《自动控制原理》试卷及答案(英文10套)

AUTOMATIC CONTROL THEOREM (1) Derive the transfer function and the differential equation of the electric network shown in Fig.1. (12% )C2R2V2(S)R1C1V1(S) Fig.1CG1G2G3G4H2H1R E Consider the system shown in Fig.2. Obtain the closed-loop transfer function, . （12%） Fig.2 The characteristic equation is given . 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 . Obtain the response to a unit-step input. What is the rise time for this system? What is the maximum overshoot? （10%）5. Sketch the root-locus plot for the system . ( The gain 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. (12%)RENC6. The system block diagram is shown Fig.3. Suppose , . Determine the value of K to ensure . (12%) Fig.37. Consider the system with the following open-loop transfer function:. Draw Nyquist diagrams. Determine the 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%)R(S)C(S)Fig.4 0K6 K0 K6 no answer the breakaway point is 1 and 1/3; k=4/27 The imaginary axis S=j; K=2 AUTOMATIC CONTROL THEOREM (2)Derive the transfer function and the differential equation of the electric network shown in Fig.1. (12% )C1C2V2(S)R1R1V1(S) Fig.1 Consider the equation group shown in Equation.1. Draw block diagram and obtain the closed-loop transfer function. （16% ）Equation.1 Use Rouths criterion to determine the number of roots in the right-half S plane for the equation . Analyze stability.（12% ） Determine the range of K value ,when , . （12% ）REC Fig.2CRREFig.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 system0.1 1 2 3 4L(dB)40302050 20 0 20 40 -60（20%） Fig.3Sketch root-locus diagram.（18% ）ImReImReImReImReImReImRe Determine the transfer function. Assume a minimum-phase transfer function.（10% ） 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. K=20 AUTOMATIC CONTROL THEOREM (3)List the major advantages and disadvantages of open-loop control systems. (12% )Fig.1R2C2R1C1U1U2Derive the transfer function and the differential equation of the electric network shown in Fig.1.（16% ） Consider the system shown in Fig.2. Obtain the closed-loop transfer function, , . （12%）PCG1G2G3G5H1R EG4H2H3Fig.2E The characteristic equation is given . Discuss the distribution of the closed-loop poles. (16%)5. Sketch the root-locus plot for the system . (The gain 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. (14%)6. The system block diagram is shown Fig.3. , . Suppose , . Determine the value of K to ensure . (15%)NRECG1G2Fig.3 7. Consider the system with the following open-loop transfer function:. Draw Nyquist diagrams. Determine the stability of the system for two cases, the gain K is small, K is large. (15%) 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. R=2, L=1 S:the breakaway point is 1 and 1/3; k=4/27 The imaginary axis S=j; K=2AUTOMATIC CONTROL THEOREM (4) Find the poles of the following : (12%)Consider the system shown in Fig.1,where and rad/sec. Obtain the rise time, peak time, maximum overshoot, and settling time when the system is subjected to a unit-step input. （10%）C(s)Fig.1R(s) Consider the system shown in Fig.2. Obtain the closed-loop transfer function, , . （12%）PCG1G2G3G5H1R EG4H2H3Fig.2E The characteristic equation is given . Discuss the distribution of the closed-loop poles. (16%)5. Sketch the root-locus plot for the system . (The gain 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. (12%)6. The system block diagram is shown Fig.3. , . Suppose , . Determine the value of K to ensure . (12%)NRECG1G2Fig.3 7. Consider the system with the following open-loop transfer function:. Draw Nyquist diagrams. Determine the 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%)R(S)C(S)Fig.4 Solution: The poles are found from or From this it follows that . Thus, the poles are located at Solution: rise time, peak time,maximum overshoot, and settling time for the criterion, settling time for the criterion. R=2, L=15. S:the breakaway point is 1 and 1/3; k=4/27 The imaginary axis S=j; K=2AUTOMATIC CONTROL THEOREM (5)CERG1G2G3H2H1H4H3Fig.1 Consider the system shown in Fig.1. Obtain the closed-loop transfer function, . （18%） The characteristic equation is given . Discuss the distribution of the closed-loop poles. (16%) Sketch the root-locus plot for the system . (The gain 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%) The system block diagram is shown Fig.2. , . Suppose , . Determine the value of . Suppose , . Determine the value of . (14%)NRECG1G2Fig.2 Sketch the Bode diagram for the following transfer function. , , . (10%) A system with the open-loop transfer function is inherently 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%)R CU1(s)U2(s)R=0, L=3,I=2AUTOMATIC CONTROL THEOREM (6) Consider the system shown in Fig.1. Obtain the closed-loop transfer function, . （18%）Fig.1CERG1G2H2H1H3The characteristic equation is given . Discuss the distribution of the closed-loop poles. (12%) Sketch the root-locus plot for the system . (The gain 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. (15%) The system block diagram is shown Fig.2. , . Suppose , . Determine the value of . (12%)NCR EG1G20.5Fig.2 Calculate the transfer function for the following Bode diagram of the minimum phase. (15%)dB0.1 1 4 8 16-40 -20 0dB/dec 20 0w For the system show as follows, , (16%) Determine the system output to a unit step, ramp input. Determine the coefficient , and the steady state error to . Plot the Bode diagram of the system described by the open-loop transfer function elements , . (12%)R=0, L=5 , , AUTOMATIC CONTROL THEOREM (7)RECG1G2G3 Consider the system shown in Fig.1. Obtain the closed-loop transfer function, . （16%）Fig.1 The characteristic equation is given . Discuss the distribution of the closed-loop poles. (10%) Sketch the root-locus plot for the system . (The gain 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. (15%) Show that the steady-state error in the response to ramp inputs can be made zero, if the closed-loop transfer function is given by: ; （12%） Calculate the transfer function for the following Bode diagram of the minimum phase.-20dB/dec-40-40w1 w2 w3dBw （15%） Sketch the Nyquist diagram (Polar plot) for the system described by the open-loop transfer function , and find the frequency and phase such that magnitude is unity. （16%） The stability of a closed-loop system with the following open-loop transfer function depends on the relative magnitudes of and .Draw Nyquist diagram and determine the stability of the system. （16%）( )R=2, I=2,L=2AUTOMATIC CONTROL THEOREM (8) Consider the system shown in Fig.1. Obtain the closed-loop transfer function , . （16%）CR EG1G2G3G4Fig.1 The characteristic equation is given . Discuss the condition of stability. (12%) Draw the root-locus plot for the system ;. Observe that values of K the system is overdamped and values of K it is underdamped. (16%) The system transfer function is,. Determine the steady-state error when input is unit impulse、unit step、unit ramp and unit parabolic function . (16%) Calculate the transfer function (minimum phase); Draw the phase-angle versus -20dB/dec-40-40w1 w2 w3dBw (12%) Draw the root locus for the system with open-loop transfer function. (14%) Draw the polar plot and determine the stability of system. (14%)S:0K14 overdamped ;0.0718K14 underdampedS: ; ; ; S:; AUTOMATIC CONTROL THEOREM (9)ENCG1G2G3G5R EG4H3Fig.1H1H2 Consider the system shown in Fig.1. Obtain the closed-loop transfer function, . （12%） The characteristic equation is given . Discuss the condition of stability. (16%) Sketch the root-locus plot for the system . (The gain is assumed to be positive.) Determine the breakaway point and value. Determine the value of at which root loci cross the imaginary axis. Discuss the stability. (12%) Consider the system shown in Fig.2. , . Assume that the input is a ramp input, or where is an arbitrary constant. Show that by properly adjusting the value of , the steady-state error in the response to ramp inputs can be made zero. (15%)C(s)E(s)R(s)G1(s)G2(s)Fig.2 Consider the closed-loop system having the following open-loop transfer function:. Sketch the polar plot ( Nyquist diagram). Determine the stability of the closed-loop system. (12%)Sketch the root-locus plot. (18%)ImReImReImReImReImReImRe Obtain the closed-loop transfer function. （15%）CG1G2G3G4H2H1R