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Design Model Predictive Controller at Equilibrium Operating Point

This example uses:

Open Script

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

植物是通过线性化模型nonlinear plant in Simulink® at a nonzero steady-state operating point.

Linearize Nonlinear Plant Model

The nonlinear plant is implemented in the Simulink modelmpc_nloffsetsand linearized at the default operating condition using thelinearizefunction 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);
操作点搜索报告 : --------------------------------- 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 timeTs, prediction horizon20, and control horizon3.

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 UsingsimCommand

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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