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E22FeedForwardDCM.onb
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E22FeedForwardDCM.onb
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<!DOCTYPE OMNotebook>
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<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Arial'; font-size:38pt; font-weight:600; color:#000000;">Exercise 2.3.1</span></p></td></tr></table></body></html></Text>
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<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Times New Roman'; font-size:12pt; color:#000000;">Create a feed-forward closed control loop for a DC-motor from the reference signal. First implement the model completing the </span><a href="../DCMotor/DCMotor.onb"><span style=" font-family:'Times New Roman'; font-size:12pt; text-decoration: underline; color:#0000ff;">DC-motor</span></a><span style=" font-family:'Times New Roman'; font-size:12pt; color:#000000;"> model with the extra transfer function, F</span><span style=" font-family:'Times New Roman'; font-size:12pt; color:#000000; vertical-align:sub;">f</span><span style=" font-family:'Times New Roman'; font-size:12pt; color:#000000;"> and later just replace the DC-motor behavior with a simple transfer function, G.</span></p></td></tr></table></body></html></Text>
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<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Times New Roman'; font-size:12pt; color:#000000;">Here G represent the transfer function of the DC-motor and </span><span style=" font-family:'Courier New'; font-size:12pt; color:#000000;">F</span><span style=" font-family:'Times New Roman'; font-size:12pt; color:#000000;"> the PID regulator. F</span><span style=" font-family:'Times New Roman'; font-size:12pt; color:#000000; vertical-align:sub;">f</span><span style=" font-family:'Times New Roman'; font-size:12pt; color:#000000;"> is the forward regulator and G</span><span style=" font-family:'Times New Roman'; font-size:12pt; color:#000000; vertical-align:sub;">m</span><span style=" font-family:'Times New Roman'; font-size:12pt; color:#000000;"> acting on the reference signal.</span></p></td></tr></table></body></html></Text>
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<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Times'; font-size:14pt; font-weight:600; color:#000000;">Hints: Deriving Transfer Function, G</span></p></td></tr></table></body></html></Text>
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<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Times New Roman'; font-size:12pt; color:#000000;">A simple model of a DC-motor is given by</span></p></td></tr></table></body></html></Text>
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<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Times New Roman'; font-size:12pt; color:#000000;">where R is the resistance of the armature coil and L the inductance. U is the terminal voltage and I is the armature current. The U</span><span style=" font-family:'Times New Roman'; font-size:12pt; color:#000000; vertical-align:sub;">e </span><span style=" font-family:'Times New Roman'; font-size:12pt; color:#000000;">is representing the back EMF voltage induced in the armature coil from the rotation of the rotor. In this model the rotor magnetic and mechanical losses as well as armature high frequency losses are all neglected.</span></p></td></tr></table></body></html></Text>
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<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Times New Roman'; font-size:12pt; color:#000000;">The armature current, I will result in a mechanical torque, T on the rotor which makes the rotor to move (K</span><span style=" font-family:'Times New Roman'; font-size:12pt; color:#000000; vertical-align:sub;">T</span><span style=" font-family:'Times New Roman'; font-size:12pt; color:#000000;"> is torque constant). </span></p></td></tr></table></body></html></Text>
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<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Times New Roman'; font-size:12pt; color:#000000;">According to Faraday's law the magnetic field produced by the rotation of the rotor induces a voltage in the armature coil (K</span><span style=" font-family:'Times New Roman'; font-size:12pt; color:#000000; vertical-align:sub;">e</span><span style=" font-family:'Times New Roman'; font-size:12pt; color:#000000;"> is back EMF constant and ω angular velocity of the rotor).</span></p></td></tr></table></body></html></Text>
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<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Times New Roman'; font-size:12pt; color:#000000;">Considering the braking friction, B, and the rotor inertia, J, will give the following load torque balance (T</span><span style=" font-family:'Times New Roman'; font-size:12pt; color:#000000; vertical-align:sub;">0</span><span style=" font-family:'Times New Roman'; font-size:12pt; color:#000000;"> is the load torque):</span></p></td></tr></table></body></html></Text>
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<Text><!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0//EN" "http://www.w3.org/TR/REC-html40/strict.dtd">
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<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Times New Roman'; font-size:12pt; color:#000000;">Putting the previous equations together yields the transfer function of the motor (Ω is the laplace transform of ω).</span></p></td></tr></table></body></html></Text>
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<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Times'; font-size:14pt; font-weight:600; color:#000000;">Hints: Deriving the Feed-forward Transfer Function, F</span><span style=" font-family:'Times'; font-size:14pt; font-weight:600; color:#000000; vertical-align:sub;">f</span></p></td></tr></table></body></html></Text>
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<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Times New Roman'; font-size:12pt; color:#000000;">The transfer function from the reference signal to the output signal is</span></p></td></tr></table></body></html></Text>
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<td style="border: none;">
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<html><head><meta name="qrichtext" content="1" /><style type="text/css">
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<tr>
<td style="border: none;">
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Times'; font-size:14pt; font-weight:600; color:#000000;">Example</span></p></td></tr></table></body></html></Text>
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<html><head><meta name="qrichtext" content="1" /><style type="text/css">
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</style></head><body style=" font-family:'MS Shell Dlg 2'; font-size:8.25pt; font-weight:400; font-style:normal;">
<table border="0" style="-qt-table-type: root; margin-top:5px; margin-bottom:5px; margin-left:5px; margin-right:5px;">
<tr>
<td style="border: none;">
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Times New Roman'; font-size:12pt; color:#000000;">Setting values in the above transfer functions will lead to</span></p></td></tr></table></body></html></Text>
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<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Times New Roman'; font-size:12pt; color:#000000;">The PID regulator is</span></p></td></tr></table></body></html></Text>
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<table border="0" style="-qt-table-type: root; margin-top:5px; margin-bottom:5px; margin-left:5px; margin-right:5px;">
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p, li { white-space: pre-wrap; }
</style></head><body style=" font-family:'MS Shell Dlg 2'; font-size:8.25pt; font-weight:400; font-style:normal;">
<table border="0" style="-qt-table-type: root; margin-top:5px; margin-bottom:5px; margin-left:5px; margin-right:5px;">
<tr>
<td style="border: none;">
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Times'; font-size:14pt; font-weight:600; color:#000000;">Answer</span></p></td></tr></table></body></html></Text>
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<html><head><meta name="qrichtext" content="1" /><style type="text/css">
p, li { white-space: pre-wrap; }
</style></head><body style=" font-family:'MS Shell Dlg 2'; font-size:8.25pt; font-weight:400; font-style:normal;">
<table border="0" style="-qt-table-type: root; margin-top:5px; margin-bottom:5px; margin-left:5px; margin-right:5px;">
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<td style="border: none;">
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Times New Roman'; font-size:12pt; color:#000000;">Taking the nominal values from the above example and implementing it with the Modelica standard library components leads to the following model. </span></p></td></tr></table></body></html></Text>
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<Input>loadModel(Modelica);</Input>
<Output>[done]</Output>
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<Input>renameComponent(Modelica.Blocks.Continuous.PID,Gain,gain2);
// This is because in MSL 3.1 and 3.2 the component type has to be different than the component name</Input>
<Output>
OMC-ERROR:
"[C:\OpenModelica1.6.0\lib\omc\omlibrary\msl31/Modelica/Mechanics/MultiBody/package.mo:1211:3-1215:15:writable] Error: Variable gravityType not found in scope Modelica.Mechanics.MultiBody.World.gravityAcceleration
Error: Base class ModelicaServices.Animation.Shape not found in scope Modelica.Mechanics.MultiBody.Visualizers.Advanced.Shape
"</Output>
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<Input>model DCMotorFForward
Modelica.Electrical.Analog.Basic.Resistor resistor(R = 1);
Modelica.Electrical.Analog.Basic.Ground ground;
Modelica.Electrical.Analog.Basic.EMF emf(k=1); // Electromagnetic force
Modelica.Electrical.Analog.Basic.Inductor inductor(L = 1);
Modelica.Electrical.Analog.Sources.SignalVoltage signalVoltage;
Modelica.Mechanics.Rotational.Components.Inertia inertia(J = 1); // Rotor inertia MSL 3.1
// Modelica.Mechanics.Rotational.Inertia inertia(J = 1); // Rotor inertia MSL 2.2
Modelica.Blocks.Continuous.PID pid1( k = 30, Ti = 3, Td = 1);
Modelica.Mechanics.Rotational.Sensors.SpeedSensor speedSensor;
Modelica.Blocks.Sources.Step step(height = 0.5); // Reference signal
Modelica.Blocks.Math.Add add( k1 = 1, k2 = 1); // Output is the error
Modelica.Blocks.Math.Gain gain( k = 1);
Modelica.Blocks.Math.Add add1( k2=1, k1=-1);
Modelica.Blocks.Continuous.TransferFunction Ff(b={100,100,100}, a={1,20,100});
Modelica.Blocks.Continuous.TransferFunction Gm(b={100}, a={1,20,100});
equation
connect(signalVoltage.n, resistor.p);
connect(resistor.n, inductor.p);
connect(inductor.n, emf.p);
connect(emf.n, ground.p);
connect(ground.p, signalVoltage.p);
connect(emf.flange, inertia.flange_a);
connect(inertia.flange_b, speedSensor.flange);
connect(add.y, signalVoltage.v);
connect(pid1.y, add.u2);
connect(add1.y, pid1.u);
connect(Gm.y, add1.u1);
connect(add1.u2, gain.y);
connect(step.y, Ff.u);
connect(add.u1, Ff.y);
connect(Gm.u, step.y);
connect(gain.u, speedSensor.w);
end DCMotorFForward;</Input>
<Output>{DCMotorFForward}</Output>
</GraphCell>
<GraphCell AutoX="true" AutoY="true" style="Graph" MinorX="0" Antialiasing="false" MinorY="0" Title="Plot title" LogX="false" LogY="false" MajorX="0" MajorY="0" closed="false" YLabel="y" Area="wEgAAAAAAADAMAAAAAAAAEBZAAAAAAAAQD4AAAAAAAA=" ShowGraph="false" Grid="false" XLabel="x" Legend="false">
<Input>simulate(DCMotorFForward)</Input>
<Output>record SimulationResult
resultFile = "DCMotorFForward_res.plt",
simulationOptions = "startTime = 0.0, stopTime = 1.0, numberOfIntervals = 500, tolerance = 1e-06, method = 'dassl', fileNamePrefix = 'DCMotorFForward', storeInTemp = false, noClean = false, options = '', outputFormat = 'plt'",
messages = "",
timeFrontend = 0.303970756059779,
timeBackend = 0.110096394932876,
timeSimCode = 0.0252518127303889,
timeTemplates = 0.0554189149738305,
timeCompile = 6.25198034945782,
timeSimulation = 0.7858627982048,
timeTotal = 7.53269277240543
end SimulationResult;</Output>
</GraphCell>
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<Input>plot({inertia.w,step.y})</Input>
<Output>true</Output>
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<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Times'; font-size:18pt; font-weight:600; color:#000000;">Question</span></p></td></tr></table></body></html></Text>
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<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Times New Roman'; font-size:12pt; color:#000000;">Replace the DC-motor model with the (resistor, induction, EMF and inertia components) following transfer function. Also update the F</span><span style=" font-family:'Times New Roman'; font-size:12pt; color:#000000; vertical-align:sub;">f </span><span style=" font-family:'Times New Roman'; font-size:12pt; color:#000000;">.</span></p></td></tr></table></body></html></Text>
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<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Times'; font-size:14pt; font-weight:600; color:#000000;">Answer</span></p></td></tr></table></body></html></Text>
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<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Times New Roman'; font-size:12pt; color:#000000;">Implementing the above transfer runction instead of the model with resitor, inductor and back-EMF component.</span></p></td></tr></table></body></html></Text>
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<Input>model FeedForward
Modelica.Blocks.Continuous.PID pid1( k = 30, Ti = 3, Td = 1);
Modelica.Blocks.Sources.Step step(height = 0.5);
Modelica.Blocks.Math.Add add( k1 = 1, k2 = 1);
Modelica.Blocks.Math.Gain gain( k = -1);
Modelica.Blocks.Math.Add add1( k2=1, k1=1);
Modelica.Blocks.Continuous.TransferFunction Ff(b={100,500,1400,2400}, a={10,220,500,2000});
Modelica.Blocks.Continuous.TransferFunction Gm(b={100}, a={1,20,100});
Modelica.Blocks.Continuous.TransferFunction G(b={10,20}, a={1,5,14,24}) ;
equation
connect(pid1.y, add.u2);
connect(add1.y, pid1.u);
connect(Gm.y, add1.u1);
connect(add1.u2, gain.y);
connect(step.y, Ff.u);
connect(add.u1, Ff.y);
connect(Gm.u, step.y);
connect(add.y, G.u);
connect(G.y, gain.u);
end FeedForward;</Input>
<Output>{FeedForward}</Output>
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<Input>simulate(FeedForward);</Input>
<Output>[done]</Output>
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<Graph Points="false" Line="true" X="time" Interpolation="Linear" Y="G.y" Color="#ff0000"/>
<Input>plot({G.y});</Input>
<Output>[done]</Output>
</GraphCell>
</GroupCell>
<GroupCell closed="false">
<GraphCell AutoX="true" AutoY="true" style="Graph" MinorX="0" Antialiasing="false" MinorY="2.78138476304982e-308" Title="Plot title" LogX="false" LogY="false" MajorX="0" MajorY="0" closed="false" YLabel="y" Area="wEgAAAAAAADAMAAAAAAAAEBZAAAAAAAAQD4AAAAAAAA=" ShowGraph="false" Grid="false" XLabel="x" Legend="false">
<Input>model CompareFForward
FeedForward feedForward;
DCMotorFForward dcMotorFForward;
end CompareFForward;</Input>
<Output>{CompareFForward}</Output>
</GraphCell>
<GraphCell AutoX="true" AutoY="true" style="Graph" MinorX="0" Antialiasing="false" MinorY="2.78138476304982e-308" Title="Plot title" LogX="false" LogY="false" MajorX="0" MajorY="0" closed="false" YLabel="y" Area="wEgAAAAAAADAMAAAAAAAAEBZAAAAAAAAQD4AAAAAAAA=" ShowGraph="false" Grid="false" XLabel="x" Legend="false">
<Input>simulate(CompareFForward)</Input>
<Output>record SimulationResult
resultFile = "CompareFForward_res.plt"
end SimulationResult;</Output>
</GraphCell>
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<Graph Points="false" Line="true" X="time" Interpolation="Linear" Y="dcMotorFForward.inertia.w" Color="#0000ff"/>
<Graph Points="false" Line="true" X="time" Interpolation="Linear" Y="feedForward.G.y" Color="#ff0000"/>
<Graph Points="false" Line="true" X="time" Interpolation="Linear" Y="feedForward.step.y" Color="#00ff00"/>
<Input>plot({feedForward.G.y,dcMotorFForward.inertia.w,feedForward.step.y})</Input>
<Output>true</Output>
</GraphCell>
</GroupCell>
</GroupCell>
</GroupCell>
</GroupCell>
</GroupCell>
</GroupCell>
</Notebook>