Control systems important questions in frequency response analysis?

1. What are the necessary conditions to have all the roots of the characteristic equation in the left half of s plane?

2. What are the limitations and advantages of R-H criteria?

3. The open loop transfer function of a unity feedback system is given by G(S) =K/S (1+0.25S) (1+0.4S) find the restriction on K so that the closed loop system is absolutely stable?

4.Using R-H Stability Criterion Determine The Stability Of The Following Systems A) It’s loop transfer function has poles at s=-3 and zero at s=-5,gain K of forward path is 10 B) It is a type 1 system with an error constant of 10 sec-1 and poles at s=-3 and s=-6

5. A unity feedback control system with G(S)=K/S(1+0.1S)(1+0.2S) 1) sketch the root locus diagram of the system 2)determine the limiting value of gain K for stability 3)determine the value of gain at which the system is critically damped?

6. The open loop transfer function of a control system is given by G(S) H(S) =K/S(S+6) (S2+4S+13). Sketch the root locus plot and determine 1)the breakaway points 2)the angle of departure from complex poles 3)the stability condition

7. Write short notes (with formulas) on how to find frequency domain specifications of resonant peak, resonant frequency, bandwidth, cut-off rate, gain cross over frequency, phase cross over frequency, gain margin, phase margin? Explain why it is important to conduct frequency domain analysis of linear control systems and explain correlation between time and frequency response analysis?

8. From the bode plots of a unity feedback system, angle of G(JW) at gain cross over frequency is found to be -1500 and magnitude of G(JW) at phase cross over frequency is found to be -12 db. Find the stability of the system.

9. Sketch the bode plot for a unity feedback system characterized by the open loop transfer function G(S) =K (1+0.2S) (1+0.025S)/S2 (1+0.01S) (1+0.005S), show that the system is conditionally stable. Find the range of K for which the system is stable?

10. Sketch the bode plots for a system of G(S) =15(S+5)/S (S2+16S+100).Hence determine the stability of the system?

11. A unity feedback control system has G(S)=K/S(S+1)(1+S/10).Find the value of K so that GM=12db and PM=300

12. Explain the procedure for determination of transfer function from Bode plots?

13. With the help of nyquist plot assess the stability of a system G(S) =3/S(S+1) S+2). What happens to stability if the numerator of the function is changed from 3 to 30?

14. Write short notes on comparison of polar and nyquist plots?

15. Sketch The Root Locus Of The Transfer Function G(S)=(S+40)/S(S+20)(S2+60S+1002)

16. The Open Loop Transfer Function Of A Unity Feed Back Control System Is Given By G(S)H(S)=K(S+5)(S+40)/S3(S+200)(S+1000).discuss the stability of closed loop system as a function of K. determine values of K which will cause sustained oscillations in the closed loop system. What are the frequencies of oscillations? Use nyquist approach.

17. Consider a feedback system having the characteristic equation 1+ (K/ (1+S) (1.5+S) (2+S)) =0 it is desired that all roots of the characteristic equation have real parts less than -1. Extend the nyquist stability criterion to find the largest value of k satisfying this condition?

18. Consider a unity fed back system having an open loop transfer function G(S) =K/S (1+0.5S) (1+4S). Sketch The Polar Plot And Determine The Value of K so that 1)gain margin is 20 db and 2) phase margin is 300

19. Explain minimum phase and all pass systems and explain constant M and N circles?

20. Explain the principle of argument and mapping theorem?