Model Predictive Control Toolbox 3.1.1

MPC with Non-Diagonal Weight Matrices

Contents

This demonstration shows how to use non-diagonal weight matrices.

MPC Controller Setup

We start defining the plant to be controlled

sys=ss(tf({1,1;1,2},{[1 .5 1],[.7 .5 1];[1 .4 2],[1 2]}),'min');

Now, setup an MPC controller object

Ts=.1;             % sampling time
model=c2d(sys,Ts); % prediction model

Define prediction and control horizons

p=20;       % prediction horizon
m=2;        % control horizon

Let us assume default value for weights and build the MPC object

MPCobj=mpc(model,Ts,p,m);

-->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.

Define constraints on the manipulated variable

clear MV
MV(1)=struct('Min',-3,'Max',3,'RateMin',-100,'RateMax',100);
MV(2)=struct('Min',-2,'Max',2,'RateMin',-100,'RateMax',100);
MPCobj.MV=MV;

Define non-diagonal output weight. Note that it is specified inside a cell !

OW=[1 -1]'*[1 -1];

% Non-diagonal output weight, corresponding to ((y1-r1)-(y2-r2))^2
MPCobj.Weights.OutputVariables={OW};
% Non-diagonal input weight, corresponding to (u1-u2)^2
MPCobj.Weights.ManipulatedVariables={0.5*OW};

Closed-loop MPC Simulation Using the Command SIM

Tstop=30;           % simulation time

Tf=round(Tstop/Ts); % number of simulation steps
r=ones(Tf,1)*[1 2];       % reference trajectory

Run the closed-loop simulation and plot results

close all
[y,t,u]=sim(MPCobj,Tf,r);
subplot(211)
plot(t,y(:,1)-r(1,1)-y(:,2)+r(1,2));grid
title('(y_1-r_1)-(y_2-r_2)');
subplot(212)
plot(t,u);grid
title('u');

-->Integrated white noise added on measured output channel #1.
-->Integrated white noise added on measured output channel #2.
-->The "Model.Noise" property of the "mpc" object is empty. Assuming whit
e noise on each measured output channel.

MPC Simulation Using Simulink®

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

The continuous-time plant to be controlled has the following state-space realization:

[A,B,C,D]=ssdata(sys);

Now simulate closed-loop MPC in Simulink®

Run simulation

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

bdclose('mpc_weightsdemo');