Model Predictive Control of a DC Motor

Control a multivariable nonlinear system subjected to constraints using model predictive control (MPC). Many simple control systems take an ad hoc approach in which they effectively just "watch what a system does" without trying to have a specific model for what is going on inside the system. Model predictive control (MPC) is about having a specific model for a system and then deriving an optimal controller based on that model.

In this example, MPC is used to control the speed of a DC motor while constraining the value of electric current flowing in the circuit.

Import the Wolfram System Modeler model of the DC motor:

(Press Shift + Enter to evaluate.)

In[]:=

CloudImport["https://www.wolframcloud.com/obj/861cd6ae-7262-46d7-9860-88ac63dfbed6","MO"];

Check the model diagram of the DC motor:

In[]:=

sm=SystemModel["DCMotor"];sm[{"Diagram",ImageSizeLarge}]

Out[]=

Check the model parameters:

In[]:=

sm["TopParameterNames"]

Out[]=

{

emfK

}

Give suitable values to the parameters:

In[]:=

params=<|"R"1.2,"L"0.001,"J"0.01,"emfK"0.05,"B"0.001|>;SetSystemModel[sm,params];

Linearize the model and see its states, input and outputs:

In[]:=

SystemModelLinearize[sm]

Out[]=

				V
inductor.i	-1200.	0.	-50.	1000.
inertiaWithDamper.phi	0.	0.	1.	0.
inertiaWithDamper.w	5.	0.	-0.1	0.
w	0.	0.	1.	0.
i	1.	0.	0.	0.

Set the model specification:

In[]:=

sspec=<|"InputModel"sm,"SamplingPeriod"0.1,"TrackedOutputs"{"w"},"SamplingMethod""ForwardRectangularRule"|>;

Predict over three time steps (time horizon) and provide weights for the error (to control the response speed) and input increment:

In[]:=

cost=<|"Horizon"3,"ErrorWeight"DiagonalMatrix[{2}],"InputIncrementWeight"DiagonalMatrix[{1}]|>;

Constrain the current flowing in the circuit:

In[]:=

cons1=0≤"i"≤1;

Create a model predictive controller:

In[]:=

cd1=ModelPredictiveController[sspec,cost,cons1]

Out[]=

SystemsModelControllerData

Design: MPC tracker

Horizon: 3



Create a controlled system:

In[]:=

csys=ConnectSystemModelController["test",sm,cd1]

Out[]=

Find its connectors:

In[]:=

SystemModel["test","Connectors"]

Out[]=

i∈

,refW∈

,w∈



Connect the controlled system to a constant reference source:

In[]:=

components={"constant1"∈"Modelica.Blocks.Sources.Constant","test1"∈"test"};connections={"constant1.y""test1.refW"};model=ConnectSystemModelComponents["testModel",components,connections]

Out[]=