(完整版)现代控制理论考试卷及答案

1、Leaders: provincial agricultural work Conferenceheld inXX, whi ch i s our concern and love, willgreatly promoteXX agricultural and r ural economicdevelopment.First of all, I am representing XX municipal partyCommittee and Government, extend a warm welng grasslacome to the attending leaders! XXhasbee

2、n given support and assista nce t o theprovince of agriculture,provincial agricultural Office, and ex presse d heartfelt thanks to all thefriends! below,I XX with a brief report.A basic XX of XX municipality located (cities, omitted).One is the superiorecol ogical environment.XX blue,clea r, green,

3、water, air, 70% of land in the territory is cov ered with forests, grasslands, wn dietlands a nd waters, built 7 thousands of square kilometers of the totalarea of nature reserves.Within major industrial pollution sources, air quality at thenational level,national levels, waterresources. A totalarea

4、 of more than 5 million m u of arable land (which ow ned1.53 million a cres), the annual grain outputof more than 2 million tons and is l ocated in t he internationally recognized gold cattle, thereshould be m ore tha n 400,000 acres of grazind, developing animal husbandryconditions; a total areaof

5、4.1 million acres of forest land, ri ch i n precious wood such as pine, ash, yell owpinea pple, standing timber volumeof more than 26 millioncubic meters.Forest Xia has hundreds of species precious wil dlife, more than200 morespe ciespreci ous her bs, a nnual Super t housand tons of wild mushroom an

6、d reserves Super 100,000 tons of mountaish; nectarplant t hroug hout, can bee 100,000 group, is China bee ofXiang, andnational Northeastblack bee reserves a nd importantof beeproductsproduction base; can using water2.5 billion cubiThird, geopolitical advantages.XX open midpoint is located in the eas

7、tern part of the province along theborder, 264 km longbor der,with nationa l roadpassenger and freight transport port,builton t he borderbetween China and Russiahas the largest permanent boundary RiverBridge, running at full capacity the annual cargocapacity of up to 2.6 million tons. Russia two (HA

8、BA and Marina), two cities (Iman and Lesozav odsk) is the Russian Far East in developed areas.Lesozavodsk isonly8 km from XXport corresponding to theport of markovo,Lu Rinuostation is one of three railway marshalling yards i n the far East, the far East-Siberian railway and a parallel road r uns thr

9、ough the pass.By rail and road, to the Northby HABAcapital Khabarovsk, the Russian hi nterland, radiation i n the CIS and Eastern Europeancountries; to the Sout h through the port of Vladivostok and thescenery of the Sino-Russia n border -river-wusul i River, a famous treasure island, k nown as the

10、Oriental Maginot line of the Japanese invading army Tiger underground fortress ruins,GeneralChi西北工业大学考试试题（卷）2008 2009学年第 2 学期学时 32开课学院自动化学院课程现代控制理论一、 简答题 （对或错， 10分）（ 1） 描述系统的状态方程不是唯一的。（ 2） 用独立变量描述的系统状态向量的维数不是唯一的。（3）对单输入单输出系统，如果C (sIA) 1 B 存在零极点对消，则系统一定不可控或者不可观测。（4）对多输入多数出系统，如果( sIA) 1 B 存在零极点对消，则系统一

11、定不可控。（ 5） 李雅普诺夫直接法的四个判定定理中所述的条件都是充分条件。（ 6） 李雅普诺夫函数是正定函数，李雅普诺夫稳定性是关于系统平衡状态的稳定性。（ 7） 线性定常系统经过非奇异线性变换后，系统的可控性不变。（ 8） 用状态反馈进行系统极点配置可能会改变系统的可观测性。（ 9） 通过全维状态观测器引入状态反馈来任意配置系统的闭环极点时，要求系统必须同时可控和可观测。（ 10） 对一个线性定常的单输入单输出5 阶系统，假定系统可控可观测，通过设计输出至输入的反馈矩阵 H 的参数能任意配置系统的闭环极点。二、 试求下述系统的状态转移矩阵(t ) 和系统状态方程的解x1(t)和 x2(t)

12、 。（ 15 分）&(t)01x1 (t )2x1(0)0tx1&(t)23x2 (t )u(t)x2(0),u(t) e, t 0x201三、 设系统的传递函数为y(s)10。试用状态反馈方法， 将闭环极点配置在2，u( s)s(s 1)(s2)1 j ， 1 j 处，并写出闭环系统的动态方程和传递函数。（ 15分）Y( s)s2并画出系统可四、 已知系统传递函数s2，试求系统可观标准型和对角标准型，U (s)4s 3Leaders: provincial agricultural work Conferenceheld inXX, whi ch i s our concern and lo

13、ve, willgreatly promoteXX agricultural and r ural economicdevelopment.First of all, I am representing XX municipal partyCommittee and Government, extend a warm welcome to the attending leaders! XXhasbeen giv en support and assista nce t o theprovince of agriculture,provincial agricultural Office, an

14、d ex pressed heartfelt thanks to all thefriends! below,I XX with a brief report.A basic XX of XX municipality located (cities, omitted).One is the superiorecol ogical environment.XX blue,clea r, green, water, air, 70% of land in the territory is cov ered with forests, grasslands, wn dietlands and wa

15、ters, built 7 thousands of square kilometers of the totalarea of nature reserves.Within major industrial pollution sources, air quality at thenational level,national levels, waterquality, soil pollution, pure laresources. A totalarea of more than 5 million m u of arable land (which ow ned1.53 millio

16、n a cres), the annual grain outputof more than 2 million tons and is l ocated in t he internationally recognized gold cattle, thereshould be m ore tha n 400,000 acres of grazi ng grassland, developing animal husbandryconditions; a total areaof 4.1 million acres of forest land, ri ch i n precious woo

17、d such as pine, ash, yell owpinea pple, standing timber volumeof more than 26 millioncubic meters.Forest Xia has hundreds of species precious wil dlife, more than200 morespe ciespreci ous her bs, a nnual Super t housand tons of wild mushroom and reserves Super 100,000 tons of mountaish; nectarplant

18、t hroug hout, can bee 100,000 group, is China bee ofXiang, andnational Northeastblack bee reserves a nd importantof beeproductsproduction base; can using water2.5 billion cubimetres, shoulThird, geopolitical advantages.XX open midpoint is located in the eastern part of the province along theborder,

19、264 km longbor der,with nationa l roadpassenger and freight transport port,builton t he borderbetween China and Russia has the largest permanent boundary RiverBridge, running at full capacity the annual cargocapacity ofup to 2.6 million tons. Russia two (HABA and Marina), two cities (Iman and Lesoza

20、vodsk) is the Russian Far East in developed areas.Lesozavodsk isonly 8 km from XXport corresponding to theport of markovo,Lu Rinuostation is one of three railway marshalling yards i n the far East, the far East-Siberian railway and a parallel road r uns through the pass.By rail and road, to the Nort

21、hby HABAcapital Khabarovsk, the Russian hi nterland, radiation i n the CIS and Eastern Europeancountries; to the Sout h through the port of Vladivostok and thenahuo card on thesea, to reascenery of the Sino-Russia n border -river-wusul i River, a famous treasure island, k nown as the Oriental Magino

22、t line of the Japanese invading army Tiger underground fortress ruins, GeneralChi观标准型的状态变量图。（ 15 分）&a2x1x10u，试确定 a， b 值，使系统完全可控、完全可五、 已知系统的动态方程为1yb0 x观。（ 15 分）六、 确定下述系统的平衡状态，并用李雅普诺夫稳定性理论判别其稳定性。（15 分）x&xkx ( x2x2 )12112x&x2x2)kx ( x21212七、以下两题任选一题（ 15 分）(1)证明状态转移矩阵性质：( t )1 (t) 。(2)证明：非奇异性变换后，线性定常系统S

23、（ A,B,C,D ）的可观测性不变。拉氏变换 H(s)时间函数拉氏变换 H(s)时间函数1 / s1(t )1/(sa)e at1 sn 1t n n!1/(sa)2te at教务处印制共 2页第2页Leaders: provincial agricultural work Conferenceheld inXX, whi ch i s our concern and love, willgreatly promoteXX agricultural and r ural economicdevelopment.First of all, I am representing XX munici

24、pal partyCommittee and Government, extend a warm welcome to the attending leaders! XXhasbeen given support and assista nce t o theprovince of agriculture,provincial agricultural Office, and ex presse d heartfelt thanks to all thefriends! below,I XX with a brief report.A basic XX of XX municipality l

25、ocated (cities, omitted).One is the superiorecol ogical environment.XX blue,clea r, green, water, air, 70% of land in the territory is cov ered with forests, grasslands, wn dietlands a nd waters, built 7 thousands of square kilometers of the totalarea of nature reserves.Within major industrial pollu

26、tion sources, air quality at thenational level,national levels, waterquality, soil pollution, pure laresources. A totalarea of more than 5 million m u of arable land (which ow ned1.53 million a cres), the annual grain outputof more than 2 million tons and is l ocated in t he internationally recogniz

27、ed gold cattle, thereshould be m ore tha n 400,000 acres of grazi ng grassland, developing animal husbandryconditions; a total areaof 4.1 million acres of forest land, ri ch i n precious wood such as pine, ash, yell owpinea pple, standing timber volumeof more than 26 millioncubic meters.Forest Xia h

28、as hundreds of species precious wil dlife, more than200 morespe ciespreci ous her bs, a nnual Super t housand tons of wild mushroom and reserves Super 100,000 tons of mountaish; nectarplant t hroug hout, can bee 100,000 group, is China bee ofXiang, andnational Northeastblack bee reserves a nd import

29、antof beeproductsproduction base; can using water2.5 billion cubimetres, shoulThird, geopolitical advantages.XX open midpoint is located in the eastern part of the province along theborder, 264 km longbor der,with nationa l roadpassenger and freight transport port,builton t he borderbetween China an

30、d Russia has the largest permanent boundary RiverBridge, running at full capacity the annual cargocapacity of up to 2.6 million tons. Russia two (HABA andMarina), two cities (Iman and Lesozav odsk) is the Russian Far East in developed areas.Lesozavodsk isonly8 km from XXport corresponding to theport

31、 of markovo,Lu Rinuostation is one of three railway marshalling yards i n the far East, the far East-Siberian railway and a parallel road r uns through the pass.By rail and road, to the Northby HABAcapital Khabarovsk, the Russian hi nterland, radiation i n the CIS and Eastern Europeancountries; to t

32、he Sout h through the port of Vladivostok and thenahuo card on thesea, to reascenery of the Sino-Russia n border -river-wusul i River, a famous treasure island, k nown as the Oriental Maginot line of the Japanese invading army Tiger underground fortress ruins,GeneralChi2009 年现代控制理论试卷A 评分标准及答案第一题（ 10

33、 分， 每个小题答对1 分，答错 0 分）（ 1）对 （ 2）错 （ 3）对 （ 4）错 （ 5）对 （ 6）对 （ 7）对 （ 8）对 （ 9）对 （ 10）错第二题（ 15 分）（ 1） (t ) （ 7 分）：公式正确3 分，计算过程及结果正确4 分sIAs12 s31s312111( sIA)1s1s2s1s2(s 1)(s 2)2s2212s1s2s1s2(t)L 1( sIA) 12e te 2te te 2t2e t2e 2te t2e 2t（ 2） 状态方程有两种解法（8 分）：公式正确4 分，计算过程及结果正确4 分tx(t )(t) x(0)()Bu(t)d0x1 (t )

34、e te 2tt2ee 2(4t1)e2e(t )x2 (t )e t2e 2 t2e2e 2d3)e0(4t或者te 2tt 2e 2tX ( s)( sIA) 1 x(0) (sIA) 1 BU (s)2(s3)x(t )L1( sI A)1x(0)1(s1) 2 ( s2)L 4(s1) 2 ( s2)x1(t)ex2(t )ete 2 t422L 1 (s1) 2s1s24tet2e 2 t4444te(s1) 2s1s2te te 2tt3et2e 2t第三题（ 15 分， 答案不唯一，这里仅给出可控标准型的结果）（ 1）系统动态方程（3 分）0100x001x0 u0231y100

35、0 xLeaders: provincial agricultural work Conferenceheld inXX, whi ch i s our concern and love, willgreatly promoteXX agricultural and r ural economicdevelopment.First of all, I am representing XX municipal partyCommittee and Government, extend a warm welcome to the attending leaders! XXhasbeen giv e

36、n support and assista nce t o theprovince of agriculture,provincial agricultural Office, and ex pressed heartfelt thanks to all thefriends! below,I XX with a brief report.A basic XX of XX municipality located (cities, omitted).One is the superiorecol ogical environment.XX blue,clea r, green, water,

37、air, 70% of land in the territory is cov ered with forests, grasslands, wn dietlands and waters, built 7 thousands of square kilometers of the totalarea of nature reserves.Within major industrial pollution sources, air quality at thenational level,national levels, waterquality, soil pollution, pure

38、laresources. A totalarea of more than 5 million m u of arable land (which ow ned1.53 million a cres), the annual grain outputof more than 2 million tons and is l ocated in t he internationally recognized gold cattle, thereshould be m ore tha n 400,000 acres of grazi ng grassland, developing animal h

39、usbandryconditions; a total areaof 4.1 million acres of forest land, ri ch i n precious wood such as pine, ash, yell owpinea pple, standing timber volumeof more than 26 millioncubic meters.Forest Xia has hundreds of species precious wil dlife, more than200 morespe ciespreci ous her bs, a nnual Super

40、 t housand tons of wild mushroom and reserves Super 100,000 tons of mountaish; nectarplant t hroug hout, can bee 100,000 group, is China bee ofXiang, andnational Northeastblack bee reserves a nd importantof beeproductsproduction base; can using water2.5 billion cubimetres, shoulThird, geopolitical a

41、dvantages.XX open midpoint is located in the eastern part of the province along theborder, 264 km longbor der,with nationa l roadpassenger and freight transport port,builton t he borderbetween China and Russia has the largest permanent boundary RiverBridge, running at full capacity the annual cargoc

42、apacity ofup to 2.6 million tons. Russia two (HABA and Marina), two cities (Iman and Lesozavodsk) is the Russian Far East in developed areas.Lesozavodsk isonly 8 km from XXport corresponding to theport of markovo,Lu Rinuostation is one of three railway marshalling yards i n the far East, the far Eas

43、t-Siberian railway and a parallel road r uns through the pass.By rail and road, to the Northby HABAcapital Khabarovsk, the Russian hi nterland, radiation i n the CIS and Eastern Europeancountries; to the Sout h through the port of Vladivostok and thenahuo card on thesea, to reascenery of the Sino-Ru

44、ssia n border -river-wusul i River, a famous treasure island, k nown as the Oriental Maginot line of the Japanese invading army Tiger underground fortress ruins, GeneralChi（ 2）状态反馈矩阵（5 分，公式正确3 分）kk0k1 k 2uv kx由闭环极点和闭环系统特征多项式有I (A BK)3(3 k 2 ) 2(2 k1 )k0(2)(1 j )( 1 j )34 264比较， k4 41。0100（ 3）闭环系统的动态

45、方程（3 分）：x001x0 v4641y100 0 x（ 4）闭环系统的传递函数（4 分）： G(s)Y(s)10U(s)s34s26s 4第四题 （ 15 分）已知系统传递函数Y(s)s2，试求系统可观标准型和对角标准型，U (s)s24s 3并画出相应的系统状态图。答：（ 1）可观标准型及状态图（5 分）x01x1034x2u可控标准型为：1x1y2 1x203x12x4x2u根据对偶原理，系统可 观标准型为：11x1y01x2（ 2）系统可观测标准型状态变量图如下：（5 分）Leaders: provincial agricultural work Conferenceheld inX

46、X, whi ch i s our concern and love, willgreatly promoteXX agricultural and r ural economicdevelopment.First of all, I am representing XX municipal partyCommittee and Government, extend a warm welcome to the attending leaders! XXhasbeen given support and assista nce t o theprovince of agriculture,pro

47、vincial agricultural Office, and ex presse d heartfelt thanks to all thefriends! below,I XX with a brief report.A basic XX of XX municipality located (cities, omitted).One is the superiorecol ogical environment.XX blue,clea r, green, water, air, 70% of land in the territory is cov ered with forests, grasslands, wn dietlands a nd waters, built 7 thousands of square kilometers of the totalarea of nature reserves.Within major industrial pollution sources, air quality at thenational level,national levels, waterq