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LINEAR CONTROL SYSTEMS

LINEAR CONTROL SYSTEMS

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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: Effect of moving poles and zeros. Design of controller in time domain. Various controller configurations. Different kind of controllers. Controller realization. Lecture 18 Time domain design of control systems

  3. Effect of moving poles. اثرات حرکت قطبها Consider following equation: Let b=1 but a=10, 9, 8, 3, 1

  4. -4.5 -1 -10 Effect of moving poles. اثرات حرکت قطبها Let a=10 Let a=10

  5. -4 -1 Effect of moving poles. اثرات حرکت قطبها Let a=9 -9

  6. -3.5 -1 Effect of moving poles. اثرات حرکت قطبها Let a=8 -8

  7. -1 Effect of moving poles. اثرات حرکت قطبها Let a=3 -3

  8. -1 Effect of moving poles. اثرات حرکت قطبها Let a=1

  9. -3 -8 -9 -4.5 -3.5 -4 -1 -1 -1 -1 -1 -10 Effect of moving poles. اثرات حرکت قطبها a= 1 a= 3 a=10 a= 9 a= 8

  10. 1 Series or cascade compensation. 1 ساختار کنترلی سری e(t) r(t) c(t) u(t) + Controller - Controlled process Various controller configurations. ساختارهای کنترلی متفاوت

  11. 2 Feedback compensation. 2 جبران سازی فیدبکی e(t) r(t) c(t) u(t) + + G ( s ) - - p Controlled process Controller Various controller configurations. ساختارهای کنترلی متفاوت

  12. 3 State-feedback control. 3 کنترل فیدبک حالت r(t) c(t) x(t) u(t) + G ( s ) - p Controlled process Controller Various controller configurations. ساختارهای کنترلی متفاوت

  13. Series-feedback compensation.(Two degree of freedom) 4 جبران سازی سری فیدبکی (دو درجه آزادی) G ( s ) p e(t) r(t) c(t) u(t) + + - - Controlled process Compensation Controller Controller Various controller configurations. ساختارهای کنترلی متفاوت

  14. 5 Forward compensation with series compensation. (Two degree of freedom) 5 جبران سازی پیش رو با جبران سازی سری (دو درجه آزادی) G ( s ) p e(t) r(t) c(t) u(t) + - Controlled process Controller Controller Various controller configurations. ساختارهای کنترلی متفاوت

  15. 6 Feed forward compensation.(Two degree of freedom) 6 کنترلر پیش خور (دو درجه آزادی) G ( s ) p + e(t) r(t) c(t) u(t) + + - Controlled process Controller Controller Various controller configurations. ساختارهای کنترلی متفاوت

  16. In this Course consider the simple SISO control loop shown in the figure. Series or cascade compensation. ساختار کنترلی سری Controller Series Compensation Structure جبران سازی سری There is a lot of different controller!

  17. Different kind of controllers In This course انواع کنترلر PID controllers. Lead lag controllers Different kind of controllers In Graduate courses H2 Controllers H∞ Controllers ………….. Adaptive Controllers Intelligent Controllers NN Controllers …………..

  18. PID has become almost universally used in industrial control. These controllers have proven to be robust and extremely beneficial in the control of many important applications. PID stands for: P (Proportional) I (Integral) D (Derivative) PID Controllers کنترلر PID

  19. Early feedback control devices implicitly or explicitly used the ideas of proportional, integral and derivative action in their structures. However, it was probably not until Minorsky’s work on ship steering* published in 1922, that rigorous theoretical consideration was given to PID control. This was the first mathematical treatment of the type of controller that is now used to control almost all industrial processes.(more that 95% of closed-loop industrial processes.) * Minorsky (1922) “Directional stability of automatically steered bodies”, J. Am. Soc. Naval Eng., 34, p.284. Historical Note وضعیت تاریخی

  20. PID Controllers کنترلر PID The standard form PID are: Proportional only: Proportional plus Integral: Proportional plus derivative: Proportional, integral and derivative:

  21. Closely related to PID control is the idea of lead-lag compensation. The transfer function of these compensators is of the form: If a<1 , then this is a lag network. Or (z>p) in other form. If a>1 this is a lead network. Or (z<p) in other form. Lead-lag Compensators کنترلر پیش فاز پس فاز

  22. A phase Lag network R1 + + R2 E1 E2 C - - یک شبکه پس فاز So it is a Lag network

  23. C + + R1 E1 E2 R2 - - A phase Lead network یک شبکه پیش فاز So it is a Lead network