Model Predictive Control Toolbox 3.1.1

MPC Control of a DC Servomotor

Contents

This demonstration shows how to design an MPC controller to control a DC servomechanism under voltage and shaft torque constraints [1].

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,'Units','V');
OutputVariables(1)=struct('Min',-Inf,'Max',Inf,'Units','rad');
OutputVariables(2)=struct('Min',Vmin,'Max',Vmax,'Units','Nm');
Weights=struct('Input',uweight,'InputRate',duweight,'Output',yweight);

clear Model
Model.Plant=sys;
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 emp
ty. Assuming default 0.10000.
-->The "Weights.OutputVariables" property of "mpc" object is empty. Assum
ing 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.
-->MPC problem is constrained and "ManipulatedVariables.RateMin" is not c
ompletely specified or has infinite values.
   Setting values to -10 to prevent numerical problems in QP.
-->The "Model.Noise" property of the "mpc" object is empty. Assuming whit
e 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')

Simulation in Simulink®

if ~mpcchecktoolboxinstalled('simulink')
    disp('Simulink(R) is required to run this part of the demo.')
    return
end

Run simulation

open_system('mpc_motor')
sim('mpc_motor',Tstop);

bdclose('mpc_motor')