Control of a Multi-Input Multi-Output Nonlinear Plant

This example uses:

Open Script

This example shows how to design a model predictive controller for a multi-input multi-output nonlinear plant. The plant has 3 manipulated variables and 2 measured outputs.

Linearize Nonlinear Plant

To run this example, Simulink® and Simulink Control Design™ are required.

if ~mpcchecktoolboxinstalled('simulink')
    disp('Simulink(R) is required to run this example.')
    return
end
if ~mpcchecktoolboxinstalled('slcontrol')
    disp('Simulink Control Design(R) is required to run this example.')
    return
end

The nonlinear plant is implemented in Simulink model mpc_nonlinmodel and linearized at the default operating condition using the linearize command from Simulink Control Design.

plant = linearize('mpc_nonlinmodel');

Assign names to I/O variables.

plant.InputName = {'Mass Flow';'Heat Flow';'Pressure'};
plant.OutputName = {'Temperature';'Level'};
plant.InputUnit = {'kg/s' 'J/s' 'Pa'};
plant.OutputUnit = {'K' 'm'};

Design MPC Controller

Create the controller object with sampling period, prediction and control horizons:

Ts = 0.2;
p = 5;
m = 2;
mpcobj = mpc(plant,Ts,p,m);

-->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.

Specify MV constraints.

mpcobj.MV = struct('Min',{-3;-2;-2},'Max',{3;2;2},'RateMin',{-1000;-1000;-1000});

Define weights on manipulated and controlled variables.

mpcobj.Weights = struct('MV',[0 0 0],'MVRate',[.1 .1 .1],'OV',[1 1]);

Simulate Using Simulink

Run simulation.

mdl1 = 'mpc_nonlinear';
open_system(mdl1)
sim(mdl1)

-->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.

Modify MPC Design to Track Ramp Signals

In order to track a ramp, a triple integrator is defined as an output disturbance model on both outputs.

outdistmodel = tf({1 0;0 1},{[1 0 0 0],1;1,[1 0 0 0]});
setoutdist(mpcobj,'model',outdistmodel);

Run simulation.

mdl2 = 'mpc_nonlinear_setoutdist';
open_system(mdl2)
sim(mdl2)

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

Simulate without Constraints

When the constraints are not active, the MPC controller behaves like a linear controller.

mpcobj.MV = [];

Reset output disturbance model to default

setoutdist(mpcobj,'integrators');

The input to the linear controller LTI is the vector [ym;r], where ym is the vector of measured outputs, and r is the vector of output references.

LTI = ss(mpcobj,'r');

-->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.

Run simulation.

refs = [1;1];                  % output references are step signals
mdl3 = 'mpc_nonlinear_ss';
open_system(mdl3)
sim(mdl3)

Compare Simulation Results

fprintf('Compare output trajectories: ||ympc-ylin|| = %g\n',norm(ympc-ylin));
disp('The MPC controller and the linear controller produce the same closed-loop trajectories.');

Compare output trajectories: ||ympc-ylin|| = 1.21921e-14
The MPC controller and the linear controller produce the same closed-loop trajectories.

bdclose(mdl1)
bdclose(mdl2)
bdclose(mdl3)

See Also

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Related Topics

Model Predictive Control Toolbox Documentation

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