Create nonlinear MPC controller with six states, six outputs, and four inputs.

nx = 6;
ny = 6;
nu = 4;
nlobj = nlmpc(nx,ny,nu);

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

Specify the controller sample time and horizons.

Ts = 0.4;
p = 30;
c = 4;
nlobj.Ts = Ts;
nlobj.PredictionHorizon = p;
nlobj.ControlHorizon = c;

Specify the prediction model state function and the Jacobian of the state function. For this example, use a model of a flying robot.

nlobj.Model.StateFcn = "FlyingRobotStateFcn";
nlobj.Jacobian.StateFcn = "FlyingRobotStateJacobianFcn";

Specify a custom cost function for the controller that replaces the standard cost function.

nlobj.Optimization.CustomCostFcn = @(X,U,e,data) Ts*sum(sum(U(1:p,:)));
nlobj.Optimization.ReplaceStandardCost = true;

Specify a custom constraint function for the controller.

nlobj.Optimization.CustomEqConFcn = @(X,U,data) X(end,:)';

Validate the prediction model and custom functions at the initial states (x0) and initial inputs (u0) of the robot.

x0 = [-10;-10;pi/2;0;0;0];
u0 = zeros(nu,1); 
validateFcns(nlobj,x0,u0);

Model.StateFcn is OK.
Jacobian.StateFcn is OK.
No output function specified. Assuming "y = x" in the prediction model.
Optimization.CustomCostFcn is OK.
Optimization.CustomEqConFcn is OK.
Analysis of user-provided model, cost, and constraint functions complete.

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

nx = 4;
ny = 2;
nu = 1;
nlobj = nlmpc(nx,ny,nu);

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 discrete-time state function uses an optional parameter, the sample time Ts, to integrate the continuous-time model. Therefore, you must specify the number of optional parameters as 1.

nlobj.Model.NumberOfParameters = 1;

Specify the output function for the controller. In this case, define the first and third states as outputs. Even though this output function does not use the optional sample time parameter, you must specify the parameter as an input argument (Ts).

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

Validate the prediction model functions for nominal states x0 and nominal inputs u0. Since the prediction model uses a custom parameter, you must pass this parameter to validateFcns.

x0 = [0.1;0.2;-pi/2;0.3];
u0 = 0.4;
validateFcns(nlobj, x0, u0, [], {Ts});

Model.StateFcn is OK.
Model.OutputFcn is OK.
Analysis of user-provided model, cost, and constraint functions complete.

Create a nonlinear MPC controller with three states, one output, and four inputs. The first two inputs are measured disturbances, the third input is the manipulated variable, and the fourth input is an unmeasured disturbance.

nlobj = nlmpc(3,1,'MV',3,'MD',[1 2],'UD',4);

To view the controller state, output, and input dimensions and indices, use the Dimensions property of the controller.

nlobj.Dimensions

ans = struct with fields:
     NumberOfStates: 3
    NumberOfOutputs: 1
     NumberOfInputs: 4
            MVIndex: 3
            MDIndex: [1 2]
            UDIndex: 4

Specify the controller sample time and horizons.

nlobj.Ts = 0.5;
nlobj.PredictionHorizon = 6;
nlobj.ControlHorizon = 3;

Specify the prediction model state function, which is in the file exocstrStateFcnCT.m.

nlobj.Model.StateFcn = 'exocstrStateFcnCT';

Specify the prediction model output function, which is in the file exocstrOutputFcn.m.

nlobj.Model.OutputFcn = 'exocstrOutputFcn';

Validate the prediction model functions using the initial operating point as the nominal condition for testing and setting the unmeasured disturbance state, x0(3), to 0. Since the model has measured disturbances, you must pass them to validateFcns.

x0 = [311.2639; 8.5698; 0];
u0 = [10; 298.15; 298.15];
validateFcns(nlobj,x0,u0(3),u0(1:2)');

Model.StateFcn is OK.
Model.OutputFcn is OK.
Analysis of user-provided model, cost, and constraint functions complete.