lecture 24: more advanced architectures
DESCRIPTION
Different Architectures So far we have primarily considered a negative feedback architecture with one loop and our controller in the forward path Many other architectures exist ME 431, Lecture 24TRANSCRIPT
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Lecture 24: More Advanced Architectures
1. Different architectures• Two degrees-of-freedom control• Feedforward control• Addressing multiple inputs• Addressing complexity with
multiple loops
2. More design with MATLAB
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Different Architectures• So far we have primarily considered a
negative feedback architecture with one loop and our controller in the forward path
• Many other architectures exist
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Two-Degrees-of-Freedom Control• Allows two of (Gyr, Gyn, Gyd) to be designed
independently
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1 Js+ b
+-
_____ 1R a+ sL a
____________K i s
+
-K p+
K bK Js+ b_____
K+
-
C (s)
+
+
Feedforward Compensator• Feedforward action can be used to correct
for “known” disturbances
• C(s) is designed by model inversion, can be static or dynamic
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θ.
Tia,desea
eb
ia
TLTL,est
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Feedforward Compensator • Pre-compensation can also be used to cancel
undesired dynamics of the plant and to scale the steady-state output
• Pre-compensator can speed response, but is susceptible to errors in the model and disturbances
• “Error” is distorted by K(s) and errors in K(s) aren’t corrected by the feedback
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Feedforward Compensator• Implementing the feedforward term as
follows avoids these problems
• Note, this is one of our 2-dof controllers
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Multiple Inputs• We have primarily designed control for
single input single output (SISO) systems
• When we had multiple inputs, we could examine the response to each input separately if the system was linear
• If inputs are coupled in a nonlinear manner, we can use heuristics to decouple them
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Example• Separately excited DC motor control
• Control both armature current and magnetic field strength
a a fF i B F Ki i
eaia
ef
if
ia,des
if,des
Tdes
ω
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Example• Permanent magnet synchronous
machine (traction motor) control often uses an approach called Vector Control or Field Orientation Control to emulate the previous case
• Employs DQ modeling ME
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Multiple Loops• Using nested controllers can help
reduce the complexity of the design for higher-order systems if the dynamics can be de-coupled based on speed
• Using a single controller can limit speed of response due to slow (dominant) dynamics M
E 43
1, L
ectu
re 2
4
K Js+b
+-
_____ 1Ra+sLa
_________
Kb
___Ki s
+- Kp+
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Multiple Loops
Approach:1. Design control for the fast inner loop2. Treat inner loop as static, then design
control for slow outer loop3. Can continue beyond two nested loops
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1 Js+b
+-
_____ 1Ra+sLa
____________Ki s
+- Kp+
KbK Js+b_____
K___K'i s
+- K'p+
torque (current)speed
desiredspeed
desiredtorque θ
.Tia
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ExampleSection 8-7 of Mohan, Electric Drives• Step 1: Design Fast Inner Loop (the current
loop)
Approach used: place zero of controller to cancel slow pole of the plant, then choose gain to achieve gain crossover frequency a decade or two below power electronics switching frequency
+-
1Ra+sLa
____________Ki s
+- Kp+
KbK Js+b_____
ia,des ia
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Example (cont)
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System Parameter ValueRa 2.0 ΩLa 5.2 mH
J 152x10-6 kg·m2
b 0Ke 0.1 V/rad/s
K 0.1 Nm/A
192.3s(s+348.3)(s+36.3)____________________+
- Kc(s+z) s_________
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-30
-20
-10
(dB)
101
102
103
104
-90
-45
0
(deg
)
(rad/sec)
Example (cont)• Magnitude plot of
• Desire Kc so that gain crossover frequency is one to two decades below switching frequency, in this case fs=200,000 rad/sec
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192.3348.3s
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Example (cont)
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( / )31.6( 36.3) p i pK s K Kss s
101
102
103
104-5
0
5
10
15
20
25
(dB)
(rad/sec)
• Controller for the current loop
• Resulting open-loop magnitude plot
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Example (cont)• Step 2: Treat inner loop as a static gain
then design slow outer loop (speed loop)
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2
31.6 1147inner CL TF DC gain 10.0052 33.6 1213
ss s
K Js+b
________K'i s
+- K'p+ 1
desiredspeed θ
.currentloop
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Example (cont)
• Since b=0,
• Desire to place gain crossover frequency one decade below crossover of inner current loop
• Desire to achieve reasonable phase margin, ≈ 60 degrees
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2
'( ')outer open-loop TF
0.00152cK s z
s
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Example (cont)• Will use SISO Design tool in MATLAB
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