09_2_Frequency_response_analysis_E2009

09_2_Frequency_response_analysis_E2009 - 1 28150....

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Unformatted text preview: 1 28150. Introduction to process control 9. Control system design based on frequency response analysis (2) Krist V. Gernaey 2 November 2009 28150 Learning objectives At the end of this lesson you should be able to: Investigate the stability of a closed-loop system using the Bode stability criterion Investigate the stability of a closed-loop system using the Nyquist stability criterion 2 November 2009 28150 Outline Introduction Closed-loop behavior and the effect of measurement noise Bode stability criterion Nyquist stability criterion Gain and phase margins 2 November 2009 28150 Outline Introduction Closed-loop behavior and the effect of measurement noise Bode stability criterion Nyquist stability criterion Gain and phase margins 2 November 2009 28150 Desirable controller features The closed-loop system is stable Quick response to set point changes (good set point tracking ) Effects of disturbances are minimal (adequate disturbance rejection ) No steady-state error (no offset) Avoids excessive controller action Insensitive to model and measurement errors (robustness) Suitable over a wide range of operating conditions (robustness) 2 November 2009 28150 Practical control = trade-off Performance versus robustness Disturbance rejection capability versus set point tracking capability Until now: Model-based design (Ch. 12) Direct synthesis method IMC tuning rules In this lecture: control system design based on frequency response analysis! 2 2 November 2009 28150 Outline Introduction Closed-loop behavior and the effect of measurement noise Bode stability criterion Nyquist stability criterion Gain and phase margins 2 November 2009 28150 Feedback loop. Block diagram representation G c G p G d G m Y sp D U E Y m Y u Y d Y + + +- 2 November 2009 28150 Feedback loop with measurement noise: block diagram representation G c G p G d G m Y sp D U E Y m Y u Y d Y + + +- N + + Y n 2 November 2009 28150 Feedback loop with measurement noise: group work! Derive the transfer functions relating the inputs (Y SP , D, N) to the output Y, for the system shown on the previous slide! 2 November 2009 28150 Feedback loop with measurement noise: transfer functions sp m p c m p c m m p c m d Y G G G N G G G G D G G G G G E + + +- +- = 1 1 1 1 sp m p c p c m p c m p c m p c d Y G G G G G N G G G G G G D G G G G Y + + +- + = 1 1 1 One characteristic equation: 1 + G c G p G m = 0 sp m p c c m p c m c m p c m d c Y G G G G N G G G G G D G G G G G G U + + +- +- = 1 1 1 As a consequence: all closed-loop TFs have identical stability characteristics!!...
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This note was uploaded on 11/20/2009 for the course CHME DTU-abroad taught by Professor Rafiqulgani during the Fall '09 term at Rensselaer Polytechnic Institute.

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09_2_Frequency_response_analysis_E2009 - 1 28150....

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