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