MATLAB Examples

Using Custom State Estimation

This example shows how to use measurable plant states in MPC control at run time.

Contents

Define Plant Model

The linear open-loop plant model is a double integrator.

plant = tf(1,[1 0 0]);

Design MPC Controller

Create the controller object with sampling period, prediction and control horizons.

Ts = 0.1;
p = 10;
m = 3;
mpcobj = mpc(plant, Ts, p, m);
-->The "Weights.ManipulatedVariables" property of "mpc" object is empty. Assuming default 0.00000.
-->The "Weights.ManipulatedVariablesRate" property of "mpc" object is empty. Assuming default 0.10000.
-->The "Weights.OutputVariables" property of "mpc" object is empty. Assuming default 1.00000.

Specify actuator saturation limits as MV constraints.

mpcobj.MV = struct('Min',-1,'Max',1);

Specify the controller to use custom state estimation.

setEstimator(mpcobj,'custom');

Simulate Using MPCMOVE Command

Configure variables to store the closed-loop responses.

Tf = round(5/Ts);
YY = zeros(Tf,1);
UU = zeros(Tf,1);

Prepare the plant used in simulation.

sys = c2d(ss(plant),Ts);
xsys = [0;0];

Use MPCSTATE object to specify the initial controller states before simulation starts.

xmpc = mpcstate(mpcobj);
-->Converting the "Model.Plant" property of "mpc" object to state-space.
-->Converting model to discrete time.
   Assuming no disturbance added to measured output channel #1.
-->The "Model.Noise" property of the "mpc" object is empty. Assuming white noise on each measured output channel.

Simulate closed-loop response iteratively.

for t = 0:Tf
    % Update plant measurement.
    ysys = sys.C*xsys;
    % Compute MPC action. Because the plant states are measurable, use
    % these values for state estimation instead of the plant output.
    xmpc.Plant = xsys;
    u = mpcmove(mpcobj,xmpc,[],1);
    % Store signals.
    YY(t+1) = ysys;
    UU(t+1) = u;
    % Update plant states.
    xsys = sys.A*xsys + sys.B*u;
end
subplot(2,1,1)
plot(0:Ts:5,YY);
title('y');
subplot(2,1,2)
plot(0:Ts:5,UU);
title('u');

Simulate Using Simulink®

To run this example, Simulink® is required.

if ~mpcchecktoolboxinstalled('simulink')
    disp('Simulink(R) is required to run this example.')
    return
end

Simulate closed-loop control of the linear plant model in Simulink. Controller "mpcobj" is specified in the MPC Controller block dialog.

mdl = 'mpc_customestimation';
open_system(mdl);
sim(mdl);

The closed-loop responses are identical between simulations in MATLAB and Simulink.

fprintf('\nDifference between simulations in MATLAB and Simulink is %g\n',norm(UU-u));
Difference between simulations in MATLAB and Simulink is 5.03764e-14
bdclose(mdl)