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Design Model Predictive Controller at Equilibrium Operating Point

This example shows how to design a model predictive controller with nonzero nominal values.

The plant model is obtained by linearization of a nonlinear plant in Simulink® at a nonzero steady-state operating point.

Linearize Nonlinear Plant Model

The nonlinear plant is implemented in the Simulink model mpc_nloffsets and linearized at the default operating condition using the linearize function from Simulink Control Design.

Create an operating point specification for the current model initial conditions.

plant_mdl = 'mpc_nloffsets';
op = operspec(plant_mdl);

Compute the operating point for these initial conditions.

[op_point, op_report] = findop(plant_mdl,op);
 Operating point search report:
---------------------------------

opreport = 


 Operating point search report for the Model mpc_nloffsets.
 (Time-Varying Components Evaluated at time t=0)

Operating point specifications were successfully met.
States: 
----------
    Min          x          Max        dxMin        dx         dxMax   
___________ ___________ ___________ ___________ ___________ ___________
                                                                       
(1.) mpc_nloffsets/Integrator
   -Inf       0.57514       Inf          0      -1.8208e-14      0     
(2.) mpc_nloffsets/Integrator2
   -Inf       2.1503        Inf          0      -8.3846e-12      0     

Inputs: 
----------
 Min     u     Max  
______ ______ ______
                    
(1.) mpc_nloffsets/In1
 -Inf  -1.252  Inf  

Outputs: 
----------
  Min       y       Max   
________ ________ ________
                          
(1.) mpc_nloffsets/Out1
  -Inf   -0.52938   Inf   

Extract nominal state, output, and input values from the computed operating point.

x0 = [op_report.States(1).x;op_report.States(2).x];
y0 = op_report.Outputs.y;
u0 = op_report.Inputs.u;

Linearize the plant at the initial conditions.

plant = linearize(plant_mdl,op_point);

Design MPC Controller

Create an MPC controller object with a specified sample time Ts, prediction horizon 20, and control horizon 3.

Ts = 0.1;
mpcobj = mpc(plant,Ts,20,3);
-->The "Weights.ManipulatedVariables" property is empty. Assuming default 0.00000.
-->The "Weights.ManipulatedVariablesRate" property is empty. Assuming default 0.10000.
-->The "Weights.OutputVariables" property is empty. Assuming default 1.00000.

Set the nominal values in the controller.

mpcobj.Model.Nominal = struct('X',x0,'U',u0,'Y',y0);

Set the output measurement noise model (white noise, zero mean, standard deviation = 0.1).

mpcobj.Model.Noise = 0.1;

Set the manipulated variable constraint.

mpcobj.MV.Max = 0.2;

Simulate Using Simulink

Specify the reference value for the output signal.

r0 = 1.5*y0;

Open and simulate the model.

mdl = 'mpc_offsets';
open_system(mdl)
sim(mdl)
-->Converting model to discrete time.
-->Assuming output disturbance added to measured output channel #1 is integrated white noise.

Simulate Using sim Command

Simulate the controller.

Tf = round(10/Ts);
r = r0*ones(Tf,1);
[y1,t1,u1,x1,xmpc1] = sim(mpcobj,Tf,r);

Plot and compare the simulation results.

subplot(1,2,1)
plot(y.time,y.signals.values,t1,y1,t1,r)
legend('Nonlinear','Linearized','Reference')
title('output')
grid

subplot(1,2,2)
plot(u.time,u.signals.values,t1,u1)
legend('Nonlinear','Linearized')
title('input')
grid

bdclose(plant_mdl)
bdclose(mdl)

See Also

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