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EE 380 Linear Control Systems Lecture 25
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EE 380 Fall 2014 Lecture 25. EE 380 Linear Control Systems Lecture 25 Professor Jeffrey Schiano Department of Electrical Engineering 1
Transcript of EE 380 Linear Control Systems Lecture 25
EE 380 Fall 2014Lecture 25.
EE 380
Linear Control Systems
Lecture 25
Professor Jeffrey SchianoDepartment of Electrical Engineering
1
EE 380 Fall 2014Lecture 25.
Lecture 25 Topics
• Common Cascade Compensators– P, PI, PD, PID– Phase-lag, Phase-Lead
• Determining Compensator Parameters using Root Locus
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EE 380 Fall 2014Lecture 25.
– Three term compensator (Minorsky, 1922)
P, PI, PD, PID Compensators
3
R
Y cG s
UE pG s
Compensator Plant
0
( )t
P I Ddeu t K e t K e d K dt
EE 380 Fall 2014Lecture 25.
Guidelines for Selecting Terms• Proportional Control
– Always try first
• Proportional plus Integral (PI) Control– Improves steady-state accuracy– Bends root locus towards the right-half plane
• Proportional plus Derivative (PD) Control– Improves transient response– Bends the root locus towards the legft-half plane
• Proportional plus Integral plus Derivative (PID) Control– Improves steady-state accuracy and transient response
4
EE 380 Fall 2014Lecture 25.
PID Disadvantages
• PD Control– Gain increases with frequency– Accentuates noise
• PI Control– Infinite gain at DC
5
EE 380 Fall 2014Lecture 25.
Exercise 1
• Sketch the Bode magnitude and phase plots for– PI Compensator– PD Compensator
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EE 380 Fall 2014Lecture 25.
Exercise 1 Solution
7
EE 380 Fall 2014Lecture 25.
Exercise 1 Solution
8
EE 380 Fall 2014Lecture 25.
Phase Lag Compensator
• Approximates PI controller– Low-frequency gain rolls-off to a finite value
• Transfer function representation
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1, 11o
co
s aG s K as
,oc o
o
s a s zKG s K p za s s p
EE 380 Fall 2014Lecture 25.
Exercise 2
• Sketch Bode magnitude and phase plot of the phase-lag compensator
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EE 380 Fall 2014Lecture 25.
Exercise 2 Solution
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EE 380 Fall 2014Lecture 25.
Exercise 2 Solution
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EE 380 Fall 2014Lecture 25.
Exercise 2 Solution
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EE 380 Fall 2014Lecture 25.
Phase Lead Compensator
• Approximates a PD controller– High-frequency gain rolls-off to a finite value
• Transfer function representation
14
1 , 11o
co
sG s K as a
,oc o
o
s s zG s Ka K p zs a s p
EE 380 Fall 2014Lecture 25.
Exercise 3
• Sketch Bode magnitude and phase plot of the phase-lead compensator
15
EE 380 Fall 2014Lecture 25.
Exercise 3 Solution
16
EE 380 Fall 2014Lecture 25.
Exercise 3 Solution
17
EE 380 Fall 2014Lecture 25.
Exercise 3 Solution
18
EE 380 Fall 2014Lecture 25.
EE 380
Linear Control Systems
Lecture 25
Professor Jeffrey SchianoDepartment of Electrical Engineering
1
EE 380 Fall 2014Lecture 25.
Lecture 25 Topics
• Common Cascade Compensators– P, PI, PD, PID– Phase-lag, Phase-Lead
• Determining Compensator Parameters using Root Locus
2
EE 380 Fall 2014Lecture 25.
– Three term compensator (Minorsky, 1922)
P, PI, PD, PID Compensators
3
EE 380 Fall 2014Lecture 25.
Guidelines for Selecting Terms• Proportional Control
– Always try first
• Proportional plus Integral (PI) Control– Improves steady-state accuracy– Bends root locus towards the right-half plane
• Proportional plus Derivative (PD) Control– Improves transient response– Bends the root locus towards the legft-half plane
• Proportional plus Integral plus Derivative (PID) Control– Improves steady-state accuracy and transient response
4
EE 380 Fall 2014Lecture 25.
PID Disadvantages
• PD Control– Gain increases with frequency– Accentuates noise
• PI Control– Infinite gain at DC
5
EE 380 Fall 2014Lecture 25.
Exercise 1
• Sketch the Bode magnitude and phase plots for– PI Compensator– PD Compensator
6
EE 380 Fall 2014Lecture 25.
Exercise 1 Solution
7
EE 380 Fall 2014Lecture 25.
Exercise 1 Solution
8
EE 380 Fall 2014Lecture 25.
Phase Lag Compensator
• Approximates PI controller– Low-frequency gain rolls-off to a finite value
• Transfer function representation
9
EE 380 Fall 2014Lecture 25.
Exercise 2
• Sketch Bode magnitude and phase plot of the phase-lag compensator
10
EE 380 Fall 2014Lecture 25.
Exercise 2 Solution
11
EE 380 Fall 2014Lecture 25.
Exercise 2 Solution
12
EE 380 Fall 2014Lecture 25.
Exercise 2 Solution
13
EE 380 Fall 2014Lecture 25.
Phase Lead Compensator
• Approximates a PD controller– High-frequency gain rolls-off to a finite value
• Transfer function representation
14
EE 380 Fall 2014Lecture 25.
Exercise 3
• Sketch Bode magnitude and phase plot of the phase-lead compensator
15
EE 380 Fall 2014Lecture 25.
Exercise 3 Solution
16
EE 380 Fall 2014Lecture 25.
Exercise 3 Solution
17
EE 380 Fall 2014Lecture 25.
Exercise 3 Solution
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