## Simulink Control Design |

- Automatic tuning of PID, gain-scheduled, and arbitrary SISO and MIMO control systems
- Operating-point calculation (trimming) and linearization of models
- Frequency response estimation from simulation data
- Batch linearization for varying parameters and operating points
- Numerical optimization of compensators to meet time-domain and frequency-domain requirements (with Simulink Design Optimization™)

Simulink Control Design™ lets you systematically tune control systems modeled in Simulink^{®} using SISO and MIMO design techniques. The product supports several approaches to control design, including automatic tuning of PID controllers, interactive tuning using root locus and Bode plots, and automatic tuning of decentralized MIMO architectures.

Simulink Control Design provides automatic gain-tuning capabilities for Simulink PID Controller blocks. You can accomplish the initial tuning of a PID controller with a single click. The product linearizes a Simulink model to obtain a linear plant model. If the model linearizes to zero due to discontinuities such as pulse width modulation (PWM), you can create a linear plant model from simulation input-output data using system identification (requires System Identification Toolbox™). The product then uses the linear plant model and a proprietary tuning method to compute the PID gains based on the closed-loop performance that you desire. An initial controller is suggested based on an analysis of your system dynamics. You can then interactively adjust the response time and transient behavior in the PID Tuner app. The PID Tuner app also provides several plots you can use to analyze the controller behavior. For example, you can use a step reference tracking plot and an open-loop Bode plot to compare the performance of the current design with the design corresponding to initial gain values.

**PID Controller Design for a DC Motor**

Design a PID controller for a DC motor modeled in Simulink^{®}. Create a closed-loop system by using the PID Controller block, then tune the gains of PID Controller block using the PID Tuner.

**PID Controller Tuning for a Model with Discontinuities**

Design a PID controller for a model that cannot be linearized. Use system identification to identify a plant model from simulation input-output data.

Simulink Control Design provides a Control System Designer app for tuning SISO control loops directly in Simulink using the graphical and automated tuning capabilities of Control System Toolbox™. You can use any control architecture that you build in Simulink that is linearizable. Tunable Simulink blocks include Gain, Transfer Function, Zero-Pole, State-Space, and PID Controller. Simulink Control Design automatically identifies the relevant control loops for the tuned blocks and launches a preconfigured session of the Control System Designer app.

**Cascaded Multi-Loop/Multi-Compensator Feedback Design** (Example)

Tune two cascaded feedback loops.

You can use the Control System Designer app to:

- Graphically tune multiple, continuous, or discrete SISO loops
- Observe loop interactions and coupling effects while tuning parameters
- Compute compensator designs using systematic design algorithms such as the proprietary Robust Response Time PID tuning, Ziegler-Nichols PID tuning, IMC design, or LQG design
- Optimize the control loops to meet time-domain and frequency-domain design requirements (requires Simulink Design Optimization™)
- Directly tune Simulink block parameters, including PID gains, zero-pole-gain representations, and masked blocks
- Examine the closed-loop response such as a reference trajectory or the ability of a control system to reject a disturbance at any portion of a model
- Write the tuned parameter values back to your Simulink model for verification with the full nonlinear system

In addition to the Control System Designer app, you can use the Control System Tuner app to tune SISO controllers modeled in Simulink. The Control System Tuner app automatically tunes controller parameters to meet time-domain and frequency-domain requirements.

Simulink Control Design lets you automatically tune decentralized controllers modeled in Simulink using the Control System Tuner app. You can use the toolbox to automatically compute and store a linearization of your Simulink model. Simulink Control Design automatically creates a tunable model of the control architecture specified in a Simulink model. You can:

- Specify Simulink model blocks that should be tuned
- Specify tuning requirements
- Automatically tune specified blocks to satisfy the must-have requirements (design constraints) and to best meet the remaining requirements (objectives)
- Validate your design by running nonlinear simulations

Using this approach, you can automatically tune complex multivariable controllers that are modeled using Simulink blocks. For example, you can automatically tune inner-loop and outer-loop PID controllers in a multi-loop control system without changing the control system architecture.

**Automatic Tuning of a Multivariable Distillation Column Controller**

Design a decoupling controller for a distillation column with Simulink^{®} Control Design™.

Gain scheduling is a linear technique for controlling nonlinear or time-varying plants. It involves computing linear approximations of the plant at various operating conditions, tuning controller gains at the operating condition, and scheduling controller gains as the plant changes operating conditions. Simulink Control Design provides tools for automatically computing gain schedules for fixed-structure control systems. You can:

- Automatically trim and linearize Simulink models at multiple operating conditions
- Parameterize controller gain surfaces as functions of scheduling variables
- Construct a linear parameter-varying (LPV) model representing the system throughout its operating range
- Specify tuning requirements such as tracking and disturbance rejection
- Automatically tune gain surface coefficients to satisfy tuning requirements at all operating conditions
- Update parameters of the Simulink Look Up Table or Interpolation blocks implementing the controller with tuned gain values

**Tuning of Gain-Scheduled Three-Loop Autopilot** (Example)

Generate smooth gain schedules for a three-loop autopilot.

Linear control design typically requires you to consider multiple operating points to account for the various set points of a nonlinear model. Simulink Control Design provides a graphical interface to determine model operating points. You can:

- Calculate operating points from user-defined set points using numerical optimization
- Take operating point snapshots at specific times or events during simulation

You can use these operating points to initialize a simulation at steady state or as a basis for linearization and control design.

**Trim, Linearization, and Control Design for an Aircraft**

Trim and linearize a nonlinear aircraft model and use the resulting linear model to design a pitch rate damper controller.

With Simulink Control Design you can linearize continuous, discrete, and multirate Simulink models. Using graphical signal annotations to specify loop opening and linearization inputs and outputs, you can linearize the whole model, a portion of the model, or a single block or subsystem. The signal annotations can be used for open-loop and closed-loop analysis. The annotations and analysis are nonintrusive and do not affect your model's simulation behavior.

Simulink Control Design automatically computes the linearized model and lets you visualize the results in a step response plot or Bode diagram. A Linearization Inspector is provided to visualize the impact of each block in your Simulink model on the linearization. You can fine-tune your results by specifying the linear behavior of any number of blocks in your model. The linear behavior can be specified as a matrix gain or LTI model, giving you flexibility to linearize Simulink models containing discontinuities or event-based components, such as Stateflow^{®} charts or pulse-width modulation signal-based systems.

When working with Robust Control Toolbox™, you can compute an uncertain linear model by specifying uncertain values for transfer functions and gains directly in the model. The resulting uncertain linear model can be used to study the impact of uncertainty on the stability and performance of your control system.

All of these tools have a command-line API to write scripts for batch mode trimming and linearization. You can write these scripts yourself or automatically create MATLAB^{®} code from the graphical interface.

**Batch Mode Trimming and Linearization**

Create a script to do batch mode trimming and linearization of Simulink^{®} models.

Simulink Control Design provides tools for the simulation-based computation of a model’s frequency response. You can use these tools to:

- Verify the results of a linearization
- Compute the model’s frequency response when linearization techniques are not appropriate, such as with models described by strong discontinuities or event-based dynamics
- Study the effects of excitation signal amplitude on a nonlinear system’s gain and phase characteristics

Simulink Control Design helps you construct the excitation signals, such as sine sweeps or chirp signals; run the simulations; collect the data; and calculate and plot the model’s frequency response. The algorithms used to compute the frequency response are designed to minimize the simulation time and support the Accelerator and Rapid Accelerator modes in Simulink to speed up the overall computation.

**Frequency Response Estimation**

Estimate the frequency response of a Simulink^{®} model using simulation.