ENTC 395 Lecture 7a. Today 4 PID control –Overview –Definitions –Open loop response 4 Example...
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Transcript of ENTC 395 Lecture 7a. Today 4 PID control –Overview –Definitions –Open loop response 4 Example...
![Page 1: ENTC 395 Lecture 7a. Today 4 PID control –Overview –Definitions –Open loop response 4 Example –SIMULINK implementation.](https://reader036.fdocuments.net/reader036/viewer/2022082821/5697c0121a28abf838ccbf0a/html5/thumbnails/1.jpg)
ENTC 395
Lecture 7a
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Today
PID control– Overview– Definitions– Open loop response
Example – SIMULINK implementation
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Reading
Last time Laplace TransformsAppendix F.1-F.4
Today: Handout - Control Theory
Next time: Handout - Control Theory
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Control Systems
Plant: A system to be controlled
Controller: Provides the excitation for the plant, controls the overall system behavior
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Controller: Inputs and Outputs
R: Desired operating point
Y: Actual operating point
e: Error signal = R-Y
u: Correction signal
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dt
tdeKdtteKteKtu DIp
)()()()(
PID Controllers
KP = Proportional gain
KI = Integral gain
KD = Derivative gain
Controller response may be a function of three components of the error signal
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PID Controller Transfer Function
KP = Proportional gain
KI = Integral gain
KD = Derivative gain
In s space the transfer function looks like this:
DIP sKKs
Kse
su
1
)(
)(
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Parameter Effects
The effect of the Ks on a system are summarized below. Actual relations are more complex. Ks are not independent.
CL RESPONSE RISE TIME OVERSHOOTSETTLING
TIME S-S ERROR
Kp Decrease Increase Small Change Decrease
Ki Decrease Increase Increase Eliminate
Kd Small Change Decrease Decrease Small Change
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Example
Our old friend the spring mass damper system
kbsmssF
sX
sFsXkbsms
Fkxxbxm
xmFxbkx
xmF
2
2
1
)(
)(
)()(
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Example
Our old friend the spring mass damper system
M = 1kg
b = 10 N.s/m
k = 20 N/m
F(t) = 1(Step input)
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Example
The goal of this example is to demonstrate how KP, KI and KD modifies the system response.
Goals: Fast rise time
Minimum overshoot
No steady-state error
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Example -- Open loop response
The open loop response is simply the response of the system with no controller in the loop.
Model of a spring, mass, damper systemOpen loop response
20
k
10
b
Sum
Scope
s
1
Integrator1s
1
IntegratorF(t)
1
1/m
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Example -- Open loop response
For a step input of 20 N the mass moves 1.0 m
x=F/k
x=20N/20(N/m)
x=20m
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Example -- Proportional Control
Change problem add an active proportional controller
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Example -- Proportional Control
Change problem add an active proportional controller
Response now changes also
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Example -- PD Control
Change active proportional controller
add KD
Response now changes also
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Example -- PD Control- Response
Change active proportional controller
add KD
Response now changes also
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Example -- PID Control
Change to active PID
controller
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Example -- PID Control ResponseChange to active PID
controller