on'

Tune flux loop — Enable flux loop tuning

on (default) | off

Use this parameter to enable or disable flux loop autotuning.

Programmatic Use

Block Parameter: TuneSpeedLoop

Type: character vector

Values: 'on' | 'off'

Default: 'on'

Use same settings for current loop controllers (D-axis + Q-axis) — Enable same tuning and experiment settings for direct-axis and quadrature-axis current loops

off (default) | on

Select this parameter to enable the same tuning and experiment settings for d-axis and q-axis current loops. When enabled, the block uses the same controller settings, target bandwidth, phase margin, and other experiment settings to tune d-axis and q-axis current loops.

Programmatic Use

Block Parameter: UseSameSettingsInner

Type: character vector

Values: 'off' | 'on'

Default: 'off'

Use same settings for outer loop controllers (Speed + Flux) — Enable same tuning and experiment settings for speed and flux loops

off (default) | on

Select this parameter to enable the same tuning and experiment settings for speed and flux loops. When enabled, the block uses the same controller settings, target bandwidth, phase margin, and other experiment settings to tune speed and flux loops.

Programmatic Use

Block Parameter: UseSameSettingsOuter

Type: character vector

Values: 'off' | 'on'

Default: 'off'

Experiment sample time — Sample time of frequency response estimation experiment

–1 (default) | positive scalar

Specify the sample time of the frequency response estimation experiment performed by the block in seconds.

By default, the experiment sample time is set to inherited (–1) and the block performs the frequency response estimation experiment, for each loop, at the inherited sample time. Use this parameter to specify a sample time for the frequency response estimation experiment that is different from the tuning and PID gain calculation sample rates. For each loop that you tune, the frequency responses are estimated at the sample time specified in this parameter.

When you specify different sample times for tuning, experiment, and loops, you can configure Simulink to treat each block module rate as a separate task to enable multitasking execution for your model. This multitasking mode helps improve performance on hardware. For more information, see Treat each discrete rate as a separate task.

Programmatic Use

Block Parameter: TsExperiment

Type: scalar

Value positive scalar

Default: –1 (inherited)

Tuning Tab

Use different sample time for tuning — Enable tuning at different sample time from loop PID controller and experiment

off (default) | on

By default, the block runs tuning for each loop at the same sample time that you specify in the Controller sample time (sec) parameter for that loop. Enable this parameter to run tuning at a sample rate that is different from the sample rate of the PID controllers you are tuning and the frequency response estimation experiment performed by the block. The PID gain tuning algorithm is computationally intensive, and when you want to deploy the block to hardware and tune a controller with a fast sample time, some hardware might not complete the PID gain calculation in a single time step. To reduce the hardware throughput requirements, specify a tuning sample time slower than the controller sample time using the Tuning sample time (sec) parameter.

Programmatic Use

Block Parameter: UseTuningTs

Type: character vector

Value 'off' | 'on'

Default: 'off'

Tuning sample time (sec) — Sample time of tuning algorithm

0.2 (default) | positive scalar

Specify the sample time of the tuning algorithm in seconds.

If you intend to deploy the block on hardware with limited processing power and want to tune a controller with a fast sample time, specify a sample time such that the tuning algorithm runs at a slower rate than the PID controllers you are tuning. For each loop that you tune, after the frequency response estimation experiment ends, controller tuning occurs at the sample time specified in this parameter.

Dependencies

To enable this parameter, select Use different sample time for tuning.

Programmatic Use

Block Parameter: TsTuning

Type: scalar

Value positive scalar

Default: 0.2

D-axis Current Loop

Type — D-axis current loop PID controller actions

PI (default) | PID | PIDF | ...

Specify the type of PID controller associated with the d-axis current control loop.

The controller type indicates what actions are present in the controller that regulates the loop. The following controller types are available for PID autotuning:

• P — Proportional only

• I — Integral only

• PI — Proportional and integral

• PD — Proportional and derivative

• PDF — Proportional and derivative with derivative filter

• PID — Proportional, integral, and derivative

• PIDF — Proportional, integral, and derivative with derivative filter

Make sure the controller type matches the controller that regulates the loop.

Programmatic Use

Block Parameter: PIDTypeDaxis

Type: character vector

Values: 'P' | 'I' | 'PI' | 'PD' | 'PDF' | 'PID' | 'PIDF'

Default: 'PI'

Form — D-axis current loop PID controller form

Parallel (default) | Ideal

Specify the PID controller form associated with your d-axis current control loop.

The controller form determines the interpretation of the PID coefficients P, I, D, and N.

• Parallel — In Parallel form, the transfer function of a discrete-time PIDF controller is

  $$C=P+I{F}_i\left(z\right)+D\left[\frac{N}{1+N{F}_d\left(z\right)}\right],$$

  where F_i(z) and F_d(z) are the integrator and filter formulas (see Integrator method and Filter method).

  Other controller actions amount to setting P, I, or D to zero.

• Ideal — In Ideal form, the transfer function of a discrete-time PIDF controller is

  $$C=P\left[1+I{F}_i\left(z\right)+D\left(\frac{N}{1+N{F}_d\left(z\right)}\right)\right].$$

  Other controller actions amount to setting D to zero or setting I to Inf. (In ideal form, the controller must have proportional action.)

Make sure the controller form matches the controller that regulates the loop.

Tunable: Yes

Programmatic Use

Block Parameter: PIDFormDaxis

Type: character vector

Values: 'Parallel' | 'Ideal'

Default: 'Parallel'

Controller sample time (sec) — D-axis current loop PID controller sample time

0.001 (default) | positive scalar | –1

Specify the sample time of your PID controller associated with the d-axis current control loop in seconds. This parameter sets the sample time used to calculate the PID controller gains for the loop.

To perform PID tuning, the block measures frequency-response information up to a frequency of 10 times the target bandwidth. To ensure that this frequency is less than the Nyquist frequency, the target bandwidth ω_c must satisfy ω_cT_s ≤ 0.3, where T_s ω_c is the controller sample time that you specify with the Controller sample time (sec) parameter.

Make sure the controller sample time matches the controller that regulates the loop.

Tips

If you want to run the deployed block with different sample times in your application, set this parameter to –1 and put the block in a Triggered Subsystem. Then, trigger the subsystem at the desired sample time. If you do not plan to change the sample time after deployment, specify a fixed and finite sample time.

Programmatic Use

Block Parameter: TsDaxis

Type: scalar

Value positive scalar | –1

Default: 0.001

Integrator method — D-axis current loop controller discrete integration formula for integrator term

Forward Euler (default) | Backward Euler | Trapezoidal

Specify the discrete integration formula for the integrator term in your controller. In discrete time, the PID controller transfer function assumed by the block is

$$C=P+I{F}_i\left(z\right)+D\left[\frac{N}{1+N{F}_d\left(z\right)}\right],$$

in parallel form, or in ideal form,

$$C=P\left[1+I{F}_i\left(z\right)+D\left(\frac{N}{1+N{F}_d\left(z\right)}\right)\right].$$

For a controller sample time T_s, the Integrator method parameter determines the formula F_i as follows.

Integrator method	Fi
Forward Euler	$$\frac{T_s}{z-1}$$
Backward Euler	$$\frac{T_{s}z}{z-1}$$
Trapezoidal	$$\frac{T_s}{2}\frac{z+1}{z-1}$$

For more information about the relative advantages of each method, see the Discrete PID Controller block reference page.

Make sure the controller integrator method matches the controller that regulates the loop.

Tunable: Yes

Dependencies

This parameter is enabled when the controller includes integral action.

Programmatic Use

Block Parameter: IntegratorMethodDaxis

Type: character vector

Values: 'Forward Euler' | 'Backward Euler' | 'Trapezoidal'

Default: 'Forward Euler'

Filter method — D-axis current loop controller discrete integration formula for derivative filter term

Forward Euler (default) | Backward Euler | Trapezoidal

Specify the discrete integration formula for the derivative filter term in your controller. In discrete time, the PID controller transfer function assumed by the block is

$$C=P+I{F}_i\left(z\right)+D\left[\frac{N}{1+N{F}_d\left(z\right)}\right],$$

in parallel form, or in ideal form,

$$C=P\left[1+I{F}_i\left(z\right)+D\left(\frac{N}{1+N{F}_d\left(z\right)}\right)\right].$$

For a controller sample time T_s, the Filter method parameter determines the formula F_d as follows.

Filter method	Fd
Forward Euler	$$\frac{T_s}{z-1}$$
Backward Euler	$$\frac{T_{s}z}{z-1}$$
Trapezoidal	$$\frac{T_s}{2}\frac{z+1}{z-1}$$

For more information about the relative advantages of each method, see the Discrete PID Controller block reference page.

Make sure the controller derivative filter method matches the controller that regulates the loop.

Tunable: Yes

Dependencies

This parameter is enabled when the controller includes derivative action with a derivative filter term.

Programmatic Use

Block Parameter: FilterMethodDaxis

Type: character vector

Values: 'Forward Euler' | 'Backward Euler' | 'Trapezoidal'

Default: 'Forward Euler'

Target bandwidth (rad/sec) — D-axis current loop target crossover frequency of tuned response

100 (default) | positive scalar

The target bandwidth is the target value for the 0 dB gain crossover frequency of the tuned open-loop response CP, where P is the plant response associated with the loop, and C is the controller response. This crossover frequency roughly sets the control bandwidth. For a rise time τ seconds, a good guess for the target bandwidth is 2/τ rad/sec.

To perform PID tuning, the autotuner block measures frequency-response information up to a frequency of 10 times the target bandwidth. To ensure that this frequency is less than the Nyquist frequency, the target bandwidth ω_c must satisfy ω_cT_s ≤ 0.3, where T_s is the controller sample time that you specify with the Controller sample time (sec) parameter. Because of this condition, the fastest rise time you can enforce for tuning is about 6.67T_s. If this rise time does not meet your design goals, consider reducing T_s.

For best results, use a target bandwidth that is within about a factor of 10 of the bandwidth with the initial PID controller. To tune a controller for a larger change in bandwidth, tune incrementally using smaller changes.

To provide the target bandwidth by using an input port, on the Block tab, select Use external source for bandwidth.

Programmatic Use

Block Parameter: BandwidthDaxis

Type: positive scalar

Default: 100

Target phase margin (degrees) — D-axis current loop target minimum phase margin

60 (default) | scalar in range 0–90

Specify a target minimum phase margin for the tuned open-loop response associated with the d-axis current control loop at the crossover frequency.

The target phase margin reflects the desired robustness of the tuned system. Typically, choose a value in the range of about 45°–60°. In general, a higher phase margin reduces overshoot, but can limit the response speed. The default value 60° tends to balance performance and robustness, yielding about 5–10% overshoot, depending on the characteristics of your plant.

To provide the target phase margin by using an input port, on the Block tab, select Use external source for target phase margins.

Tunable: Yes

Programmatic Use

Block Parameter: TargetPMDaxis

Type: scalar

Values: 0–90

Default: 60

Q-axis Current Loop

Type — Q-axis current loop PID controller actions

PI (default) | PID | PIDF | ...

Specify the type of PID controller associated with the q-axis current control loop.

The controller type indicates what actions are present in the controller that regulates the loop. The following controller types are available for PID autotuning:

• P — Proportional only

• I — Integral only

• PI — Proportional and integral

• PD — Proportional and derivative

• PDF — Proportional and derivative with derivative filter

• PID — Proportional, integral, and derivative

• PIDF — Proportional, integral, and derivative with derivative filter

Make sure the controller type matches the controller that regulates the loop.

Programmatic Use

Block Parameter: PIDTypeQaxis

Type: character vector

Values: 'P' | 'I' | 'PI' | 'PD' | 'PDF' | 'PID' | 'PIDF'

Default: 'PI'

Form — Q-axis current loop PID controller form

Parallel (default) | Ideal

Specify the PID controller form associated with your q-axis current control loop.

The controller form determines the interpretation of the PID coefficients P, I, D, and N.

• Parallel — In Parallel form, the transfer function of a discrete-time PIDF controller is

  $$C=P+I{F}_i\left(z\right)+D\left[\frac{N}{1+N{F}_d\left(z\right)}\right],$$

  where F_i(z) and F_d(z) are the integrator and filter formulas (see Integrator method and Filter method).

  Other controller actions amount to setting P, I, or D to zero.

• Ideal — In Ideal form, the transfer function of a discrete-time PIDF controller is

  $$C=P\left[1+I{F}_i\left(z\right)+D\left(\frac{N}{1+N{F}_d\left(z\right)}\right)\right].$$

  Other controller actions amount to setting D to zero or setting I to Inf. (In ideal form, the controller must have proportional action.)

Make sure the controller form matches the controller that regulates the loop.

Tunable: Yes

Programmatic Use

Block Parameter: PIDFormQaxis

Type: character vector

Values: 'Parallel' | 'Ideal'

Default: 'Parallel'

Controller sample time (sec) — Q-axis current loop PID controller sample time

0.001 (default) | positive scalar | –1

Specify the sample time of your PID controller associated with the q-axis current control loop in seconds. This parameter sets the sample time used to calculate the PID controller gains for the loop.

To perform PID tuning, the block measures frequency-response information up to a frequency of 10 times the target bandwidth. To ensure that this frequency is less than the Nyquist frequency, the target bandwidth ω_c must satisfy ω_cT_s ≤ 0.3, where T_s ω_c is the controller sample time that you specify with the Controller sample time (sec) parameter.

Make sure the controller sample time matches the controller that regulates the loop.

Tips

If you want to run the deployed block with different sample times in your application, set this parameter to –1 and put the block in a Triggered Subsystem. Then, trigger the subsystem at the desired sample time. If you do not plan to change the sample time after deployment, specify a fixed and finite sample time.

Programmatic Use

Block Parameter: TsQaxis

Type: scalar

Value positive scalar | –1

Default: 0.001

Integrator method — Q-axis current loop controller discrete integration formula for integrator term

Forward Euler (default) | Backward Euler | Trapezoidal

Specify the discrete integration formula for the integrator term in your controller. In discrete time, the PID controller transfer function assumed by the block is

$$C=P+I{F}_i\left(z\right)+D\left[\frac{N}{1+N{F}_d\left(z\right)}\right],$$

in parallel form, or in ideal form,

$$C=P\left[1+I{F}_i\left(z\right)+D\left(\frac{N}{1+N{F}_d\left(z\right)}\right)\right].$$

For a controller sample time T_s, the Integrator method parameter determines the formula F_i as follows.

Integrator method	Fi
Forward Euler	$$\frac{T_s}{z-1}$$
Backward Euler	$$\frac{T_{s}z}{z-1}$$
Trapezoidal	$$\frac{T_s}{2}\frac{z+1}{z-1}$$

For more information about the relative advantages of each method, see the Discrete PID Controller block reference page.

Make sure the controller integrator method matches the controller that regulates the loop.

Tunable: Yes

Dependencies

This parameter is enabled when the controller includes integral action.

Programmatic Use

Block Parameter: IntegratorMethodQaxis

Type: character vector

Values: 'Forward Euler' | 'Backward Euler' | 'Trapezoidal'

Default: 'Forward Euler'

Filter method — Q-axis current loop controller discrete integration formula for derivative filter term

Forward Euler (default) | Backward Euler | Trapezoidal

Specify the discrete integration formula for the derivative filter term in your controller. In discrete time, the PID controller transfer function assumed by the block is

$$C=P+I{F}_i\left(z\right)+D\left[\frac{N}{1+N{F}_d\left(z\right)}\right],$$

in parallel form, or in ideal form,

$$C=P\left[1+I{F}_i\left(z\right)+D\left(\frac{N}{1+N{F}_d\left(z\right)}\right)\right].$$

For a controller sample time T_s, the Filter method parameter determines the formula F_d as follows.

Filter method	Fd
Forward Euler	$$\frac{T_s}{z-1}$$
Backward Euler	$$\frac{T_{s}z}{z-1}$$
Trapezoidal	$$\frac{T_s}{2}\frac{z+1}{z-1}$$

For more information about the relative advantages of each method, see the Discrete PID Controller block reference page.

Make sure the controller derivative filter method matches the controller that regulates the loop.

Tunable: Yes

Dependencies

This parameter is enabled when the controller includes derivative action with a derivative filter term.

Programmatic Use

Block Parameter: FilterMethodQaxis

Type: character vector

Values: 'Forward Euler' | 'Backward Euler' | 'Trapezoidal'

Default: 'Forward Euler'

Target bandwidth (rad/sec) — Q-axis current loop target crossover frequency of tuned response

100 (default) | positive scalar

The target bandwidth is the target value for the 0 dB gain crossover frequency of the tuned open-loop response CP, where P is the plant response associated with the loop, and C is the controller response. This crossover frequency roughly sets the control bandwidth. For a rise time τ seconds, a good guess for the target bandwidth is 2/τ rad/sec.

To perform PID tuning, the autotuner block measures frequency-response information up to a frequency of 10 times the target bandwidth. To ensure that this frequency is less than the Nyquist frequency, the target bandwidth ω_c must satisfy ω_cT_s ≤ 0.3, where T_s is the controller sample time that you specify with the Controller sample time (sec) parameter. Because of this condition, the fastest rise time you can enforce for tuning is about 6.67T_s. If this rise time does not meet your design goals, consider reducing T_s.

For best results, use a target bandwidth that is within about a factor of 10 of the bandwidth with the initial PID controller. To tune a controller for a larger change in bandwidth, tune incrementally using smaller changes.

To provide the target bandwidth by using an input port, on the Block tab, select Use external source for bandwidth.

Programmatic Use

Block Parameter: BandwidthQaxis

Type: positive scalar

Default: 100

Target phase margin (degrees) — Q-axis current loop target minimum phase margin

60 (default) | scalar in range 0–90

Specify a target minimum phase margin for the tuned open-loop response associated with the q-axis current control loop at the crossover frequency.

The target phase margin reflects the desired robustness of the tuned system. Typically, choose a value in the range of about 45°–60°. In general, a higher phase margin reduces overshoot, but can limit the response speed. The default value 60° tends to balance performance and robustness, yielding about 5–10% overshoot, depending on the characteristics of your plant.

To provide the target phase margin by using an input port, on the Block tab, select Use external source for target phase margins.

Tunable: Yes

Programmatic Use

Block Parameter: TargetPMQaxis

Type: scalar

Values: 0–90

Default: 60

Speed Loop

Type — Speed loop PID controller actions

PI (default) | PID | PIDF | ...

Specify the type of PID controller associated with the speed control loop.

The controller type indicates what actions are present in the controller that regulates the loop. The following controller types are available for PID autotuning:

• P — Proportional only

• I — Integral only

• PI — Proportional and integral

• PD — Proportional and derivative

• PDF — Proportional and derivative with derivative filter

• PID — Proportional, integral, and derivative

• PIDF — Proportional, integral, and derivative with derivative filter

Make sure the controller type matches the controller that regulates the loop.

Programmatic Use

Block Parameter: PIDTypeSpeed

Type: character vector

Values: 'P' | 'I' | 'PI' | 'PD' | 'PDF' | 'PID' | 'PIDF'

Default: 'PI'

Form — Speed loop PID controller form

Parallel (default) | Ideal

Specify the PID controller form associated with your speed control loop.

The controller form determines the interpretation of the PID coefficients P, I, D, and N.

• Parallel — In Parallel form, the transfer function of a discrete-time PIDF controller is

  $$C=P+I{F}_i\left(z\right)+D\left[\frac{N}{1+N{F}_d\left(z\right)}\right],$$

  where F_i(z) and F_d(z) are the integrator and filter formulas (see Integrator method and Filter method).

  Other controller actions amount to setting P, I, or D to zero.

• Ideal — In Ideal form, the transfer function of a discrete-time PIDF controller is

  $$C=P\left[1+I{F}_i\left(z\right)+D\left(\frac{N}{1+N{F}_d\left(z\right)}\right)\right].$$

  Other controller actions amount to setting D to zero or setting I to Inf. (In ideal form, the controller must have proportional action.)

Make sure the controller form matches the controller that regulates the loop.

Tunable: Yes

Programmatic Use

Block Parameter: PIDFormSpeed

Type: character vector

Values: 'Parallel' | 'Ideal'

Default: 'Parallel'

Controller sample time (sec) — Speed loop PID controller sample time

0.1 (default) | positive scalar | –1

Specify the sample time of your PID controller associated with the speed control loop in seconds. This parameter sets the sample time used to calculate the PID controller gains for the loop.

To perform PID tuning, the block measures frequency-response information up to a frequency of 10 times the target bandwidth. To ensure that this frequency is less than the Nyquist frequency, the target bandwidth ω_c must satisfy ω_cT_s ≤ 0.3, where T_s ω_c is the controller sample time that you specify with the Controller sample time (sec) parameter.

Make sure the controller sample time matches the controller that regulates the loop.

Tips

If you want to run the deployed block with different sample times in your application, set this parameter to –1 and put the block in a Triggered Subsystem. Then, trigger the subsystem at the desired sample time. If you do not plan to change the sample time after deployment, specify a fixed and finite sample time.

Programmatic Use

Block Parameter: TsSpeed

Type: scalar

Value positive scalar | –1

Default: 0.1

Integrator method — Speed loop controller discrete integration formula for integrator term

Forward Euler (default) | Backward Euler | Trapezoidal

Specify the discrete integration formula for the integrator term in your controller. In discrete time, the PID controller transfer function assumed by the block is

$$C=P+I{F}_i\left(z\right)+D\left[\frac{N}{1+N{F}_d\left(z\right)}\right],$$

in parallel form, or in ideal form,

$$C=P\left[1+I{F}_i\left(z\right)+D\left(\frac{N}{1+N{F}_d\left(z\right)}\right)\right].$$

For a controller sample time T_s, the Integrator method parameter determines the formula F_i as follows.

Integrator method	Fi
Forward Euler	$$\frac{T_s}{z-1}$$
Backward Euler	$$\frac{T_{s}z}{z-1}$$
Trapezoidal	$$\frac{T_s}{2}\frac{z+1}{z-1}$$

For more information about the relative advantages of each method, see the Discrete PID Controller block reference page.

Make sure the controller integrator method matches the controller that regulates the loop.

Tunable: Yes

Dependencies

This parameter is enabled when the controller includes integral action.

Programmatic Use

Block Parameter: IntegratorMethodSpeed

Type: character vector

Values: 'Forward Euler' | 'Backward Euler' | 'Trapezoidal'

Default: 'Forward Euler'

Filter method — Speed loop controller discrete integration formula for derivative filter term

Forward Euler (default) | Backward Euler | Trapezoidal

Specify the discrete integration formula for the derivative filter term in your controller. In discrete time, the PID controller transfer function assumed by the block is

$$C=P+I{F}_i\left(z\right)+D\left[\frac{N}{1+N{F}_d\left(z\right)}\right],$$

in parallel form, or in ideal form,

$$C=P\left[1+I{F}_i\left(z\right)+D\left(\frac{N}{1+N{F}_d\left(z\right)}\right)\right].$$

For a controller sample time T_s, the Filter method parameter determines the formula F_d as follows.

Filter method	Fd
Forward Euler	$$\frac{T_s}{z-1}$$
Backward Euler	$$\frac{T_{s}z}{z-1}$$
Trapezoidal	$$\frac{T_s}{2}\frac{z+1}{z-1}$$

For more information about the relative advantages of each method, see the Discrete PID Controller block reference page.

Make sure the controller derivative filter method matches the controller that regulates the loop.

Tunable: Yes

Dependencies

This parameter is enabled when the controller includes derivative action with a derivative filter term.

Programmatic Use

Block Parameter: FilterMethodSpeed

Type: character vector

Values: 'Forward Euler' | 'Backward Euler' | 'Trapezoidal'

Default: 'Forward Euler'

Target bandwidth (rad/sec) — Speed loop target crossover frequency of tuned response

1 (default) | positive scalar

The target bandwidth is the target value for the 0 dB gain crossover frequency of the tuned open-loop response CP, where P is the plant response associated with the loop, and C is the controller response. This crossover frequency roughly sets the control bandwidth. For a rise time τ seconds, a good guess for the target bandwidth is 2/τ rad/sec.

To perform PID tuning, the autotuner block measures frequency-response information up to a frequency of 10 times the target bandwidth. To ensure that this frequency is less than the Nyquist frequency, the target bandwidth ω_c must satisfy ω_cT_s ≤ 0.3, where T_s is the controller sample time that you specify with the Controller sample time (sec) parameter. Because of this condition, the fastest rise time you can enforce for tuning is about 6.67T_s. If this rise time does not meet your design goals, consider reducing T_s.

For best results, use a target bandwidth that is within about a factor of 10 of the bandwidth with the initial PID controller. To tune a controller for a larger change in bandwidth, tune incrementally using smaller changes.

To provide the target bandwidth by using an input port, on the Block tab, select Use external source for bandwidth.

Programmatic Use

Block Parameter: BandwidthSpeed

Type: positive scalar

Default: 1

Target phase margin (degrees) — Speed loop target minimum phase margin

60 (default) | scalar in range 0–90

Specify a target minimum phase margin for the tuned open-loop response associated with the speed control loop at the crossover frequency.

The target phase margin reflects the desired robustness of the tuned system. Typically, choose a value in the range of about 45°–60°. In general, a higher phase margin reduces overshoot, but can limit the response speed. The default value 60° tends to balance performance and robustness, yielding about 5–10% overshoot, depending on the characteristics of your plant.

To provide the target phase margin by using an input port, on the Block tab, select Use external source for target phase margins.

Tunable: Yes

Programmatic Use

Block Parameter: TargetPMSpeed

Type: scalar

Values: 0–90

Default: 60

Flux Loop

Type — Flux loop PID controller actions

PI (default) | PID | PIDF | ...

Specify the type of PID controller associated with the flux control loop.

The controller type indicates what actions are present in the controller that regulates the loop. The following controller types are available for PID autotuning:

• P — Proportional only

• I — Integral only

• PI — Proportional and integral

• PD — Proportional and derivative

• PDF — Proportional and derivative with derivative filter

• PID — Proportional, integral, and derivative

• PIDF — Proportional, integral, and derivative with derivative filter

Make sure the controller type matches the controller that regulates the loop.

Programmatic Use

Block Parameter: PIDTypeFlux

Type: character vector

Values: 'P' | 'I' | 'PI' | 'PD' | 'PDF' | 'PID' | 'PIDF'

Default: 'PI'

Form — Flux loop PID controller form

Parallel (default) | Ideal

Specify the PID controller form associated with your flux control loop.

The controller form determines the interpretation of the PID coefficients P, I, D, and N.

• Parallel — In Parallel form, the transfer function of a discrete-time PIDF controller is

  $$C=P+I{F}_i\left(z\right)+D\left[\frac{N}{1+N{F}_d\left(z\right)}\right],$$

  where F_i(z) and F_d(z) are the integrator and filter formulas (see Integrator method and Filter method).

  Other controller actions amount to setting P, I, or D to zero.

• Ideal — In Ideal form, the transfer function of a discrete-time PIDF controller is

  $$C=P\left[1+I{F}_i\left(z\right)+D\left(\frac{N}{1+N{F}_d\left(z\right)}\right)\right].$$

  Other controller actions amount to setting D to zero or setting I to Inf. (In ideal form, the controller must have proportional action.)

Make sure the controller form matches the controller that regulates the loop.

Tunable: Yes

Programmatic Use

Block Parameter: PIDFormFlux

Type: character vector

Values: 'Parallel' | 'Ideal'

Default: 'Parallel'

Controller sample time (sec) — Flux loop PID controller sample time

0.1 (default) | positive scalar | –1

Specify the sample time of your PID controller associated with the flux control loop in seconds. This parameter sets the sample time used to calculate the PID controller gains for the loop.

To perform PID tuning, the block measures frequency-response information up to a frequency of 10 times the target bandwidth. To ensure that this frequency is less than the Nyquist frequency, the target bandwidth ω_c must satisfy ω_cT_s ≤ 0.3, where T_s ω_c is the controller sample time that you specify with the Controller sample time (sec) parameter.

Make sure the controller sample time matches the controller that regulates the loop.

Tips

If you want to run the deployed block with different sample times in your application, set this parameter to –1 and put the block in a Triggered Subsystem. Then, trigger the subsystem at the desired sample time. If you do not plan to change the sample time after deployment, specify a fixed and finite sample time.

Programmatic Use

Block Parameter: TsFlux

Type: scalar

Value positive scalar | –1

Default: 0.1

Integrator method — Flux loop controller discrete integration formula for integrator term

Forward Euler (default) | Backward Euler | Trapezoidal

Specify the discrete integration formula for the integrator term in your controller. In discrete time, the PID controller transfer function assumed by the block is

$$C=P+I{F}_i\left(z\right)+D\left[\frac{N}{1+N{F}_d\left(z\right)}\right],$$

in parallel form, or in ideal form,

$$C=P\left[1+I{F}_i\left(z\right)+D\left(\frac{N}{1+N{F}_d\left(z\right)}\right)\right].$$

For a controller sample time T_s, the Integrator method parameter determines the formula F_i as follows.

Integrator method	Fi
Forward Euler	$$\frac{T_s}{z-1}$$
Backward Euler	$$\frac{T_{s}z}{z-1}$$
Trapezoidal	$$\frac{T_s}{2}\frac{z+1}{z-1}$$

For more information about the relative advantages of each method, see the Discrete PID Controller block reference page.

Make sure the controller integrator method matches the controller that regulates the loop.

Tunable: Yes

Dependencies

This parameter is enabled when the controller includes integral action.

Programmatic Use

Block Parameter: IntegratorMethodFlux

Type: character vector

Values: 'Forward Euler' | 'Backward Euler' | 'Trapezoidal'

Default: 'Forward Euler'

Filter method — Flux loop controller discrete integration formula for derivative filter term

Forward Euler (default) | Backward Euler | Trapezoidal

Specify the discrete integration formula for the derivative filter term in your controller. In discrete time, the PID controller transfer function assumed by the block is

$$C=P+I{F}_i\left(z\right)+D\left[\frac{N}{1+N{F}_d\left(z\right)}\right],$$

in parallel form, or in ideal form,

$$C=P\left[1+I{F}_i\left(z\right)+D\left(\frac{N}{1+N{F}_d\left(z\right)}\right)\right].$$

For a controller sample time T_s, the Filter method parameter determines the formula F_d as follows.

Filter method	Fd
Forward Euler	$$\frac{T_s}{z-1}$$
Backward Euler	$$\frac{T_{s}z}{z-1}$$
Trapezoidal	$$\frac{T_s}{2}\frac{z+1}{z-1}$$

For more information about the relative advantages of each method, see the Discrete PID Controller block reference page.

Make sure the controller derivative filter method matches the controller that regulates the loop.

Tunable: Yes

Dependencies

This parameter is enabled when the controller includes derivative action with a derivative filter term.

Programmatic Use

Block Parameter: FilterMethodFlux

Type: character vector

Values: 'Forward Euler' | 'Backward Euler' | 'Trapezoidal'

Default: 'Forward Euler'

Target bandwidth (rad/sec) — Flux loop target crossover frequency of tuned response

1 (default) | positive scalar

The target bandwidth is the target value for the 0 dB gain crossover frequency of the tuned open-loop response CP, where P is the plant response associated with the loop, and C is the controller response. This crossover frequency roughly sets the control bandwidth. For a rise time τ seconds, a good guess for the target bandwidth is 2/τ rad/sec.

To perform PID tuning, the autotuner block measures frequency-response information up to a frequency of 10 times the target bandwidth. To ensure that this frequency is less than the Nyquist frequency, the target bandwidth ω_c must satisfy ω_cT_s ≤ 0.3, where T_s is the controller sample time that you specify with the Controller sample time (sec) parameter. Because of this condition, the fastest rise time you can enforce for tuning is about 6.67T_s. If this rise time does not meet your design goals, consider reducing T_s.

For best results, use a target bandwidth that is within about a factor of 10 of the bandwidth with the initial PID controller. To tune a controller for a larger change in bandwidth, tune incrementally using smaller changes.

To provide the target bandwidth by using an input port, on the Block tab, select Use external source for bandwidth.

Programmatic Use

Block Parameter: BandwidthFlux

Type: positive scalar

Default: 1

Target phase margin (degrees) — Flux loop target minimum phase margin

60 (default) | scalar in range 0–90

Specify a target minimum phase margin for the tuned open-loop response associated with the flux control loop at the crossover frequency.

The target phase margin reflects the desired robustness of the tuned system. Typically, choose a value in the range of about 45°–60°. In general, a higher phase margin reduces overshoot, but can limit the response speed. The default value 60° tends to balance performance and robustness, yielding about 5–10% overshoot, depending on the characteristics of your plant.

To provide the target phase margin by using an input port, on the Block tab, select Use external source for target phase margins.

Tunable: Yes

Programmatic Use

Block Parameter: TargetPMFlux

Type: scalar

Values: 0–90

Default: 60

Current Loops (Q-axis + D-axis)

Type — Current loop PID controller actions

PI (default) | PID | PIDF | ...

Specify the type of PID controller associated with the current control loops.

The controller type indicates what actions are present in the controller that regulates the loop. The following controller types are available for PID autotuning:

• P — Proportional only

• I — Integral only

• PI — Proportional and integral

• PD — Proportional and derivative

• PDF — Proportional and derivative with derivative filter

• PID — Proportional, integral, and derivative

• PIDF — Proportional, integral, and derivative with derivative filter

Make sure the controller type matches the controller that regulates the loop.

Programmatic Use

Block Parameter: PIDTypeAllInner

Type: character vector

Values: 'P' | 'I' | 'PI' | 'PD' | 'PDF' | 'PID' | 'PIDF'

Default: 'PI'

Form — Current loop PID controller form

Parallel (default) | Ideal

Specify the PID controller form associated with your current control loops.

The controller form determines the interpretation of the PID coefficients P, I, D, and N.

• Parallel — In Parallel form, the transfer function of a discrete-time PIDF controller is

  $$C=P+I{F}_i\left(z\right)+D\left[\frac{N}{1+N{F}_d\left(z\right)}\right],$$

  where F_i(z) and F_d(z) are the integrator and filter formulas (see Integrator method and Filter method).

  Other controller actions amount to setting P, I, or D to zero.

• Ideal — In Ideal form, the transfer function of a discrete-time PIDF controller is

  $$C=P\left[1+I{F}_i\left(z\right)+D\left(\frac{N}{1+N{F}_d\left(z\right)}\right)\right].$$

  Other controller actions amount to setting D to zero or setting I to Inf. (In ideal form, the controller must have proportional action.)

Make sure the controller form matches the controller that regulates the loop.

Tunable: Yes

Programmatic Use

Block Parameter: PIDFormAllInner

Type: character vector

Values: 'Parallel' | 'Ideal'

Default: 'Parallel'

Controller sample time (sec) — Current loop PID controller sample time

0.001 (default) | positive scalar | –1

Specify the sample time of your PID controllers associated with the current control loops in seconds. This parameter sets the sample time used to calculate the PID controller gains for the loop.

To perform PID tuning, the block measures frequency-response information up to a frequency of 10 times the target bandwidth. To ensure that this frequency is less than the Nyquist frequency, the target bandwidth ω_c must satisfy ω_cT_s ≤ 0.3, where T_s ω_c is the controller sample time that you specify with the Controller sample time (sec) parameter.

Make sure the controller sample time matches the controller that regulates the loop.

Tips

If you want to run the deployed block with different sample times in your application, set this parameter to –1 and put the block in a Triggered Subsystem. Then, trigger the subsystem at the desired sample time. If you do not plan to change the sample time after deployment, specify a fixed and finite sample time.

Programmatic Use

Block Parameter: TsAllInner

Type: scalar

Value positive scalar | –1

Default: 0.001

Integrator method — Current loop controller discrete integration formula for integrator term

Forward Euler (default) | Backward Euler | Trapezoidal

Specify the discrete integration formula for the integrator term in your controller. In discrete time, the PID controller transfer function assumed by the block is

$$C=P+I{F}_i\left(z\right)+D\left[\frac{N}{1+N{F}_d\left(z\right)}\right],$$

in parallel form, or in ideal form,

$$C=P\left[1+I{F}_i\left(z\right)+D\left(\frac{N}{1+N{F}_d\left(z\right)}\right)\right].$$

For a controller sample time T_s, the Integrator method parameter determines the formula F_i as follows.

Integrator method	Fi
Forward Euler	$$\frac{T_s}{z-1}$$
Backward Euler	$$\frac{T_{s}z}{z-1}$$
Trapezoidal	$$\frac{T_s}{2}\frac{z+1}{z-1}$$

For more information about the relative advantages of each method, see the Discrete PID Controller block reference page.

Make sure the controller integrator method matches the controller that regulates the loop.

Tunable: Yes

Dependencies

This parameter is enabled when the controller includes integral action.

Programmatic Use

Block Parameter: IntegratorMethodAllInner

Type: character vector

Values: 'Forward Euler' | 'Backward Euler' | 'Trapezoidal'

Default: 'Forward Euler'

Filter method — Current loop controller discrete integration formula for derivative filter term

Forward Euler (default) | Backward Euler | Trapezoidal

Specify the discrete integration formula for the derivative filter term in your controller. In discrete time, the PID controller transfer function assumed by the block is

$$C=P+I{F}_i\left(z\right)+D\left[\frac{N}{1+N{F}_d\left(z\right)}\right],$$

in parallel form, or in ideal form,

$$C=P\left[1+I{F}_i\left(z\right)+D\left(\frac{N}{1+N{F}_d\left(z\right)}\right)\right].$$

For a controller sample time T_s, the Filter method parameter determines the formula F_d as follows.

Filter method	Fd
Forward Euler	$$\frac{T_s}{z-1}$$
Backward Euler	$$\frac{T_{s}z}{z-1}$$
Trapezoidal	$$\frac{T_s}{2}\frac{z+1}{z-1}$$

For more information about the relative advantages of each method, see the Discrete PID Controller block reference page.

Make sure the controller derivative filter method matches the controller that regulates the loop.

Tunable: Yes

Dependencies

This parameter is enabled when the controller includes derivative action with a derivative filter term.

Programmatic Use

Block Parameter: FilterMethodAllInner

Type: character vector

Values: 'Forward Euler' | 'Backward Euler' | 'Trapezoidal'

Default: 'Forward Euler'

Target bandwidth (rad/sec) — Current loop target crossover frequency of tuned responses

100 (default) | positive scalar

The target bandwidth is the target value for the 0 dB gain crossover frequency of the tuned open-loop response CP, where P is the plant response associated with the loop, and C is the controller response. This crossover frequency roughly sets the control bandwidth. For a rise time τ seconds, a good guess for the target bandwidth is 2/τ rad/sec.

To perform PID tuning, the autotuner block measures frequency-response information up to a frequency of 10 times the target bandwidth. To ensure that this frequency is less than the Nyquist frequency, the target bandwidth ω_c must satisfy ω_cT_s ≤ 0.3, where T_s is the controller sample time that you specify with the Controller sample time (sec) parameter. Because of this condition, the fastest rise time you can enforce for tuning is about 6.67T_s. If this rise time does not meet your design goals, consider reducing T_s.

For best results, use a target bandwidth that is within about a factor of 10 of the bandwidth with the initial PID controller. To tune a controller for a larger change in bandwidth, tune incrementally using smaller changes.

To provide the target bandwidth by using an input port, on the Block tab, select Use external source for bandwidth.

Programmatic Use

Block Parameter: BandwidthAllInner

Type: positive scalar

Default: 1

Target phase margin (degrees) — Current loop target minimum phase margins

60 (default) | scalar in range 0–90

Specify target minimum phase margin for the tuned open-loop responses associated with the current control loops at the crossover frequency.

The target phase margin reflects the desired robustness of the tuned system. Typically, choose a value in the range of about 45°–60°. In general, a higher phase margin reduces overshoot, but can limit the response speed. The default value 60° tends to balance performance and robustness, yielding about 5–10% overshoot, depending on the characteristics of your plant.

To provide the target phase margin by using an input port, on the Block tab, select Use external source for target phase margins.

Tunable: Yes

Programmatic Use

Block Parameter: TargetPMAllInner

Type: scalar

Values: 0–90

Default: 60

Outer Loops (Speed + Flux)

Type — Outer loop PID controller actions

PI (default) | PID | PIDF | ...

Specify the type of PID controllers associated with the outer control loops.

The controller type indicates what actions are present in the controller that regulates the loop. The following controller types are available for PID autotuning:

• P — Proportional only

• I — Integral only

• PI — Proportional and integral

• PD — Proportional and derivative

• PDF — Proportional and derivative with derivative filter

• PID — Proportional, integral, and derivative

• PIDF — Proportional, integral, and derivative with derivative filter

Make sure the controller type matches the controller that regulates the loop.

Programmatic Use

Block Parameter: PIDTypeAllOuter

Type: character vector

Values: 'P' | 'I' | 'PI' | 'PD' | 'PDF' | 'PID' | 'PIDF'

Default: 'PI'

Form — Outer loop PID controller form

Parallel (default) | Ideal

Specify the PID controller form associated with your outer control loops.

The controller form determines the interpretation of the PID coefficients P, I, D, and N.

• Parallel — In Parallel form, the transfer function of a discrete-time PIDF controller is

  $$C=P+I{F}_i\left(z\right)+D\left[\frac{N}{1+N{F}_d\left(z\right)}\right],$$

  where F_i(z) and F_d(z) are the integrator and filter formulas (see Integrator method and Filter method).

  Other controller actions amount to setting P, I, or D to zero.

• Ideal — In Ideal form, the transfer function of a discrete-time PIDF controller is

  $$C=P\left[1+I{F}_i\left(z\right)+D\left(\frac{N}{1+N{F}_d\left(z\right)}\right)\right].$$

  Other controller actions amount to setting D to zero or setting I to Inf. (In ideal form, the controller must have proportional action.)

Make sure the controller form matches the controller that regulates the loop.

Tunable: Yes

Programmatic Use

Block Parameter: PIDFormAllOuter

Type: character vector

Values: 'Parallel' | 'Ideal'

Default: 'Parallel'

Controller sample time (sec) — Outer loop PID controller sample time

0.1 (default) | positive scalar | –1

Specify the sample time of your PID controllers associated with the outer control loop in seconds. This parameter sets the sample time used to calculate the PID controller gains for the loop.

To perform PID tuning, the block measures frequency-response information up to a frequency of 10 times the target bandwidth. To ensure that this frequency is less than the Nyquist frequency, the target bandwidth ω_c must satisfy ω_cT_s ≤ 0.3, where T_s ω_c is the controller sample time that you specify with the Controller sample time (sec) parameter.

Make sure the controller sample time matches the controller that regulates the loop.

Tips

If you want to run the deployed block with different sample times in your application, set this parameter to –1 and put the block in a Triggered Subsystem. Then, trigger the subsystem at the desired sample time. If you do not plan to change the sample time after deployment, specify a fixed and finite sample time.

Programmatic Use

Block Parameter: TsAllOuter

Type: scalar

Value positive scalar | –1

Default: 0.1

Integrator method — Outer loop controller discrete integration formula for integrator term

Forward Euler (default) | Backward Euler | Trapezoidal

Specify the discrete integration formula for the integrator term in your controller. In discrete time, the PID controller transfer function assumed by the block is

$$C=P+I{F}_i\left(z\right)+D\left[\frac{N}{1+N{F}_d\left(z\right)}\right],$$

in parallel form, or in ideal form,

$$C=P\left[1+I{F}_i\left(z\right)+D\left(\frac{N}{1+N{F}_d\left(z\right)}\right)\right].$$

For a controller sample time T_s, the Integrator method parameter determines the formula F_i as follows.

Integrator method	Fi
Forward Euler	$$\frac{T_s}{z-1}$$
Backward Euler	$$\frac{T_{s}z}{z-1}$$
Trapezoidal	$$\frac{T_s}{2}\frac{z+1}{z-1}$$

For more information about the relative advantages of each method, see the Discrete PID Controller block reference page.

Make sure the controller integrator method matches the controller that regulates the loop.

Tunable: Yes

Dependencies

This parameter is enabled when the controller includes integral action.

Programmatic Use

Block Parameter: IntegratorMethodAllOuter

Type: character vector

Values: 'Forward Euler' | 'Backward Euler' | 'Trapezoidal'

Default: 'Forward Euler'

Filter method — Outer loop controller discrete integration formula for derivative filter term

Forward Euler (default) | Backward Euler | Trapezoidal

Specify the discrete integration formula for the derivative filter term in your controller. In discrete time, the PID controller transfer function assumed by the block is

$$C=P+I{F}_i\left(z\right)+D\left[\frac{N}{1+N{F}_d\left(z\right)}\right],$$

in parallel form, or in ideal form,

$$C=P\left[1+I{F}_i\left(z\right)+D\left(\frac{N}{1+N{F}_d\left(z\right)}\right)\right].$$

For a controller sample time T_s, the Filter method parameter determines the formula F_d as follows.

Filter method	Fd
Forward Euler	$$\frac{T_s}{z-1}$$
Backward Euler	$$\frac{T_{s}z}{z-1}$$
Trapezoidal	$$\frac{T_s}{2}\frac{z+1}{z-1}$$

For more information about the relative advantages of each method, see the Discrete PID Controller block reference page.

Make sure the controller derivative filter method matches the controller that regulates the loop.

Tunable: Yes

Dependencies

This parameter is enabled when the controller includes derivative action with a derivative filter term.

Programmatic Use

Block Parameter: FilterMethodAllOuter

Type: character vector

Values: 'Forward Euler' | 'Backward Euler' | 'Trapezoidal'

Default: 'Forward Euler'

Target bandwidth (rad/sec) — Outer loop target crossover frequency of tuned responses

1 (default) | positive scalar

The target bandwidth is the target value for the 0 dB gain crossover frequency of the tuned open-loop response CP, where P is the plant response associated with the loop, and C is the controller response. This crossover frequency roughly sets the control bandwidth. For a rise time τ seconds, a good guess for the target bandwidth is 2/τ rad/sec.

To perform PID tuning, the autotuner block measures frequency-response information up to a frequency of 10 times the target bandwidth. To ensure that this frequency is less than the Nyquist frequency, the target bandwidth ω_c must satisfy ω_cT_s ≤ 0.3, where T_s is the controller sample time that you specify with the Controller sample time (sec) parameter. Because of this condition, the fastest rise time you can enforce for tuning is about 6.67T_s. If this rise time does not meet your design goals, consider reducing T_s.

For best results, use a target bandwidth that is within about a factor of 10 of the bandwidth with the initial PID controller. To tune a controller for a larger change in bandwidth, tune incrementally using smaller changes.

To provide the target bandwidth by using an input port, on the Block tab, select Use external source for bandwidth.

Programmatic Use

Block Parameter: BandwidthAllOuter

Type: positive scalar

Default: 1

Target phase margin (degrees) — Outer loop target minimum phase margins

60 (default) | scalar in range 0–90

Specify a target minimum phase margin for the tuned open-loop responses associated with the outer control loops at the crossover frequency.

The target phase margin reflects the desired robustness of the tuned system. Typically, choose a value in the range of about 45°–60°. In general, a higher phase margin reduces overshoot, but can limit the response speed. The default value 60° tends to balance performance and robustness, yielding about 5–10% overshoot, depending on the characteristics of your plant.

To provide the target phase margin by using an input port, on the Block tab, select Use external source for target phase margins.

Tunable: Yes

Programmatic Use

Block Parameter: TargetPMAllOuter

Type: scalar

Values: 0–90

Default: 60

Experiment Tab

Experiment Start/Stop

D-axis current loop start time (sec) — Specify direct-axis current loop tuning experiment start time

1 (default)

Specify the simulation time when the d-axis current loop tuning experiment starts.

Programmatic Use

Block Parameter: StartTimeDaxis

Type: positive scalar

Default: 1

D-axis current loop experiment duration (sec) — Specify direct-axis current loop tuning experiment duration

0.05 (default)

Specify the d-axis current loop tuning experiment duration.

Programmatic Use

Block Parameter: DurationDaxis

Type: positive scalar

Default: 0.05

Q-axis current loop start time (sec) — Specify quadrature-axis current loop tuning experiment start time

1.1 (default)

Specify the simulation time when the q-axis current loop tuning experiment starts.

Programmatic Use

Block Parameter: StartTimeQaxis

Type: positive scalar

Default: 1.1

Q-axis current loop experiment duration (sec) — Specify quadrature-axis current loop tuning experiment duration

0.05 (default)

Specify the q-axis current loop tuning experiment duration.

Programmatic Use

Block Parameter: DurationQaxis

Type: positive scalar

Default: 0.05

Speed loop start time (sec) — Specify speed loop tuning experiment start time

2 (default)

Specify the simulation time when the speed loop tuning experiment starts.

Programmatic Use

Block Parameter: StartTimeSpeed

Type: positive scalar

Default: 2

Speed loop experiment duration (sec) — Specify speed loop tuning experiment duration

3 (default)

Specify the speed loop tuning experiment duration.

Programmatic Use

Block Parameter: DurationSpeed

Type: positive scalar

Default: 3

Flux loop start time (sec) — Specify flux loop tuning experiment start time

6 (default)

Specify the simulation time when the flux tuning experiment starts.

Programmatic Use

Block Parameter: StartTimeFlux

Type: positive scalar

Default: 6

Flux loop experiment duration (sec) — Specify flux loop tuning experiment duration

3 (default)

Specify the flux loop tuning experiment duration.

Programmatic Use

Block Parameter: DurationFlux

Type: positive scalar

Default: 3

Loop Experiment Settings

Experiment Mode — Sinusoidal perturbation signal type

Superposition (default) | Sinestream | PRBS (since R2024a)

Specify whether the perturbation at each frequency is applied as sequential sinusoidal (Sinestream), simultaneous sinusoidal (Superposition), or pseudorandom binary sequence (PRBS).

• Sinestream — In this mode, the block applies perturbation at each frequency separately. For more information about sinestream signals for estimation, see Sinestream Input Signals (Simulink Control Design).

• Superposition — In this mode, the perturbation signal includes all specified frequencies at once. For frequency response estimation at a vector of frequencies ω = [ω₁, … , ω_N] at amplitudes A = [A₁, … , A_N], the perturbation signal is:

  $$\Delta u={\displaystyle \sum _i{A}_i\sin \left({\omega }_{i}t\right)}.$$

• PRBS — A deterministic pseudorandom binary sequence that shifts between two values and has white-noise-like properties. PRBS signals reduce total estimation time compared to using sinestream input signals, while producing comparable estimation results. PRBS signals are useful for estimating frequency responses for communications and power electronics systems. For more information, see PRBS Input Signals (Simulink Control Design). (since R2024a)

Sinestream mode can be more accurate and can also be less intrusive, because the total size of the perturbation is never bigger than the values specified by the Sine Amplitudes parameter. However, due to the sequential nature of the sinestream perturbation, each frequency point you add increases the recommended experiment time (see the start/stop input port for details). Thus, the estimation experiment is typically much faster in Superposition mode with satisfactory results.

Sinestream signals reduce the execution time compared to superposition input signals, but also take longer to estimate the frequency response. Frequency response estimation using sinestream signals is useful when you have limited processing power and you want to reduce the execution time.

To cover a similar frequency range, the experiment length in PRBS mode is typically much shorter than the other two modes. However, there is a tradeoff between the speed and quality of results. (since R2024a)

Programmatic Use

Block Parameter: ExperimentMode

Type: character vector

Values: 'Superposition' | 'Sinestream' | 'PRBS'

Default: 'Superposition'

D-axis Current Loop

Plant Type — Stability of direct-axis current plant

Stable (default) | Integrating

Specify whether the plant associated with the d-axis current control loop is stable or integrating. If the plant has one or more integrators, select Integrating.

Programmatic Use

Block Parameter: PlantTypeDaxis

Type: character vector

Values: 'Stable' | 'Integrating'

Default: 'Stable'

Plant Sign — Sign of direct-axis current plant

Positive (default) | Negative

Specify whether the plant associated with the d-axis current control loop is positive or negative. If a positive change in the plant input at the nominal operating point results in a positive change in the plant output, specify Positive. Otherwise, specify negative. For stable plants, the sign of the plant is the sign of the plant DC gain.

Programmatic Use

Block Parameter: PlantSignDaxis

Type: character vector

Values: 'Positive' | 'Negative'

Default: 'Positive'

Sine Amplitudes — Amplitude of sinusoidal perturbations in direct-axis current loop

1 (default) | scalar | vector of length 5

During the experiment, the block injects a sinusoidal signal into the plant associated with the loop at the frequencies [1/10, 1/3, 1, 3, 10]ω_c , where ω_c is the target bandwidth for tuning. Use Sine Amplitudes to specify the amplitude of each of these injected signals. Specify a:

• Scalar value to inject the same amplitude at each frequency

• Vector of length 5 to specify a different amplitude at each of [1/10, 1/3, 1, 3, 10]ω_c

In a typical plant with typical target bandwidth, the magnitudes of the plant responses at the experiment frequencies do not vary widely. In such cases, you can use a scalar value to apply the same magnitude perturbation at all frequencies. However, if you know that the response decays sharply over the frequency range, consider decreasing the amplitude of the lower frequency inputs and increasing the amplitude of the higher frequency inputs. It is numerically better for the estimation experiment when all the plant responses have comparable magnitudes.

The perturbation amplitudes must be:

• Large enough that the perturbation overcomes any deadband in the plant actuator and generates a response above the noise level

• Small enough to keep the plant running within the approximately linear region near the nominal operating point, and to avoid saturating the plant input or output

When Experiment mode is Superposition, the sinusoidal signals are superimposed. Thus, the perturbation can be at least as large as the sum of all amplitudes. Make sure that the largest possible perturbation is within the range of your plant actuator. Saturating the actuator can introduce errors into the estimated frequency response.

To provide the sine amplitudes by using an input port, on the Block tab, select Use external source for sine amplitudes.

Tunable: Yes

Programmatic Use

Block Parameter: AmpSineDaxis

Type: scalar, vector of length 5

Default: 1

Q-axis Current Loop

Plant Type — Stability of quadrature-axis current plant

Stable (default) | Integrating

Specify whether the plant associated with the q-axis current control loop is stable or integrating. If the plant has one or more integrators, select Integrating.

Programmatic Use

Block Parameter: PlantTypeQaxis

Type: character vector

Values: 'Stable' | 'Integrating'

Default: 'Stable'

Plant Sign — Sign of quadrature-axis current plant

Positive (default) | Negative

Specify whether the plant associated with the q-axis current control loop is positive or negative. If a positive change in the plant input at the nominal operating point results in a positive change in the plant output, specify Positive. Otherwise, specify negative. For stable plants, the sign of the plant is the sign of the plant DC gain.

Programmatic Use

Block Parameter: PlantSignQaxis

Type: character vector

Values: 'Positive' | 'Negative'

Default: 'Positive'

Sine Amplitudes — Amplitude of sinusoidal perturbations in quadrature-axis current loop

1 (default) | scalar | vector of length 5

During the experiment, the block injects a sinusoidal signal into the plant associated with the loop at the frequencies [1/10, 1/3, 1, 3, 10]ω_c , where ω_c is the target bandwidth for tuning. Use Sine Amplitudes to specify the amplitude of each of these injected signals. Specify a:

• Scalar value to inject the same amplitude at each frequency

• Vector of length 5 to specify a different amplitude at each of [1/10, 1/3, 1, 3, 10]ω_c

In a typical plant with typical target bandwidth, the magnitudes of the plant responses at the experiment frequencies do not vary widely. In such cases, you can use a scalar value to apply the same magnitude perturbation at all frequencies. However, if you know that the response decays sharply over the frequency range, consider decreasing the amplitude of the lower frequency inputs and increasing the amplitude of the higher frequency inputs. It is numerically better for the estimation experiment when all the plant responses have comparable magnitudes.

The perturbation amplitudes must be:

• Large enough that the perturbation overcomes any deadband in the plant actuator and generates a response above the noise level

• Small enough to keep the plant running within the approximately linear region near the nominal operating point, and to avoid saturating the plant input or output

When Experiment mode is Superposition, the sinusoidal signals are superimposed. Thus, the perturbation can be at least as large as the sum of all amplitudes. Make sure that the largest possible perturbation is within the range of your plant actuator. Saturating the actuator can introduce errors into the estimated frequency response.

To provide the sine amplitudes by using an input port, on the Block tab, select Use external source for sine amplitudes.

Tunable: Yes

Programmatic Use

Block Parameter: AmpSineQaxis

Type: scalar, vector of length 5

Default: 1

Speed Loop

Plant Type — Stability of speed loop plant

Stable (default) | Integrating

Specify whether the plant associated with the speed control loop is stable or integrating. If the plant has one or more integrators, select Integrating.

Programmatic Use

Block Parameter: PlantTypeSpeed

Type: character vector

Values: 'Stable' | 'Integrating'

Default: 'Stable'

Plant Sign — Sign of speed loop plant

Positive (default) | Negative

Specify whether the plant associated with the speed control loop is positive or negative. If a positive change in the plant input at the nominal operating point results in a positive change in the plant output, specify Positive. Otherwise, specify negative. For stable plants, the sign of the plant is the sign of the plant DC gain.

Programmatic Use

Block Parameter: PlantSignSpeed

Type: character vector

Values: 'Positive' | 'Negative'

Default: 'Positive'

Sine Amplitudes — Amplitude of sinusoidal perturbations in speed loop

1 (default) | scalar | vector of length 5

During the experiment, the block injects a sinusoidal signal into the plant associated with the loop at the frequencies [1/10, 1/3, 1, 3, 10]ω_c , where ω_c is the target bandwidth for tuning. Use Sine Amplitudes to specify the amplitude of each of these injected signals. Specify a:

• Scalar value to inject the same amplitude at each frequency

• Vector of length 5 to specify a different amplitude at each of [1/10, 1/3, 1, 3, 10]ω_c

In a typical plant with typical target bandwidth, the magnitudes of the plant responses at the experiment frequencies do not vary widely. In such cases, you can use a scalar value to apply the same magnitude perturbation at all frequencies. However, if you know that the response decays sharply over the frequency range, consider decreasing the amplitude of the lower frequency inputs and increasing the amplitude of the higher frequency inputs. It is numerically better for the estimation experiment when all the plant responses have comparable magnitudes.

The perturbation amplitudes must be:

• Large enough that the perturbation overcomes any deadband in the plant actuator and generates a response above the noise level

• Small enough to keep the plant running within the approximately linear region near the nominal operating point, and to avoid saturating the plant input or output

When Experiment mode is Superposition, the sinusoidal signals are superimposed. Thus, the perturbation can be at least as large as the sum of all amplitudes. Make sure that the largest possible perturbation is within the range of your plant actuator. Saturating the actuator can introduce errors into the estimated frequency response.

To provide the sine amplitudes by using an input port, on the Block tab, select Use external source for sine amplitudes.

Tunable: Yes

Programmatic Use

Block Parameter: AmpSineSpeed

Type: scalar, vector of length 5

Default: 1

Flux Loop

Plant Type — Stability of flux loop plant

Stable (default) | Integrating

Specify whether the plant associated with the flux control loop is stable or integrating. If the plant has one or more integrators, select Integrating.

Programmatic Use

Block Parameter: PlantTypeFlux

Type: character vector

Values: 'Stable' | 'Integrating'

Default: 'Stable'

Plant Sign — Sign of flux loop plant

Positive (default) | Negative

Specify whether the plant associated with the flux control loop is positive or negative. If a positive change in the plant input at the nominal operating point results in a positive change in the plant output, specify Positive. Otherwise, specify negative. For stable plants, the sign of the plant is the sign of the plant DC gain.

Programmatic Use

Block Parameter: PlantSignFlux

Type: character vector

Values: 'Positive' | 'Negative'

Default: 'Positive'

Sine Amplitudes — Amplitude of sinusoidal perturbations in flux loop

1 (default) | scalar | vector of length 5

During the experiment, the block injects a sinusoidal signal into the plant associated with the loop at the frequencies [1/10, 1/3, 1, 3, 10]ω_c , where ω_c is the target bandwidth for tuning. Use Sine Amplitudes to specify the amplitude of each of these injected signals. Specify a:

• Scalar value to inject the same amplitude at each frequency

• Vector of length 5 to specify a different amplitude at each of [1/10, 1/3, 1, 3, 10]ω_c

In a typical plant with typical target bandwidth, the magnitudes of the plant responses at the experiment frequencies do not vary widely. In such cases, you can use a scalar value to apply the same magnitude perturbation at all frequencies. However, if you know that the response decays sharply over the frequency range, consider decreasing the amplitude of the lower frequency inputs and increasing the amplitude of the higher frequency inputs. It is numerically better for the estimation experiment when all the plant responses have comparable magnitudes.

The perturbation amplitudes must be:

• Large enough that the perturbation overcomes any deadband in the plant actuator and generates a response above the noise level

• Small enough to keep the plant running within the approximately linear region near the nominal operating point, and to avoid saturating the plant input or output

When Experiment mode is Superposition, the sinusoidal signals are superimposed. Thus, the perturbation can be at least as large as the sum of all amplitudes. Make sure that the largest possible perturbation is within the range of your plant actuator. Saturating the actuator can introduce errors into the estimated frequency response.

To provide the sine amplitudes by using an input port, on the Block tab, select Use external source for sine amplitudes.

Tunable: Yes

Programmatic Use

Block Parameter: AmpSineFlux

Type: scalar, vector of length 5

Default: 1

Current Loops (D-axis + Q-axis)

Plant Type — Stability of current loop plants

Stable (default) | Integrating

Specify whether the plants associated with the current control loops are stable or integrating. If the plant has one or more integrators, select Integrating.

Programmatic Use

Block Parameter: PlantTypeAllInner

Type: character vector

Values: 'Stable' | 'Integrating'

Default: 'Stable'

Plant Sign — Sign of current loop plants

Positive (default) | Negative

Specify whether the plants associated with the current control loops are positive or negative. If a positive change in the plant input at the nominal operating point results in a positive change in the plant output, specify Positive. Otherwise, specify negative. For stable plants, the sign of the plant is the sign of the plant DC gain.

Programmatic Use

Block Parameter: PlantSignAllInner

Type: character vector

Values: 'Positive' | 'Negative'

Default: 'Positive'

Sine Amplitudes — Amplitude of sinusoidal perturbations in current loops

1 (default) | scalar | vector of length 5

During the experiment, the block injects a sinusoidal signal into the plant associated with the loop at the frequencies [1/10, 1/3, 1, 3, 10]ω_c , where ω_c is the target bandwidth for tuning. Use Sine Amplitudes to specify the amplitude of each of these injected signals. Specify a:

• Scalar value to inject the same amplitude at each frequency

• Vector of length 5 to specify a different amplitude at each of [1/10, 1/3, 1, 3, 10]ω_c

In a typical plant with typical target bandwidth, the magnitudes of the plant responses at the experiment frequencies do not vary widely. In such cases, you can use a scalar value to apply the same magnitude perturbation at all frequencies. However, if you know that the response decays sharply over the frequency range, consider decreasing the amplitude of the lower frequency inputs and increasing the amplitude of the higher frequency inputs. It is numerically better for the estimation experiment when all the plant responses have comparable magnitudes.

The perturbation amplitudes must be:

• Large enough that the perturbation overcomes any deadband in the plant actuator and generates a response above the noise level

• Small enough to keep the plant running within the approximately linear region near the nominal operating point, and to avoid saturating the plant input or output

When Experiment mode is Superposition, the sinusoidal signals are superimposed. Thus, the perturbation can be at least as large as the sum of all amplitudes. Make sure that the largest possible perturbation is within the range of your plant actuator. Saturating the actuator can introduce errors into the estimated frequency response.

To provide the sine amplitudes by using an input port, on the Block tab, select Use external source for sine amplitudes.

Tunable: Yes

Programmatic Use

Block Parameter: AmpSineAllInner

Type: scalar, vector of length 5

Default: 1

Outer Loops (Speed + Flux)

Plant Type — Stability of outer loop plants

Stable (default) | Integrating

Specify whether the plants associated with the outer control loops are stable or integrating. If the plant has one or more integrators, select Integrating.

Programmatic Use

Block Parameter: PlantTypeAllOuter

Type: character vector

Values: 'Stable' | 'Integrating'

Default: 'Stable'

Plant Sign — Sign of outer loop plants

Positive (default) | Negative

Specify whether the plants associated with the outer control loops are positive or negative. If a positive change in the plant input at the nominal operating point results in a positive change in the plant output, specify Positive. Otherwise, specify negative. For stable plants, the sign of the plant is the sign of the plant DC gain.

Programmatic Use

Block Parameter: PlantSignAllOuter

Type: character vector

Values: 'Positive' | 'Negative'

Default: 'Positive'

Sine Amplitudes — Amplitude of sinusoidal perturbations in outer loops

1 (default) | scalar | vector of length 5

During the experiment, the block injects a sinusoidal signal into the plant associated with the loop at the frequencies [1/10, 1/3, 1, 3, 10]ω_c , where ω_c is the target bandwidth for tuning. Use Sine Amplitudes to specify the amplitude of each of these injected signals. Specify a:

• Scalar value to inject the same amplitude at each frequency

• Vector of length 5 to specify a different amplitude at each of [1/10, 1/3, 1, 3, 10]ω_c

In a typical plant with typical target bandwidth, the magnitudes of the plant responses at the experiment frequencies do not vary widely. In such cases, you can use a scalar value to apply the same magnitude perturbation at all frequencies. However, if you know that the response decays sharply over the frequency range, consider decreasing the amplitude of the lower frequency inputs and increasing the amplitude of the higher frequency inputs. It is numerically better for the estimation experiment when all the plant responses have comparable magnitudes.

The perturbation amplitudes must be:

• Large enough that the perturbation overcomes any deadband in the plant actuator and generates a response above the noise level

• Small enough to keep the plant running within the approximately linear region near the nominal operating point, and to avoid saturating the plant input or output

When Experiment mode is Superposition, the sinusoidal signals are superimposed. Thus, the perturbation can be at least as large as the sum of all amplitudes. Make sure that the largest possible perturbation is within the range of your plant actuator. Saturating the actuator can introduce errors into the estimated frequency response.

To provide the sine amplitudes by using an input port, on the Block tab, select Use external source for sine amplitudes.

Tunable: Yes

Programmatic Use

Block Parameter: AmpSineAllOuter

Type: scalar, vector of length 5

Default: 1

Block Tab

Use external source for bandwidths — Supply external signal for target bandwidths

off (default) | on

Select this parameter to enable the bandwidth input port of the block. You can specify the target bandwidth for all the loops the block tunes at this port. When this parameter is disabled, specify the target bandwidths at the block parameters. For more details, see the bandwidth port description.

Programmatic Use

Block Parameter: UseExternalWc

Type: character vector

Values: 'off' | 'on'

Default: 'off'

Use external source for target phase margins — Supply external signal for target phase margin

off (default) | on

Select this parameter to enable the target PM input port of the block. You can specify the target phase margin for all the loops the block tunes at this port. When this parameter is disabled, specify the target phase margins at the block parameters. For more details, see the target PM port description.

Programmatic Use

Block Parameter: UseExternalPM

Type: character vector

Values: 'off' | 'on'

Default: 'off'

Use external source for start/stops of experiment — Supply external signal for start and stop of tuning experiment

off (default) | on

Select this parameter to enable the start/stop and ActiveLoop input ports of the block. You can specify the start and stop of the experiment and which loop the block tunes at these ports. When this parameter is disabled, specify the start time and duration of the tuning experiment at the block parameters. For more details, see the start/stop and ActiveLoop port descriptions.

Programmatic Use

Block Parameter: UseExternalSourceStartStop

Type: character vector

Values: 'off' | 'on'

Default: 'off'

Use external source for sine amplitudes — Supply external signal for sinusoidal perturbation amplitude

off (default) | on

Select this parameter to enable the sine Amp input port of the block. You can specify sinusoidal perturbation amplitude for all the loops the block tunes at this port. When this parameter is disabled, supply the sine amplitudes at block parameters. For more details, see the sine Amp port description.

Programmatic Use

Block Parameter: UseExternalAmpSine

Type: character vector

Values: 'off' | 'on'

Default: 'off'

Data Type — Floating point precision

double (default) | single

Specify the floating-point precision based on the simulation environment or hardware requirements.

Programmatic Use

Block Parameter: BlockDataType

Type: character vector

Values: 'double' | 'single'

Default: 'double'

Estimated phase margin achieved by tuned controllers — Phase margin achieved by most recently tuned loop

off (default) | on

Select this parameter to enable the estimated PM output port of the block. The block returns the phase margin achieved by the tuned controller of the most recently tuned loop. When this parameter is disabled, you can see the tuning results by using the Export to MATLAB parameter. For more details, see the estimated PM port description.

Programmatic Use

Block Parameter: UseExternalAchievedPM

Type: character vector

Values: 'off' | 'on'

Default: 'off'

Plant frequency responses near bandwidth — Estimated frequency response for most recently tuned loop

off (default) | on

Select this parameter to enable the frd output port of the block. The block returns the phase margin achieved by the tuned controller of the most recently tuned loop. When this parameter is disabled, you can see the tuning results by using the Export to MATLAB parameter. For more details, see the frd port description.

Programmatic Use

Block Parameter: UseExternalFRD

Type: character vector

Values: 'off' | 'on'

Default: 'off'

Plant nominal input and output — Plant input and output at nominal operating point

off (default) | on

Select this parameter to enable the nominal output port of the block. The block returns the plant input and output at the nominal operating point of the most recently tuned loop. When this parameter is disabled, you can see the tuning results by using the Export to MATLAB parameter. For more details, see the port description.

Programmatic Use

Block Parameter: UseExternalU0

Type: character vector

Values: 'off' | 'on'

Default: 'off'

Start/stop of autotuning process — Signal indicating start and end of experiment for each tuned loop

off (default) | on

Select this parameter to enable loop start/stops output port of the block. The block returns a signal indicating the times at which the autotuning experiment started and ended for each loop tuned by the block. When this parameter is disabled, you can see the tuning results by using the Export to MATLAB parameter. For more details, see the loop start/stops port description.

Programmatic Use

Block Parameter: UseExternalActiveLoop

Type: character vector

Values: 'off' | 'on'

Default: 'off'

Export to MATLAB — Send experiment and tuning results to MATLAB workspace

button

When you click this button, the block creates a structure in the MATLAB^® workspace containing the experiment and tuning results. This structure, FOCTuningResult, contains the tuning results for each loop the block tunes.

• Daxis — D-axis current loop tuning results

• Qaxis — Q-axis current loop tuning results

• Speed — Speed loop tuning results

• Flux — Flux loop tuning results

For each loop tuned by the block, the result contains the following fields:

• P, I, D, N — Tuned PID gains. The structure contains whichever of these fields are necessary for the controller type you are tuning. For instance, if you are tuning a PI controller, the structure contains P and I, but not D and N.

• TargetBandwidth — The value you specified in the Target bandwidth (rad/sec) parameter of the block.

• TargetPhaseMargin — The value you specified in the Target phase margin (degrees) parameter of the block.

• EstimatedPhaseMargin — Estimated phase margin achieved by the tuned system.

• Controller — The tuned PID controller, returned as a pid (for parallel form) or pidstd (for ideal form) model object.

• Plant — The estimated plant, returned as an frd model object. This frd contains the response data obtained at the experiment frequencies [1/10, 1/3, 1, 3, 10]ω_c.

• PlantNominal — The plant input and output at the nominal operating point when the experiment begins, specified as a structure with the fields u (input) and y (output).

You can export to the MATLAB workspace while the simulation is running, including when running in external mode.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using Simulink® Coder™.

The generated code for this block can be resource heavy. For real-time applications, deploying the code on rapid prototyping hardware, such as the Speedgoat real-time target machine, is recommended.

PLC Code Generation
Generate Structured Text code using Simulink® PLC Coder™.

Version History

Introduced in R2020a

R2024a: Support for PRBS input signals

The Field Oriented Control Autotuner block now supports estimation using pseudorandom binary sequence (PRBS) input signals. A PRBS signal is a periodic, deterministic signal with white-noise-like properties that shifts between two values. PRBS signals reduce total estimation time compared to using sinestream or superposition input signals, while producing comparable estimation results. PRBS signals are useful for estimating frequency responses for communications and power electronics applications.