2022年完整word版,《自动控制原理》试卷及答案.docx
精选学习资料 - - - - - - - - - AUTOMATIC CONTROL THEOREM 1 Derive the transfer function and the differential equation of the electric network shown in Fig.1. 12% R1 C1 V1S C2 R2 V2S Fig.1 Consider the system shown in Fig.2. Obtain the closed-loop transfer function C S , E S . （12%）R S R S G4 R E G1 G2 G3 C H2 H1 Fig.2 The characteristic equation is given 1GHSS35S26KS10K0. Discuss the distribution of the closed-loop poles. 16% There are 3 roots on the LHP There are 2 roots on the LHP There are 1 roots on the LHP There are no roots on the LHP . K=. Consider a unity-feedback control system whose open-loop transfer function is GS04.S01. Obtain the response to a unit-step input. What is the rise time for S S.6this system. What is the maximum overshoot. （10%）名师归纳总结 - - - - - - -第 1 页,共 29 页精选学习资料 - - - - - - - - - 5. Sketch the root-locus plot for the system GHSSK1 . The gain K is Sassumed to be positive. Determine the breakaway point and K value. Determine the value of K at which root loci cross the imaginary axis. Discuss the stability. 12% r2t, n1 . Determine 6. The system block diagram is shown Fig.3. Suppose the value of K to ensure e SS1. 12% N R E SK2S43C SFig.3 7. Consider the system with the following open-loop transfer function: GHSS T 1SKT2S1 . Draw Nyquist diagrams. Determine the 1 stability of the system for two cases, the gain K is small, K is large. 12% 8. Sketch the Bode diagram of the system shown in Fig.4. 14% RS S32SS2 10 CS S5 SFig.4 名师归纳总结 - - - - - - -第 2 页,共 29 页精选学习资料 - - - - - - - - - V2S R 1R 2C 1C2SC 1C2V 1S R2C1C2SC 1CS 1G1 G2H1G 1G2G3G 1G42G3H2G4H2R S G 1 G2G3G 1G4G 0<K<6 K0 K6 no answer the breakaway point is 1 and 1/3; k=4/27 The imaginary axis S=± j; K=2 名师归纳总结 .3 5KS 7 . 5S1 31 . 62 S 10 1.S S1 .3 481 34 . 811 S1第 3 页,共 29 页GH0 . 31682 . 54- - - - - - -精选学习资料 - - - - - - - - - AUTOMATIC CONTROL THEOREM 2 Derive the transfer function and the differential equation of the electric network shown in Fig.1. 12% V1S R1 R1 C2 V2S Fig.1 C1 Consider the equation group shown in Equation.1. Draw block diagram and obtain the closed-loop transfer function CRS . （16% ）S SX1S G 1S R S G 1S G 7 S G 8S CEquation.1 X2S G 2S X1S G 6S X3S X3S X2S CS G 5S G 3S C S G 4S X3 S Use Rouths criterion to determine the number of roots in the right-half S plane for the equation 1GHS S53S428S3226S2600S4000. Analyze stability.（12% ） Determine the range of K value ,when r1t2t, e SS0 .5. （12% ）R E 3 S 24 SKC S 2 S2Fig.2 名师归纳总结 - - - - - - -第 4 页,共 29 页精选学习资料 - - - - - - - - - Fig.3 shows a unity-feedback control system. By sketching the Nyquist diagram of the system, determine the maximum value of K consistent with stability, and check the result using Rouths criterion. Sketch the root-locus for the system（20%）R S S2K5 R C Fig.3 E 4 SSketch root-locus diagram.（18% ）Im Re Im Re Im Re Im Im Im Re Re Re Determine the transfer function. Assume a minimum-phase transfer function.（10% ）LdB 0 20 0 20 40 -60 40 30 20 名师归纳总结 5 0.1 1 2 3 4 第 5 页,共 29 页- - - - - - -精选学习资料 - - - - - - - - - V2S R 1C1R 2C2S2R 11R 2C2R 1C2S1V 1S C 1CS 1G2G 3G6G3G 1G2G3G42G3G4G7G8R S G4G 5G1G There are 4 roots in the left-half S plane, 2 roots on the imaginary axes, 0 root in the RSP. The system is unstable. 8K20K=20 名师归纳总结 GHS S1 31 . 62 S 10 1.S S1 .3 481 34 . 811 S1第 6 页,共 29 页0 . 31682 . 54- - - - - - -精选学习资料 - - - - - - - - - AUTOMATIC CONTROL THEOREM 3 List the major advantages and disadvantages of open-loop control systems. 12% Derive the transfer function and the differential equation of the electric network shown in Fig.1.（16% ）C1 U1 R1 R2 U2 Fig.1 C2 Consider the system shown in Fig.2. Obtain the closed-loop transfer functionCS, ES , CS . （12%）G5 C R SRS P SR E G1 P G4 G2 G3 H2 H1 Fig.2 H3 The characteristic equation is given 1GHS S33S22 S200. Discuss the distribution of the closed-loop poles. 16% 5. Sketch the root-locus plot for the system GHSS K1 . The gain K is Sassumed to be positive. Determine the breakaway point and K value. Determine the value of K at which root loci cross the imaginary axis. 名师归纳总结 Discuss the stability. 14% 第 7 页,共 29 页- - - - - - -精选学习资料 - - - - - - - - - 6. The system block diagram is shown Fig.3. G1SK2, G2S43 . Suppose Sr2t, n1. Determine the value of K to ensure e SS1. 15% R E N C G1 G2 Fig.3 7. Consider the system with the following open-loop transfer function: GHSS T 1SKT2S1 . Draw Nyquist diagrams. Determine the 1 stability of the system for two cases, the gain K is small, K is large. 15% 名师归纳总结 - - - - - - -第 8 页,共 29 页精选学习资料 - - - - - - - - - Solution: The advantages of open-loop control systems are as follows: Simple construction and ease of maintenance Less expensive than a corresponding closed-loop system There is no stability problem Convenient when output is hard to measure or economically not feasible. For example, it would be quite expensive to provide a device to measure the quality of the output of a toaster. The disadvantages of open-loop control systems are as follows: Disturbances and changes in calibration cause errors, and the output may be different from what is desired. To maintain the required quality in the output, recalibration is necessary from time to time. U2S R 1C 1R 2C2S2R 1C 1R 2C2S13U1S R 1C 1R 2C2S2R 1C 1R 2C 2R 1 C2S1CSG1 G2G3G4G 1 G5R S1G1 G2H1G2G3H2G 1 G2G3G4H3G 1G5HCSG3G41G1 G2H1G3G5H2P S1G1G2H1G2G3H2G 1 G2G3G4H3G 1 G5H3R=2, L=1 S:the breakaway point is 1 and 1/3; k=4/27 The imaginary axis S=± j; K=2 名师归纳总结 .3 5K7 . 5第 9 页,共 29 页- - - - - - -精选学习资料 - - - - - - - - - AUTOMATIC CONTROL THEOREM 4 Find the poles of the following Fs : Fs 11s12% 0 .6and n5rad/sec. Obtain the eConsider the system shown in Fig.1,whererise timert , peak timet , maximum overshoot MP, and settling timestwhen the system is subjected to a unit-step input. （10%）2 nRs s s2nCs Fig.1 Consider the system shown in Fig.2. Obtain the closed-loop transfer functionCS, ES , CS . （12%）G5 C R SRS P SR E G1 P G4 G2 G3 H2 H1 Fig.2 H3 The characteristic equation is given 1GHS S33S22 S200. Discuss the distribution of the closed-loop poles. 16% 名师归纳总结 - - - - - - -第 10 页,共 29 页精选学习资料 - - - - - - - - - 5. Sketch the root-locus plot for the system GHSS K1 . The gain K is Sassumed to be positive. Determine the breakaway point and K value. Determine the value of K at which root loci cross the imaginary axis. Discuss the stability. 12% G2. S43 . Suppose 6. The system block diagram is shown Fig.3. G1SK2, Sr2t, n1. Determine the value of K to ensure e SS112% C N R E G1 G2 Fig.3 7. Consider the system with the following open-loop transfer function: GHSS T 1SKT2S1 . Draw Nyquist diagrams. Determine the 1 stability of the system for two cases, the gain K is small, K is large. 12% 8. Sketch the Bode diagram of the system shown in Fig.4. 14% RS S32SS2 10 CS S5 SFig.4 名师归纳总结 - - - - - - -第 11 页,共 29 页精选学习资料 - - - - - - - - - Solution: The poles are found from es1or ejecosjsin1From this it follows that 0 , 2 n n 0 ,1, 2 , . Thus, the poles are located at s j 2 nSolution: rise time rt 0 . 55 sec , peak time t p 0 . 785 sec , maximum overshoot M P 0 . 095 , and settling time st 1 . 33 sec for the 2 % criterion, settling time st 1 sec for the %criterion. SCS112G1 G2H13G1 G2G3G4G 1 G54H35G 1G5H3R SG2G3H2G 1 G2G3GCG3G41G1 G2H1G3G5H2P S1GGH1G2GH2G 1 G2G3G4H3G 1 GH3R=2, L=1 5. S:the breakaway point is 1 and 1/3; k=4/27 The imaginary axis S=± j; K=2 名师归纳总结 .3 5K7 . 5第 12 页,共 29 页- - - - - - -精选学习资料 - - - - - - - - - AUTOMATIC CONTROL THEOREM 5 Consider the system shown in Fig.1. Obtain the closed-loop transfer functionCS, ES . （18%）R SRS H2 R E G1 G2 G3 C H1 H4 H3 Fig.1 The characteristic equation is given 1GHS S53 S412S324S232S480. Discuss the distribution of the closed-loop poles. 16% Sketch the root-locus plot for the system GHSSSK5S1 . The gain 1 0 .K is assumed to be positive. Determine the breakaway point and K value. Determine the value of K at which root loci cross the imaginary axis. Discuss the stability. 18% 1T 1K11, G2T 2K21. The system block diagram is shown Fig.2. GSSSuppose r0, n1. Determine the value of e SS. Suppose r1, n1. C Determine the value of eSS. 14% N R E G1 G2 Fig.2 名师归纳总结 - - - - - - -第 13 页,共 29 页精选学习资料 - - - - - - - - - Sketch the Bode diagram for the following transfer function. GHss 1KTs, K7, T0 . 087. 10% GHSsK 2 TS1 is inherently A system with the open-loop transfer function unstable. This system can be stabilized by adding derivative control. Sketch the polar plots for the open-loop transfer function with and without derivative control. 14% Draw the block diagram and determine the transfer function. 10% U1s R C U2s 名师归纳总结 - - - - - - -第 14 页,共 29 页精选学习资料 - - - - - - - - - CSG 1G2G3R SR=0, L=3,I=2 名师归纳总结 ess1K22ess11K22第 15 页,共 29 页K1KK1KU U2s111s RCs- - - - - - -精选学习资料 - - - - - - - - - AUTOMATIC CONTROL THEOREM 6 Consider the system shown in Fig.1. Obtain the closed-loop transfer functionCS, ES . （18%）G2 C R SRS R E G1 H1 H2 Fig.1 H3 The characteristic equation is given 1GHS 25S5105S4120S3122S220S10. Discuss the distribution of the closed-loop poles. 12% Sketch the root-locus plot for the system GHS KS1. The gain K is S S3 assumed to be positive. Determine the breakaway point and K value. Determine the value of K at which root loci cross the imaginary axis. Discuss the stability. 15% 1, G2S0101 . Suppose The system block diagram is shown Fig.2. G1S. 25S名师归纳总结 rR 1t, n0 1. Determine the value of e SS. 12% 第 16 页,共 29 页E G1 N C G2 0.5 Fig.2 - - - - - - -精选学习资料 - - - - - - - - - Calculate the transfer function for the following Bode diagram of the minimum phase. 15% dB 0.1 1 4 8 16 w . -40 -20 0dB/dec 20 0 ss s45 ,Hs1, 16% For the system show as follows, G Determine the system output ctto a unit step, ramp input. Determine the coefficient KP, KVand the steady state error to rt2 t Plot the Bode diagram of the system described by the open-loop transfer function 名师归纳总结 elements Gs10 10s , Hs 1. 12% 第 17 页,共 29 页s 15.s - - - - - - -精选学习资料 - - - - - - - - - CS1G1H1G2H2G1 G23 1G2H22H1H2G2H2H3G 1G2HH2G 1GR SR=0, L=5 名师归纳总结 G s 50 . 05 10s1 s1 sc 1 t54et1e4tKP, KV08., 第 18 页,共 29 页4s2 11 16s tc t14et1e4t334312ess2.- - - - - - -精选学习资料 - - - - - - - - - AUTOMATIC CONTROL THEOREM 7 Consider the system shown in Fig.1. Obtain the closed-loop transfer functionCS, ES . （16%）G3 C R SRS R E G1 G2 Fig.1 The characteristic equation is given 1GHS S64 S54S44S37S28S100. Discuss the distribution of the closed-loop poles. 10% Sketch the root-locus plot for the system GHS KS1. The gain K is S3assumed to be positive. Determine the breakaway
