机械工程测试与控制技术课后习题答案

机械工程测试与控制技术课后习题答案内容摘要：

y to control accurately the velocity of the tape. The speed control of the tape drive is represented by the system shown in Fig . a) Determine the limiting gain for a stable system. b) Determine a suitable gain so that the overshoot to a step mand is approximately 5%. a) the Routh array: 1 4400 140 40000+10K 40000+10K the system is stable if b) so the desired characteristic polynomial is the actual characteristic polynomial is dominate poles. so the suitable gain is A control system as shown in has a plant (a) When show that the system is always unstable by sketching the root locus. (b) When , sketch the root locus and determine the range of K for which the system is stable. Determine the value of K and the plex roots when two roots lie on the . Answer: (a) When show that the system is always unstable by sketching the root locus. Unstable. (b) When , sketch the root locus and determine the range of K for which the system is stable. Determine the value of K and the plex roots when two roots lie on the . Poles: 0， 1， –20。 zeros: 2。 n=3， m=1。 Centroid of asymptotes: Angle of asymptotes: Rewriting the characteristic equation as following: Routh array is s3 1 K 20 s2 19 2K s1 (17K380)/19 s0 2K The critical gain for stability can be found from equation (17K380)/19=0 . K=380/17 and the auxiliary equation is 19s2+760/17=0 Determine the breakaway point the breakaway point is K= the range of K for which the system is stable: K A Unity feedback system has Find (a) the breakaway point on the real axis and the gain K for this point. (b) The gain and the roots when two roots lie on the imaginary axis. (a) the breakaway point on the real axis and the gain K for this point. Characteristic equation: (b) The gain and the roots when two roots lie on the imaginary axis. Routh array is s3 1 10 s2 7 K s1 (70K)/7 s0 K K=70, the frequency response for a process of the form is shown in Fig. . Determine K and a by examining the frequency response curves. The transfer function: When , when openloop gain: from the magnitude relationship: the frequency response for a process of the form is shown in Fig. . Determine K and a by examining the frequency response curves. The transfer function: When , when openloop gain: from the magnitude relationship: Several studies have proposed an extravehicular robot that could move about a NASA space station and perform physical tasks at various worksites. The arm is controlled by a unity feedback control with Draw the Bode diagram for K=100, and determine the frequency when 20log|G| is 0dB. Low frequency: 90176。 High frequency: 270176。 Determine the frequency when20log|G| is 0dB: feedback system has a loop transfer function (a) Determine the corner frequencies (break frequencies) for the Bode plot. (b) Determine the slope of the asymptotic plot at very low frequencies and at high frequencies. (c) Sketch the Bode magnitude plot. (a) the corner frequencies: (b) the slope of the asymptotic plot at very low frequencies is 0dB/dec the slope of the asymptotic plot at high frequencies is 20dB/de (c) the Bode magnitude plot the phase: 180176。 ~ 90176。 control system for controlling the pressure in a closed chamber is shown in . The transfer function for the measuring element is and the transfer function for the valve is The controller transfer function is Obtain the frequency response characteristics for the loop transfer function the transfer function: the corner frequencies: K=1 the phase: 90176。 ~360176。 The robot industry in the United States is growing at a rate of 30% a year. A typical industrial robot has six axes or degrees of freedom. A position control system for a forcesensing joint has a transfer function where H(s)=1 and K=10. Sketch the Bode diagram of this system. the phase: 0176。 ~360176。 The asymptotic logmagnitude curves for two transfer function are given in . Sketch the corresponding asymptotic phase shift curves for each system. Determine the transfer function for each s。