《自動(dòng)控制原理》試卷及答案(英文10套),推薦文檔

1、automatic control theorem(1) derive the transfer function and the differential equation of the electric network shown in fig.1.(12% )r1c1v1(s)c2r2v2(s)fig.1 consider the system shown in fig.2. obtain the closed-loop transfer function c(s ) ,r(s ).（12%）eg4rg1g2g3ch2h1e(s )r(s )fig.2 the characteristi

2、c equation is given1 + gh (s ) = s 3 + 5s 2 + (6 + k )s + 10k = 0 . 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-

3、loop transfer function isg(s ) =0.4s + 1s(s + 0.6). obtain the response to a unit-step input. what is the rise time forthis system? what is the maximum overshoot? （10%）5. sketch the root-locus plot for the system assumed to be positive.) determine the breakaway point and k value.gh (s ) =ks (s + 1).

4、 ( the gain k is 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 r = (2 + t) , n = 1. determinethe value of k to ensure ess 1.(12%)nrec4s(s + 3)ks + 2fig.37. consider the system with the following op

5、en-loop transfer function:gh (s ) =ks (t1s + 1)(t2s + 1). draw nyquist diagrams. determine the stabilityof 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%)s + 2s 3(s + 2)(s + 5)(s + 10)r(s)c(s)fig.4v2 (s ) =r2c1c2 s + c1v1

6、(s )(r1 + r2 )c1c2 s + c1 + c2 c(s ) =r(s ) g1g2g3 + g1g41 + g1g2 h1 + g1g2g3 + g1g4 + g2g3 h 2 + g4 h 2 0k6 k0 k6 no answerthe breakaway point is 1 and 1/3; k=4/27 the imaginary axis s=j; k=2 3.5 k 7.531.62( s + 1)gh (s ) =0.1(s0.316+ 1)(s3.481+ 1)(s34.81+ 1)(s82.54+ 1)automatic control theorem(2)d

7、erive the transfer function and the differential equation of the electric network shown in fig.1.(12% )r1r1v1(s)c1c2v2(s)fig.1 consider the equation group shown in equation.1. draw block diagram and obtainthe closed-loop transfer function c(s ) . （16% ）r(s )x 1 (s ) = g1 (s )r(s ) - g1 (s )g7 (s ) -

8、 g8 (s )c(s )equation.1 x 2 (s ) = g2 (s ) x 1 (s ) - g6 (s ) x 3 (s )x (s ) = x (s ) - c(s )g (s )g(s )3253c(s ) = g4 (s ) x 3 (s ) use rouths criterion to determine the number of roots in the right-half s plane fortheequation1 + gh (s ) = s 5 + 3s 4 + 28s 3 + 226s 2 + 600s + 400 = 0 .analyze stabi

9、lity.（12% ） determine the range of k value ,when r = (1+ t + t 2 ) , e ss 0.5 . （12% ）fig.23s 2 + 4s + k s 2 (s + 2)recr the syuths crn. sketch the root-locfig.3 shows a unity-feedback control system. by sketching the nyquist diagram of the system, determine the maximum value of k consistent with st

10、ability, and checkthe result using roiteriorks (s 2 + 4s + 5)us fostem（20%）cr efig.3sketch root-locus diagram.（18% ）imimimrerereimimimrerere02002040 -60 determine the transfer function. assume a minimum-phase transfer function.（10%）l(db)40302050.1 123 4=v2 (s )v (s )r c r c s 2+ (r c1+ r c + r c )s

11、+ 111 1 2 21 12 21 2 c(s ) =r(s ) g1g2g3g41 + g2g3g6 + g3g4g5 + g1g2g3g4 (g7 - g8 ) 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. 8 k 0t1 0t2 0 ) c(s ) =r(s )g1 + g1g2g32 + g1 - g1g2 + g2g3 + g1g2g3r=2, i=2,l=2d2 ( s + 1) g(s) =

12、2 d 1s 2 (s)d3 + 1d= 0.986rad / sf = -95.5oautomatic control theorem(8) consider the system shown in fig.1. obtain the closed-loop transfer functionc(s ) ,r(s )e(s ) .（16%）r(s )recfig.1g4g3g2g1 the characteristic equation is given discuss the condition of stability. (12%)1 + gh (s ) = s 3 + 3ks 2 +

13、(2 + k )s + 4 = 0 . draw the root-locus plot for the systemgh (s ) =k(s + 1)2 (s + 4)2; h (s) = 1 .observe that values of k the system is overdamped and values of k it is underdamped. (16%)k (1 + 0.5s) the system transfer function is g(s) =s(1 + 2s)(1 + s), h (s) = 1 . determine thesteady-state erro

14、r ess when input is unit impulsed(t) 、unit step1(t) 、unit ramp tandunit parabolic function 1 t 2 . (16%)2 calculate the transfer function (minimum phase); draw the phase-angle versus d-40-20db/decw1w2w3dbw-40(12%) draw the root locus for the system with open-loop transfer function.gh (s) =k (1 + s)s

15、(s + 2)(s + 3)(14%)k gh (s) = s3 (ts + 1)draw the polar plot and determine the stability of system.(14%) c(s ) = g1g2 + g3g4 - 1 - g1g2g3g4 r(s )g1g2 + g3g4 - g1g2g3g4 0.528 p k p s:0k14 overdamped ;0.0718k14 underdampeds: d(t)ess= 0 ; 1(t) ess= 0 ; t ess= 1 ;k1 t2 e= 2ssdd ( s + 1)s: k = dd ; g(s)

16、=1 21 2 d 1s 2 (s)d3 + 1automatic control theorem(9) consider the system shown in fig.1. obtain the closed-loop transfer function c(s ) ,12s )nfig.1h2h1g4g5g3r(s )e(s ) .n ( r（ %）ech3g1g2 the characteristic equation is given1 + gh (s ) = s 3 + 34.5s 2 + 7500s + 7500k = 0 . discuss the condition of s

17、tability. (16%) sketch the root-locus plot for the systemgh (s ) = (s + a) 4 . (the gain a iss 2 (s + 1)assumed to be positive.) determine the breakaway point and a value. determine the value of a at which root loci cross the imaginary axis. discuss the stability.(12%) consider the system shown in f

18、ig.2. g (s) = k s + 1 , g (s) =k. assume1i2s(ts + 1)that the input is a ramp input, or r(t) = atwhere a is an arbitrary constant. show that by properly adjusting the value ofki , the steady-state erroress in the response toramp inputs can be made zero.(15%)fig.2g2(s)g1(s)r(s)e(s)c(s) consider the cl

19、osed-loop system having the following open-loop transfer function:gh (s ) =ks (ts - 1). sketch the polar plot ( nyquist diagram). determine thestability of the closed-loop system. (12%)sketch the root-locus plot. (18%)imimimrerereimimimrerere obtain the closed-loop transfer function c(s ) .（15%）r(s

20、)g4rg1g2g3ch2h1 c(s ) =r(s )e(s ) =g1g2g3g4 - g1g2g4g5 (1 + g3 h1 )1 +g 3 h1 + g2g3 h 2 + g1g2g3g4 h 2 - g1g2g4g5 h 3 - g3 h1g1g2g4g5 h 3- g4 h 3 - h 2g2g4g5 h 3n (s )1 +g 3 h1 + g2g3 h 2 + g1g2g3g4 h 2 - g1g2g4g5 h 3 - g3 h1g1g2g4g5 h 3 0 p k p 3.45s: n=1 p=1 z=0; the closed-loop system is stable c

21、(s ) =r(s )g1g2g3 + g1g41 + g1g2 h1 + g1g2g3 + g1g4 + g2g3 h 2 + g4 h 2automatic control theorem(10) consider the system shown in fig.1. obtain the closed-loop transfer functionc(s ) ,r(s )c(s ) .（16%）g3n (s )ng2g1 rcg4g5fig.1h the characteristic equation is given1 + gh (s ) = s 4 + 20ks 3 + 5s 2 +

22、10s + 15 = 0 . discuss the condition of stability. (14%) consider a unity-feedback control system whose open-loop transfer function isg(s ) =0.4s + 1s(s + 0.6). obtain the response to a unit-step input. what is the rise time forthis system? what is the maximum overshoot? （10%） sketch the root-locus

23、plot for the system assumed to be positive.)gh (s ) = k (1 - 0.5s)s (1+ 0.25s). (the gain k is 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 transfer function is g(s) =4s(s + 5) , h (s) = 1 . de

24、termine the steady-state output c(t) when input is unit step1(t) 、 unit ramp t . determine the kp 、kv and ka , obtain the steady-state error ess when input is r(t) = 2t . （12%） consider the closed-loop system whose open-loop transfer function is given by: gh (s ) =k1 + tsk; gh (s ) = 1 - tsk; gh (s ) = ts - 1. examine the stability ofthe system.（15%） sketch the root-locus plot 。 （18%）imimimrerereimimimrerere c(s ) =r(s )g1g2 (1 - g4g5 )1 - g4g5 + g2g5 + g1g2 h - g4g5g1g2 hunstable es: