mpcmoveMultiple

Compute gain-scheduling MPC control action at a single time instant

Syntax

mv = mpcmoveMultiple(MPCArray,states,index,ym,r,v)

[mv,info] = mpcmoveMultiple(MPCArray,states,index,ym,r,v)

[___] = mpcmoveMultiple(___,options)

Description

mv = mpcmoveMultiple(MPCArray,states,index,ym,r,v) computes the optimal manipulated variable moves at the current time using a model predictive controller selected by index from an array of MPC controllers. This results depends upon the properties contained in the MPC controller and the controller states. The result also depends on the measured plant outputs, the output references (setpoints), and the measured disturbance inputs. mpcmoveMultiple updates the controller state when default state estimation is used. Call mpcmoveMultiple repeatedly to simulate closed-loop model predictive control.

[mv,info] = mpcmoveMultiple(MPCArray,states,index,ym,r,v) returns additional details about the computation in a structure. To determine whether the optimal control calculation completed normally, check the data in info.

[___] = mpcmoveMultiple(___,options) alters selected controller settings using options you specify with mpcmoveopt. These changes apply for the current time instant only, allowing a command-line simulation using mpcmoveMultiple to mimic the Multiple MPC Controllers block in Simulink^® in a computationally efficient manner.

Input Arguments

MPCArray — MPC controllers

cell array of MPC controller objects

MPC controllers to simulate, specified as a cell array of traditional (implicit) MPC controller objects. Use the mpc command to create the MPC controllers.

All the controllers in MPCArray must use either default state estimation or custom state estimation. Mismatch is not permitted.

states — Current MPC controller states

cell array of mpcstate objects

Current controller states for each MPC controller in MPCArray, specified as a cell array of mpcstate objects.

Before you begin a simulation with mpcmoveMultiple, initialize each controller state using x = mpcstate(mpcobj). Then, modify the default properties of each state as appropriate.

If you are using default state estimation, mpcmoveMultiple expects x to represent x[n|n-1] (where x is one entry in states, the current state of one MPC controller in MPCArray). The mpcmoveMultiple command updates the state values in the previous control interval with that information. Therefore, you should not programmatically update x at all. The default state estimator employs a steady-state Kalman filter.

If you are using custom state estimation, mpcmoveMultiple expects x to represent x[n|n]. Therefore, prior to each mpcmoveMultiple command, you must set x.Plant, x.Disturbance, and x.Noise to the best estimates of these states (using the latest measurements) at the current control interval.

index — Index of selected controller

positive integer

Index of selected controller in the cell array MPCArray, specified as a positive integer.

ym — Current measured outputs

row vector

Current measured outputs, specified as a row vector of length N_ym, where N_ym is the number of measured outputs. If you are using custom state estimation, ym is ignored. If you set ym = [], then mpcmoveMultiple uses the appropriate nominal value.

r — Plant output reference values

array

Plant output reference values, specified as a p-by-N_y array, where p is the prediction horizon of the selected controller and N_y is the number of outputs. Row r(i,:) defines the reference values at step i of the prediction horizon.

r must contain at least one row. If r contains fewer than p rows, mpcmoveMultiple duplicates the last row to fill the p-by-N_y array. If you supply exactly one row, therefore, a constant reference applies for the entire prediction horizon.

If you set r = [], then mpcmoveMultiple uses the appropriate nominal value.

To implement reference previewing, which can improve tracking when a reference varies in a predictable manner, r must contain the anticipated variations, ideally for p steps.

v — Current and anticipated measured disturbances

array

Current and anticipated measured disturbances, specified as a p-by-N_md array, where p is the prediction horizon of the selected controller and N_md is the number of measured disturbances. Row v(i,:) defines the expected measured disturbance values at step i of the prediction horizon.

Modeling of measured disturbances provides feedforward control action. If your plant model does not include measured disturbances, use v = [].

v must contain at least one row. If v contains fewer than p rows, mpcmoveMultiple duplicates the last row to fill the p-by-N_md array. If you supply exactly one row, therefore, a constant measured disturbance applies for the entire prediction horizon.

If you set v = [], then mpcmoveMultiple uses the appropriate nominal value.

To implement disturbance previewing, which can improve tracking when a disturbance varies in a predictable manner, v must contain the anticipated variations, ideally for p steps.

options — Override values for selected controller properties

mpcmoveopt object

Override values for selected properties of the selected MPC controller, specified as an options object you create with mpcmoveopt. These options apply to the current mpcmoveMultiple time instant only. Using options yields the same result as redefining or modifying the selected controller before each call to mpcmoveMultiple, but involves considerably less overhead. Using options is equivalent to using a Multiple MPC Controllers Simulink block in combination with optional input signals that modify controller settings, such as MV and OV constraints.

Output Arguments

mv — Optimal manipulated variable moves

column vector

Optimal manipulated variable moves, returned as a column vector of length N_mv, where N_mv is the number of manipulated variables.

If the controller detects an infeasible optimization problem or encounters numerical difficulties in solving an ill-conditioned optimization problem, mv remains at its most recent successful solution, xc.LastMove.

Otherwise, if the optimization problem is feasible and the solver reaches the specified maximum number of iterations without finding an optimal solution, mv:

• Remains at its most recent successful solution if the Optimizer.UseSuboptimalSolution property of the controller is false.

• Is the suboptimal solution reached after the final iteration if the Optimizer.UseSuboptimalSolution property of the controller is true. For more information, see Suboptimal QP Solution.

info — Solution details

structure

Solution details, returned as a structure with the following fields.

Uopt — Optimal manipulated variable sequence

(p+1)-by-N_mv array

Predicted optimal manipulated variable adjustments (moves), returned as a (p+1)-by-N_mv array, where p is the prediction horizon and N_mv is the number of manipulated variables.

Uopt(i,:) contains the calculated optimal values at time k+i-1, for i = 1,...,p, where k is the current time. The first row of Info.Uopt contains the same manipulated variable values as output argument mv. Since the controller does not calculate optimal control moves at time k+p, Uopt(p+1,:) is equal to Uopt(p,:).

Yopt — Optimal output variable sequence

(p+1)-by-N_y array

Optimal output variable sequence, returned as a (p+1)-by-N_y array, where p is the prediction horizon and N_y is the number of outputs.

The first row of Info.Yopt contains the calculated outputs at time k based on the estimated states and measured disturbances; it is not the measured output at time k. Yopt(i,:) contains the predicted output values at time k+i-1, for i = 1,...,p+1.

Yopt(i,:) contains the calculated output values at time k+i-1, for i = 2,...,p+1, where k is the current time. Yopt(1,:) is computed based on the estimated states and measured disturbances.

Xopt — Optimal prediction model state sequence

(p+1)-by-N_x array

Optimal prediction model state sequence, returned as a (p+1)-by-N_x array, where p is the prediction horizon and N_x is the number of states in the plant and unmeasured disturbance models (states from noise models are not included).

Xopt(i,:) contains the calculated state values at time k+i-1, for i = 2,...,p+1, where k is the current time. Xopt(1,:) is the same as the current states state values.

Topt — Time intervals

column vector of length p+1

Time intervals, returned as a column vector of length p+1. Topt(1) = 0, representing the current time. Subsequent time steps Topt(i) are given by Ts*(i-1), where Ts = mpcobj.Ts is the controller sample time.

Use Topt when plotting the Uopt, Xopt, or Yopt sequences.

Slack — Slack variable

nonnegative scalar

Slack variable, ε, used in constraint softening, returned as 0 or a positive scalar value.

• ε = 0 — All constraints were satisfied for the entire prediction horizon.

• ε > 0 — At least one soft constraint is violated. When more than one constraint is violated, ε represents the worst-case soft constraint violation (scaled by your ECR values for each constraint).

See QP Optimization Problem for Linear MPC for more information.

Iterations — Number of solver iterations

positive integer | 0 | -1 | -2

Number of solver iterations, returned as one of the following:

• Positive integer — Number of iterations needed to solve the optimization problem that determines the optimal sequences.

• 0 — Optimization problem could not be solved in the specified maximum number of iterations.

• –1 — Optimization problem was infeasible. An optimization problem is infeasible if no solution can satisfy all the hard constraints.

• –2 — Numerical error occurred when solving the optimization problem.

QPCode — Optimization solution status

'feasible' | 'infeasible' | 'unrealiable'

Optimization solution status, returned as one of the following:

• 'feasible' — Optimal solution was obtained (Iterations > 0)

• 'infeasible' — Solver detected a problem with no feasible solution (Iterations = –1) or a numerical error occurred (Iterations = –2)

• 'unreliable' — Solver failed to converge (Iterations = 0). In this case, if mpcobj.Optimizer.UseSuboptimalSolution is false, u freezes at the most recent successful solution. Otherwise, it uses the suboptimal solution found during the last solver iteration.

Cost — Objective function cost

nonnegative scalar

Objective function cost, returned as a nonnegative scalar value. The cost quantifies the degree to which the controller has achieved its objectives. For more information, see QP Optimization Problem for Linear MPC.

The cost value is only meaningful when QPCode = 'feasible', or when QPCode = 'feasible' and mpcobj.Optimizer.UseSuboptimalSolution is true.

Tips

• Use the Multiple MPC Controllers Simulink block for simulations and code generation.

Version History

Introduced in R2014b