MATLAB Examples

# 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]); ```

```if ~mpcchecktoolboxinstalled('simulink') disp('Simulink(R) is required to run this example.') return end ```
```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 no disturbance added to measured output channel #1. -->The "Model.Noise" property of the "mpc" object is empty. Assuming white noise on each measured output channel. ```
```bdclose(mdl); ```