自动控制理论第九章新.docVIP

E9.1 A system has a transfer function . Plot the Bode diagram for the frequency range of 0.1 to 10. Show that the phase margin is approximately and that the gain margin is approximately 16 dB. E9.2 A system has a transfer function , where K=6.14. Show that the system crossover (0 dB) frequency is 3.5 rad/s and that the phase margin is . E9.4 Consider a system with a loop transfer function , where H(s)=1. We wish to obtain a resonant peak =3.0 dB for the closed-loop system. The peak occurs between 6 and 9 rad/s and is only 1.25 dB. Plot the Nichols chart for the range of frequency from 6 to 15 rad/s. Show that the system gain needs to be raised by 4.6 dB to 171. Determine the resonant frequency for the adjusted system. Answer: rad/sec E9.5 An integrated CMOS digital circuit can be represented by the Bode diagram shown in Figure E9.5. (a) Find the gain and phase margins of the circuit. (b) Estimate how much we would need to reduce the system gain (dB) to obtain a phase margin of . E9.6 A system has an open-loop transfer function . When K=500, the system is unstable. Show that if we reduce the gain to 50, the resonant peak is 3.5dB. Find the phase margin of the system with K=50. E9.7 A unity feedback system has a process . Determine the range of K for which the system is stable by drawing the plot. E9.16 The pure time delay may be approximated by a transfer function as for 0θ2/T. Obtain the Bode diagram for the actual transfer function and the approximation for T=2 for 0ω1. E9.28 A unity feedback system has . (a) Determine the phase margin of the system when K=0.16. (b) Use the phase margin to estimate ζ and predict the overshoot. (c) Calculate the actual response for this second-order system, and compare the result with the part (b) estimate. E9.30 Consider the system represented in state variable from where C=[1000 0], and D=[0]. Sketch the Bode plot. E9.31 A closed-loop feedback system is shown in Figure E9.31. Sketch the Bode plot and determine the phase margin