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# Model Predictive Control Toolbox

## Using Custom Input and Output Constraints

This example shows how to design model predictive controller with mixed input/output constraints.

Design MPC Controller

The basic setup of the MPC controller includes:

• A double integrator as the prediction model

• Prediction horizon of 20

• Control horizon of 20

• Input constraints -1 <= u(t) <= 1

plant = tf(1,[1 0 0]);                          % Prediction model
Ts = .1;                                        % Sampling time
p = 20;                                         % Prediction horizon
m = 20;                                         % Control horizon
mpcobj = mpc(plant,Ts,p,m);                     % MPC object
mpcobj.MV = struct('Min',-1,'Max',1);           % Input saturation constraints
-->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.

Define Mixed Input/Output (I/O) Constraint

The sum of the input u(t) and output y(t) must be nonnegative and smaller than 1.2:

0 <= u(t) + y(t) <= 1.2

To impose this combined (mixed) I/O constraint, formulate it as a set of inequality constraints involving u(t) and y(t):

u(t) +  y(t) <= 1.2
-u(t) + -y(t) <= 0
setconstraint(mpcobj,[1;-1],[1;-1],[1.2;0]);

Simulate Using Simulink®

To run this example, Simulink® is required.

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

Simulate closed-loop control of the linear plant model in Simulink. Controller "mpcobj" is specified in the block dialog.

mdl = 'mpc_mixedconstraints';
open_system(mdl);            % Open Simulink(R) Model
sim(mdl);                    % Start Simulation
-->Converting the "Model.Plant" property of "mpc" object to state-space.
-->Converting model to discrete time.
Assuming unmeasured input disturbance #1 is white noise.
-->The "Model.Noise" property of the "mpc" object is empty. Assuming white noise on each measured output channel.

As you can see, the MPC Controller always keeps the sum u+y between 0 and 1.2 while tracking the reference signal r=1.

bdclose(mdl);