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DC Servomotor with Constraint on Unmeasured Output

This example shows how to design a model predictive controller for a DC servomechanism under voltage and shaft torque constraints.

Reference

[1] A. Bemporad and E. Mosca, ``Fulfilling hard constraints in uncertain linear systems by reference managing,'' Automatica, vol. 34, no. 4, pp. 451-461, 1998.

Define the parameters of the DC-servo motor [1].

mpcmotormodel

MPC Controller Setup

clear ManipulatedVariables OutputVariables

Define MPC object fields.

ManipulatedVariables=struct('Min',umin,'Max',umax);
OutputVariables(1)=struct('Min',-Inf,'Max',Inf);
OutputVariables(2)=struct('Min',Vmin,'Max',Vmax);
Weights=struct('Input',uweight,'InputRate',duweight,'Output',yweight);

clear Model
Model.Plant=sys;
Model.Plant.InputUnit = {'V'};
Model.Plant.OutputGroup={1 'Measured';2 'Unmeasured'};

PredictionHorizon=10;
ControlHorizon=2;

Create MPC object in workspace.

ServoMPC=mpc(Model,Ts,PredictionHorizon,ControlHorizon);
ServoMPC.Weights=Weights;
ServoMPC.ManipulatedVariables=ManipulatedVariables;
ServoMPC.OutputVariables=OutputVariables;
-->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.
for output(s) y1 and zero weight for output(s) y2

Simulation Using SIM

disp('Now simulating nominal closed-loop behavior');

Tf=round(Tstop/Ts);
r=pi*ones(Tf,2);

[y1,t1,u1,xp1,xmpc1]=sim(ServoMPC,Tf,r);
Now simulating nominal closed-loop behavior
-->Converting model to discrete time.
-->The "Model.Noise" property of the "mpc" object is empty. Assuming white noise on each measured output channel.

Plot results.

subplot(311)
stairs(t1,y1(:,1));
hold on
stairs(t1,r(:,1));
hold off
title('Angular Position')
subplot(312)
stairs(t1,u1);
title('Voltage')
subplot(313)
stairs(t1,y1(:,2));
title('Torque')