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Frequency Response Analysis - Process Control - Lecture Slides, Slides of Process Control

This lecture is from Process Control course. Some key points for this lecture are: Frequency Response Analysis, Closed Loop Behavior, Closed Loop Stability, Good Disturbance, Set Point Tracking, Satisfactory, Degree of Robustness, Process Variations, Model Uncertainty, Low Sensitivity

Typology: Slides

2012/2013

Uploaded on 03/18/2013

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Control System Design Based on
Frequency Response Analysis
Frequency response concepts and techniques play an important
role in control system design and analysis.
Closed-Loop Behavior
In general, a feedback control system should satisfy the following
design objectives:
1. Closed-loop stability
2. Good disturbance rejection (without excessive control action)
3. Fast set-point tracking (without excessive control action)
4. A satisfactory degree of robustness to process variations and
model uncertainty
5. Low sensitivity to measurement noise
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Download Frequency Response Analysis - Process Control - Lecture Slides and more Slides Process Control in PDF only on Docsity!

Control System Design Based on

Frequency Response Analysis

Frequency response concepts and techniques play an important role in control system design and analysis.

Closed-Loop Behavior

In general, a feedback control system should satisfy the following design objectives:

  1. Closed-loop stability
  2. Good disturbance rejection (without excessive control action)
  3. Fast set-point tracking (without excessive control action)
  4. A satisfactory degree of robustness to process variations and model uncertainty
  5. Low sensitivity to measurement noise Docsity.com

Chapter 14

Controller Design Using Frequency Response Criteria Advantages of FR Analysis:

  1. Applicable to dynamic model of any order (including non-polynomials).
  2. Designer can specify desired closed-loop response characteristics.
  3. Information on stability and sensitivity/robustness is provided. Disadvantage: The approach tends to be iterative and hence time- consuming -- interactive computer graphics desirable (MATLAB)

Chapter 14

( )

( ) ( )( ) ( )

( ) ( ) ( ) ( )

( )

1 2 1 1 2 1 1 2 1

will increase by 2 clockwise from each zero

inside the contour, but decrease by 2 for eac

Comformal Mapping

h pole

inside the c

s z s z

F s

s p

F s z s z s p

F s

s F

s z s z s

F s

s

p

π π

ontour,

⇒ (2 -1) encirclements

Dynamic Behavior of Closed- Loop Control Systems

Chapter 11

(^) 4-20 mA

Application of Z-P=N Theorem to

Stability

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

(1) Consider the characteristic equation of the closed-loop

control system:

(2) Let 1 1 , where

and.

(3) Select a contou

OL c v p m OL M c M v p m

G s G s G s G s G s

F s G s B s G s

B s G s G s G s G s G s

( )

r that goes completely around the entire

right-half of -plane.

(4) Plot and determine -.

s

F s N = Z P

Nyquist Stability Criterion

( )

If is the number of times the Nyquist plot encircles the point ( 1, 0) in the complex plane in the clockwise direction, and is the number of open-loop poles of that lie

in the RHP, then

OL

N

P G s Z N P

= + ( )

is the number of unstable roots of 1 + GOL s = 0.

Example

3

3

/ 8 1 0

  1. contour: and 0 / 8 1 0 / 8 0 0 270

OL^ c

OL c

OL c OL OL OL

G s K s P

C s j G j K j G K G j G G j

=

∴ =

= < < ∞

= = ∠ = → ∞ → ∠ → −

 

Important Conclusion

The C+ contour, i.e., Nyquist plot,

is the only one we need to

determine the system stability!

Ultimate Gain and Ultimate

Frequency

( )

( ) (^) ( ) ( ) ( )

( ) (^) ( ) ( ) ( ) ( ) (^) ( ) ( ) ( ) ( ) (^) ( ) ( ) ( )

3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

OL^ c s j c c

c cu c u

G j j K
s s s
K K
j
K
K
K

ω

ω

ω ω ω ω ω ω ω ω ω ω ω ω ω ω ω ω ω ω ω

=

= − + = ^ 

Example 2

( ) (^) ( )( )

( ) ( )

( ) ( ) ( )

( ) (^) ( )( )

2 (^2 2 2 2 2 )

2 2

1 5 1 0

(a) contour: (^1 5 ) (^1 5 6 1 5 36 1 5 )

(b) contour:

lim lim 1 5 1 lim 5 0

(c) contour: cojugate of.

OL^ c

OL c^ c c

R OL j^ j c^ j c j R R R

G s K P s s

C

G j K^ K j K j C G R e K^ K e R e R e R C C

φ φ φ φ

− →∞ →∞ →∞ − +

= (^) + + ⇒ =

= = − − − + (^) − + − +

⋅ = (^) ⋅ + ⋅ + ≈ →