Define Plant Model

Define the parameters of the nominal plant which the MPC controller is based on. Systems from MV to MO and UD to MO are identical.

p1 = tf(1,[1 2 1])*[1 1; 0 1];
plant = ss([p1 p1],'min');
plant.InputName = {'mv1','mv2','ud3','ud4'};

Design MPC Controller

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

plant = setmpcsignals(plant,'MV',[1 2],'UD',[3 4]);
% Create the controller object with sampling period, prediction and control
% horizons:
mpcobj = mpc(plant,1,40,2);

-->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 unmeasured input disturbances, the MPC controller will use the following unmeasured disturbance model.

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

Define the Real Plant Model Used in Simulation

Define the parameters of the actual plant in closed loop with the MPC controller.

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

Simulate Closed-Loop Response Using the SIM Command

Define reference trajectories and unmeasured disturbances entering the actual plant.

dist = ones(1,2);   % unmeasured disturbance signal
refs = [1 2];       % output reference signal
Tf = 20;            % total number of simulation steps

Create an MPC simulation object.

options = mpcsimopt(mpcobj);
options.unmeas = dist;  % unmeasured disturbance signal
options.model = psim;   % real plant model

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

sim(mpcobj,Tf,refs,options);

-->Converting model to discrete time.
-->Assuming output disturbance added to measured output channel #1 is integrated white noise.
-->Assuming output disturbance added to measured output channel #2 is integrated white noise.
-->The "Model.Noise" property of the "mpc" object is empty. Assuming white noise on each measured output channel.
-->Converting model to discrete time.

The closed loop tracking performance is acceptable with the presence of unmeasured disturbances.