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LINEAR CONTROL SYSTEMS

This lecture covers frequency domain analysis of control systems, including resolution of sensitivity and complementary sensitivity functions, command tracking, disturbance rejection, noise attenuation, peak of resonance, bandwidth, impact of poles and zeros on transfer functions. The importance of open-loop and closed-loop configurations is discussed to optimize control systems performance. The topics aim to enhance understanding of control system dynamics and design processes for efficient performance.

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LINEAR CONTROL SYSTEMS

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  1. LINEAR CONTROL SYSTEMS Ali Karimpour Assistant Professor Ferdowsi University of Mashhad

  2. Topics to be covered include: Frequency domain analysis of control systems. Frequency domain specification. Peak of resonance and resonance frequency. Bandwidth. Effect of adding poles and zeros to open loop transfer function. Effect of adding poles and zeros to closed loop transfer function. Lecture 21 Frequency Domain Analysis

  3. One degree-of-freedom configuration T(s) S(s) T(s) S(s) is : Sensitivity Function Why? T(s) is : Complementary Sensitivity Function Since S+T=1

  4. One degree-of-freedom configuration Where T(s) and S(s) are How to derive command tracking How to derive disturbance rejection How to derive noise attenuation

  5. One degree-of-freedom configuration Derive command tracking and disturbance rejection

  6. Derive command tracking and disturbance rejection One degree-of-freedom configuration How to derive noise attenuation

  7. Ideal |T| for command tracking, disturbance rejection and noise attenuation Ideal |L| for command tracking, disturbance rejection and noise attenuation Actual |T| for command tracking, disturbance rejection and noise attenuation Actual |L| for command tracking, disturbance rejection and noise attenuation One degree-of-freedom configuration

  8. + e c r - c r Frequency (rad/s) A prototype second order system. یک سیستم نمونه درجه 2

  9. Drawing procedure

  10. + e c r - 10 1 0.1 0.01 Drawing procedure

  11. Peak of resonance ( ) Resonance frequency ( ) Frequency domain specification

  12. Closed-loop bandwidth ( ) Open - loop bandwidth ( ) Gain crossover frequency ( ) Frequency domain specification -3

  13. Peak of resonance ( ) + Resonance frequency ( ) e c r c r - Introducing a prototype second order system.

  14. + Closed-loop bandwidth ( ) e c r c r - -3 Introducing a prototype second order system.

  15. + e c r c r - Introducing a prototype second order system.

  16. r c2 P.O. tr System speed BW Adding poles to closed loop transfer functions اضافه کردن قطب به تابع انتقال حلقه بسته τ=0.5 τ=1.0 τ=0 τ=2.0 τ=5.0

  17. c2 c1 r r P.O. tr System speed BW Adding zeros to closed loop transfer functions اضافه کردن صفر به تابع انتقال حلقه بسته

  18. c2 e r - P.O. tr System speed BW Adding poles to open loop transfer functions اضافه کردن قطب به تابع انتقال حلقه باز τ=5.0 τ=2.0 τ=1.0 τ=0 More problem as poles go to ??

  19. c2 e r - P.O. tr System speed BW Adding zeros to open loop transfer functions اضافه کردن صفر به تابع انتقال حلقه باز τ=0 τ=0.2 τ=10 τ=0.5 τ=5.0 τ=2.0

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