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Model Predictive Control of a DC Motor
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.
(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:
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sm=SystemModel["DCMotor"];sm[{"Diagram",ImageSizeLarge}]
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Check the model parameters:
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sm["TopParameterNames"]
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{,,,,}
R
L
J
emfK
B
Give suitable values to the parameters:
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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:
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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:
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cons1=0≤"i"≤1;
Create a model predictive controller:
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cd1=ModelPredictiveController[sspec,cost,cons1]
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SystemsModelControllerData
Create a controlled system:
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csys=ConnectSystemModelController["test",sm,cd1]
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Find its connectors:
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SystemModel["test","Connectors"]
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i∈
,refW∈
,w∈
Connect the controlled system to a constant reference source:
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components={"constant1"∈"Modelica.Blocks.Sources.Constant","test1"∈"test"};connections={"constant1.y""test1.refW"};model=ConnectSystemModelComponents["testModel",components,connections]
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Simulate and plot the angular velocity of the shaft of the DC motor:
In[]:=
sim=SystemModelSimulate["testModel",100];SystemModelPlot[sim,{"test1.w","constant1.y"},PlotRangeAll]
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Check the value of the constrained current:
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SystemModelPlot[sim,{"test1.i"},PlotRangeAll]
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Look for the name of the voltage variable in the controlled system:
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controlledVoltage=sim[{"VariableNames","*.V"}]
Out[]=
{test1.eSys.sys.V}
Check the controlled voltage supplied to the circuit:
In[]:=
SystemModelPlot[sim,controlledVoltage,PlotRangeAll]
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Compute the performance of the controlled system: