ee 380 linear control systems lecture 25
TRANSCRIPT
![Page 1: EE 380 Linear Control Systems Lecture 25](https://reader030.vdocument.in/reader030/viewer/2022012716/61ae3b5102e9a012074991cd/html5/thumbnails/1.jpg)
EE 380 Fall 2014Lecture 25.
EE 380
Linear Control Systems
Lecture 25
Professor Jeffrey SchianoDepartment of Electrical Engineering
1
![Page 2: EE 380 Linear Control Systems Lecture 25](https://reader030.vdocument.in/reader030/viewer/2022012716/61ae3b5102e9a012074991cd/html5/thumbnails/2.jpg)
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
![Page 3: EE 380 Linear Control Systems Lecture 25](https://reader030.vdocument.in/reader030/viewer/2022012716/61ae3b5102e9a012074991cd/html5/thumbnails/3.jpg)
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
![Page 4: EE 380 Linear Control Systems Lecture 25](https://reader030.vdocument.in/reader030/viewer/2022012716/61ae3b5102e9a012074991cd/html5/thumbnails/4.jpg)
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
![Page 5: EE 380 Linear Control Systems Lecture 25](https://reader030.vdocument.in/reader030/viewer/2022012716/61ae3b5102e9a012074991cd/html5/thumbnails/5.jpg)
EE 380 Fall 2014Lecture 25.
PID Disadvantages
• PD Control– Gain increases with frequency– Accentuates noise
• PI Control– Infinite gain at DC
5
![Page 6: EE 380 Linear Control Systems Lecture 25](https://reader030.vdocument.in/reader030/viewer/2022012716/61ae3b5102e9a012074991cd/html5/thumbnails/6.jpg)
EE 380 Fall 2014Lecture 25.
Exercise 1
• Sketch the Bode magnitude and phase plots for– PI Compensator– PD Compensator
6
![Page 7: EE 380 Linear Control Systems Lecture 25](https://reader030.vdocument.in/reader030/viewer/2022012716/61ae3b5102e9a012074991cd/html5/thumbnails/7.jpg)
EE 380 Fall 2014Lecture 25.
Exercise 1 Solution
7
![Page 8: EE 380 Linear Control Systems Lecture 25](https://reader030.vdocument.in/reader030/viewer/2022012716/61ae3b5102e9a012074991cd/html5/thumbnails/8.jpg)
EE 380 Fall 2014Lecture 25.
Exercise 1 Solution
8
![Page 9: EE 380 Linear Control Systems Lecture 25](https://reader030.vdocument.in/reader030/viewer/2022012716/61ae3b5102e9a012074991cd/html5/thumbnails/9.jpg)
EE 380 Fall 2014Lecture 25.
Phase Lag Compensator
• Approximates PI controller– Low-frequency gain rolls-off to a finite value
• Transfer function representation
9
1, 11o
co
s aG s K as
,oc o
o
s a s zKG s K p za s s p
![Page 10: EE 380 Linear Control Systems Lecture 25](https://reader030.vdocument.in/reader030/viewer/2022012716/61ae3b5102e9a012074991cd/html5/thumbnails/10.jpg)
EE 380 Fall 2014Lecture 25.
Exercise 2
• Sketch Bode magnitude and phase plot of the phase-lag compensator
10
![Page 11: EE 380 Linear Control Systems Lecture 25](https://reader030.vdocument.in/reader030/viewer/2022012716/61ae3b5102e9a012074991cd/html5/thumbnails/11.jpg)
EE 380 Fall 2014Lecture 25.
Exercise 2 Solution
11
![Page 12: EE 380 Linear Control Systems Lecture 25](https://reader030.vdocument.in/reader030/viewer/2022012716/61ae3b5102e9a012074991cd/html5/thumbnails/12.jpg)
EE 380 Fall 2014Lecture 25.
Exercise 2 Solution
12
![Page 13: EE 380 Linear Control Systems Lecture 25](https://reader030.vdocument.in/reader030/viewer/2022012716/61ae3b5102e9a012074991cd/html5/thumbnails/13.jpg)
EE 380 Fall 2014Lecture 25.
Exercise 2 Solution
13
![Page 14: EE 380 Linear Control Systems Lecture 25](https://reader030.vdocument.in/reader030/viewer/2022012716/61ae3b5102e9a012074991cd/html5/thumbnails/14.jpg)
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
![Page 15: EE 380 Linear Control Systems Lecture 25](https://reader030.vdocument.in/reader030/viewer/2022012716/61ae3b5102e9a012074991cd/html5/thumbnails/15.jpg)
EE 380 Fall 2014Lecture 25.
Exercise 3
• Sketch Bode magnitude and phase plot of the phase-lead compensator
15
![Page 16: EE 380 Linear Control Systems Lecture 25](https://reader030.vdocument.in/reader030/viewer/2022012716/61ae3b5102e9a012074991cd/html5/thumbnails/16.jpg)
EE 380 Fall 2014Lecture 25.
Exercise 3 Solution
16
![Page 17: EE 380 Linear Control Systems Lecture 25](https://reader030.vdocument.in/reader030/viewer/2022012716/61ae3b5102e9a012074991cd/html5/thumbnails/17.jpg)
EE 380 Fall 2014Lecture 25.
Exercise 3 Solution
17
![Page 18: EE 380 Linear Control Systems Lecture 25](https://reader030.vdocument.in/reader030/viewer/2022012716/61ae3b5102e9a012074991cd/html5/thumbnails/18.jpg)
EE 380 Fall 2014Lecture 25.
Exercise 3 Solution
18
![Page 19: EE 380 Linear Control Systems Lecture 25](https://reader030.vdocument.in/reader030/viewer/2022012716/61ae3b5102e9a012074991cd/html5/thumbnails/19.jpg)
EE 380 Fall 2014Lecture 25.
EE 380
Linear Control Systems
Lecture 25
Professor Jeffrey SchianoDepartment of Electrical Engineering
1
![Page 20: EE 380 Linear Control Systems Lecture 25](https://reader030.vdocument.in/reader030/viewer/2022012716/61ae3b5102e9a012074991cd/html5/thumbnails/20.jpg)
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
![Page 21: EE 380 Linear Control Systems Lecture 25](https://reader030.vdocument.in/reader030/viewer/2022012716/61ae3b5102e9a012074991cd/html5/thumbnails/21.jpg)
EE 380 Fall 2014Lecture 25.
– Three term compensator (Minorsky, 1922)
P, PI, PD, PID Compensators
3
![Page 22: EE 380 Linear Control Systems Lecture 25](https://reader030.vdocument.in/reader030/viewer/2022012716/61ae3b5102e9a012074991cd/html5/thumbnails/22.jpg)
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
![Page 23: EE 380 Linear Control Systems Lecture 25](https://reader030.vdocument.in/reader030/viewer/2022012716/61ae3b5102e9a012074991cd/html5/thumbnails/23.jpg)
EE 380 Fall 2014Lecture 25.
PID Disadvantages
• PD Control– Gain increases with frequency– Accentuates noise
• PI Control– Infinite gain at DC
5
![Page 24: EE 380 Linear Control Systems Lecture 25](https://reader030.vdocument.in/reader030/viewer/2022012716/61ae3b5102e9a012074991cd/html5/thumbnails/24.jpg)
EE 380 Fall 2014Lecture 25.
Exercise 1
• Sketch the Bode magnitude and phase plots for– PI Compensator– PD Compensator
6
![Page 25: EE 380 Linear Control Systems Lecture 25](https://reader030.vdocument.in/reader030/viewer/2022012716/61ae3b5102e9a012074991cd/html5/thumbnails/25.jpg)
EE 380 Fall 2014Lecture 25.
Exercise 1 Solution
7
![Page 26: EE 380 Linear Control Systems Lecture 25](https://reader030.vdocument.in/reader030/viewer/2022012716/61ae3b5102e9a012074991cd/html5/thumbnails/26.jpg)
EE 380 Fall 2014Lecture 25.
Exercise 1 Solution
8
![Page 27: EE 380 Linear Control Systems Lecture 25](https://reader030.vdocument.in/reader030/viewer/2022012716/61ae3b5102e9a012074991cd/html5/thumbnails/27.jpg)
EE 380 Fall 2014Lecture 25.
Phase Lag Compensator
• Approximates PI controller– Low-frequency gain rolls-off to a finite value
• Transfer function representation
9
![Page 28: EE 380 Linear Control Systems Lecture 25](https://reader030.vdocument.in/reader030/viewer/2022012716/61ae3b5102e9a012074991cd/html5/thumbnails/28.jpg)
EE 380 Fall 2014Lecture 25.
Exercise 2
• Sketch Bode magnitude and phase plot of the phase-lag compensator
10
![Page 29: EE 380 Linear Control Systems Lecture 25](https://reader030.vdocument.in/reader030/viewer/2022012716/61ae3b5102e9a012074991cd/html5/thumbnails/29.jpg)
EE 380 Fall 2014Lecture 25.
Exercise 2 Solution
11
![Page 30: EE 380 Linear Control Systems Lecture 25](https://reader030.vdocument.in/reader030/viewer/2022012716/61ae3b5102e9a012074991cd/html5/thumbnails/30.jpg)
EE 380 Fall 2014Lecture 25.
Exercise 2 Solution
12
![Page 31: EE 380 Linear Control Systems Lecture 25](https://reader030.vdocument.in/reader030/viewer/2022012716/61ae3b5102e9a012074991cd/html5/thumbnails/31.jpg)
EE 380 Fall 2014Lecture 25.
Exercise 2 Solution
13
![Page 32: EE 380 Linear Control Systems Lecture 25](https://reader030.vdocument.in/reader030/viewer/2022012716/61ae3b5102e9a012074991cd/html5/thumbnails/32.jpg)
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
![Page 33: EE 380 Linear Control Systems Lecture 25](https://reader030.vdocument.in/reader030/viewer/2022012716/61ae3b5102e9a012074991cd/html5/thumbnails/33.jpg)
EE 380 Fall 2014Lecture 25.
Exercise 3
• Sketch Bode magnitude and phase plot of the phase-lead compensator
15
![Page 34: EE 380 Linear Control Systems Lecture 25](https://reader030.vdocument.in/reader030/viewer/2022012716/61ae3b5102e9a012074991cd/html5/thumbnails/34.jpg)
EE 380 Fall 2014Lecture 25.
Exercise 3 Solution
16
![Page 35: EE 380 Linear Control Systems Lecture 25](https://reader030.vdocument.in/reader030/viewer/2022012716/61ae3b5102e9a012074991cd/html5/thumbnails/35.jpg)
EE 380 Fall 2014Lecture 25.
Exercise 3 Solution
17
![Page 36: EE 380 Linear Control Systems Lecture 25](https://reader030.vdocument.in/reader030/viewer/2022012716/61ae3b5102e9a012074991cd/html5/thumbnails/36.jpg)
EE 380 Fall 2014Lecture 25.
Exercise 3 Solution
18