Create a nonlinear MPC controller with four states, two outputs, and one input.

nlobj = nlmpc(4,2,1);

In standard cost function, zero weights are applied by default to one or more OVs because there are fewer MVs than OVs.

Specify the sample time and horizons of the controller.

Ts = 0.1;
nlobj.Ts = Ts;
nlobj.PredictionHorizon = 10;
nlobj.ControlHorizon = 5;

Specify the state function for the controller, which is in the file pendulumDT0.m. This discrete-time model integrates the continuous-time model defined in pendulumCT0.m using a multistep forward Euler method.

nlobj.Model.StateFcn = "pendulumDT0";
nlobj.Model.IsContinuousTime = false;

The prediction model uses an optional parameter, Ts, to represent the sample time. Specify the number of parameters.

nlobj.Model.NumberOfParameters = 1;

Specify the output function of the model, passing the sample-time parameter as an input argument.

nlobj.Model.OutputFcn = @(x,u,Ts) [x(1); x(3)];

Define standard constraints for the controller.

nlobj.Weights.OutputVariables = [3 3];
nlobj.Weights.ManipulatedVariablesRate = 0.1;
nlobj.OV(1).Min = -10;
nlobj.OV(1).Max = 10;
nlobj.MV.Min = -100;
nlobj.MV.Max = 100;

Open Simulink model.

mdl = 'mpc_pendcartNMPC';
open_system(mdl)

In this model, the Nonlinear MPC Controller block is configured to use the controller nlobj.

To use the optional parameter in the prediction model, the model has a Simulink Bus block connected to the params input port of the Nonlinear MPC Controller block. To configure this bus block to use the Ts parameter, create a Bus object in the MATLAB® workspace, and configure the Bus Creator block to use this object. Name the Bus object 'myBusObject'.

createParameterBus(nlobj,[mdl '/Nonlinear MPC Controller'],'myBusObject',{Ts});

bdclose(mdl)

A Simulink Bus object "myBusObject" created in the MATLAB Workspace, and Bus Creator block "mpc_pendcartNMPC/Nonlinear MPC Controller" is configured to use it.