© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-3 Closed-loop design by root locus... © 2015 Quoc Chi Nguyen, Head of Control & Automation Laborator
Trang 1© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-1
Control Designs
Trang 2© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-2
Trang 3© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-3
Closed-loop design by root locus
Trang 4© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-4
Closed-loop design by root locus
Trang 5© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-5
General effect of addition of zeros
Trang 6© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-6
Compensators
Trang 7© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-7
Cascade compensation
Trang 8© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-8
Compensator design
Trang 9© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-9
Lead compensation
Trang 10© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-10
Lead compensation
Trang 11© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-11
Active lead and lag networks
Trang 12© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-12
Principles of Lead design via Root Locus
Trang 13© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-13
Root Locus Principles
Trang 14© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-14
RL design: Basic procedure
Trang 15© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-15
Lead compensator example
Trang 16© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-16
Attempt proportional control
Trang 17© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-17
Attempt proportional control
Trang 18© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-18
Proportional control, step response
Trang 19© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-19
Lead compensated design
Trang 20© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-20
Lead compensated design
Trang 21© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-21
Lead compensator example
Trang 22© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-22
Lead compensator example
Trang 23© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-23
Lead compensator example
Trang 24© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-24
Lead compensator example
Trang 25© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-25
What to do now?
Trang 26© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-26
Root Locus, new lead compensator
Trang 27© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-27
New lead compensator
Trang 28© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-28
New lead compensator, ramp response
Trang 29© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-29
New lead compensator, step response
Note faster settling time than prop
ζ ≈ 0.40
in order to better control the overshoot
Trang 30© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-30
• Root locus approach to phase lead design was reasonably
successful in terms of putting dominant poles in desired
positions; e.g., in terms of ζ and ω n
• We did this by positioning the pole and zero of the lead
compensator so as to change the shape of the root locus
• However, root locus approach does not provide
independent control over steady-state error constants
(details upcoming)
• That said, since lead compensators reduce the DC gain
(they resemble differentiators), they are not normally used to
control steady-state error
• The goal of our lag compensator design will be to increase
the steady-state error constants, without moving the other
poles too far
Remark points of the lead compensator
Trang 31© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-31
Cascade compensation and steady-state errors
Trang 32© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-32
Steady-state errors
Trang 33© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-33
Steady-state errors
Trang 34© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-34
Trang 35© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-35
Trang 36© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-36
Compensator and Bode Diagram
Trang 37© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-37
Trang 38© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-38
Trang 39© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-39
Trang 40© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-40
Trang 41© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-41
Trang 42© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-42
Trang 43© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-43
Trang 44© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-44
Trang 45© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-45
Lag compensation
Trang 46© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-46
Frequency response
Trang 47© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-47
Trang 48© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-48
Trang 49© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-49
Active lead and lag networks
Trang 50© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-50
Lag compensator design
Trang 51© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-51
Lag compensator design
Trang 52© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-52
Lag comp design via Root Locus
Trang 53© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-53
Trang 54© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-54
Trang 55© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-55
Trang 56© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-56
Trang 57© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-57
Trang 58© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-58
Trang 59© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-59
Trang 60© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-60
Trang 61© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-61
Trang 62© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-62
Trang 63© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-63
Trang 64© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-64
Lag compensator design in frequency response
Trang 65© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-65
Trang 66© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-66
Trang 67© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-67
Trang 68© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-68
Trang 69© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-69
Trang 70© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-70
Trang 71© 2015 Quoc Chi Nguyen, Head of Control & Automation Laboratory, nqchi@hcmut.edu.vn 4-71