Model Predictive Control Toolbox 3.1.1

MPC Control of a MIMO System Under Plant Model Mismatch

This demonstration shows how to test an MPC controller under a mismatch between the nominal model which the controller is based on and the actual plant which is controlled by MPC. The nominal system has 2 manipulated variables, 2 unmeasured input disturbances, and 2 measured outputs. The actual plant has 3 unmeasured input disturbances and a different dynamics.

Define the parameters of the nominal plant which the MPC controller is based on

p1 = tf(1,[1 2 1])*[1 1; 0 1];
plant = ss([p1 p1],'min');

Define inputs 1 and 2 as manipulated variables, 3 and 4 as unmeasured disturbances

plant=setmpcsignals(plant,'MV',[1 2],'UD',[3 4]);

Also define input names

set(plant,'InputName',{'mv1','mv2','umd3','umd4'});

For unmeasured input disturbances, the MPC controller will use the following model

distModel = eye(2,2)*ss(-.5,1,1,0);

We are ready to create the MPC object

mpcobj = mpc(plant,1,40,2);
mpcobj.Model.Disturbance = distModel;

-->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 the parameters of the actual plant in closed loop with the MPC controller. Note that the actual plant has three unmeasured disturbances, while the nominal one has two

p2 = tf(1.5,[0.1 1 2 1])*[1 1; 0 1];
psim = ss([p2 p2 tf(1,[1 1])*[0;1]],'min');
psim=setmpcsignals(psim,'MV',[1 2],'UD',[3 4 5]);

Define reference trajectories and unmeasured disturbances entering the actual plant

dist=ones(1,3); % unmeasured disturbance trajectory
refs=[1 2];     % output reference trajectory

Tf=100; % total number of simulation steps

Create an MPC simulation object

options=mpcsimopt(mpcobj);
options.unmeas=dist;
options.model=psim;

Run the closed-loop MPC simulation with model mismatch and unforeseen unmeasured disturbance inputs

sim(mpcobj,Tf,refs,options);

-->Converting model to discrete time.
-->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.