This example shows how to use measurable plant states in MPC control at run time.
The linear open-loop plant model is a double integrator.
plant = tf(1,[1 0 0]);
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.
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');
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 7.27097e-14