《(完整版)哈尔滨工业大学2010《现代控制理论基础》考试题A卷及答案.doc》由会员分享，可在线阅读，更多相关《(完整版)哈尔滨工业大学2010《现代控制理论基础》考试题A卷及答案.doc（8页珍藏版）》请在金锄头文库上搜索。
1、rapid development of the market economy environment to explore public servants duty consumption monetization reform has provided a good foundation. The socialization of rear service work has been launched, and rapid progress in some places and departments, duty consumption monetization of carrier an
2、d approach to management has been resolved. Third, in recent years, exploring the monetization of duty consumption has made some progress, have gained some experience and can provide reference to the comprehensive reform of the system of public servants duty consumption further. Implementing an hone
3、st canteen, standardize official entertaining management; enhancing the telecommunication expense management; elimination of County travel and countryside subsidies; research village officials capitalization management of corporate spending, and so on. Finally, group .18 session to be held in Beijin
4、g from November 9, 2013 to 12th. 35 years ago blew the third plenary session of the reform and opening up in the spring breeze, changed, affect the world; today, 35 years later, in the eyes of the nation and the world expect, again to reform mark China, ushered in the 18 session. XI General Secretar
5、y pointed out that Chinas reform has entered a crucial period and the Sham Shui Po District, must be based on greater political courage and wisdom, lose no time in deepening reform in important fields. Dares to crack a hard nut, dares to question the Rapids, which dares to break the barrier of ideas
6、, and dare to benefit cure barriers. Deepening reform and opening up is on schedule to achieve institutional safeguards of the moderately well-off. Under the five in one the General layout of socialist modernization requirements, 18 session of the decision was a five in one and the improvement of ov
7、erall scheme of reform, will promote an integrated and coordinated economic, political, cultural, social and ecological civilization construction of the five reforms and the partys construction in the area of institutional reform. The five in one programme is to achieve a comprehensive reform of ins
8、titutional guarantees for objectives of build a well-off society, the smooth progress of the construction of a well-off society and reform the objectives of the programme. One, holding time and place importance on November 9, 2013 to the 18 session of the 12th Beijing since 1978, 35, have been 7 ple
9、nary session, each time on major issues of political and economic life of the country has made important deployment. In accordance with PRC political practice, often at every session of the CPC Central Committee in a plenary session was held immediately after the partys Congress, on the theme person
10、nel, discussing election Centrals top leaders, such as the election of the Standing Committee of the political Bureau, through the Central Committee members, decisions, such as members of the Central Military Commission. The second plenary session, is held in two sessions before the general election
11、, mainly to discuss a new State personnel issues. But by the third 哈尔滨工业大学 现代控制理论基础 (A卷答案) 班号： 姓名：一 （本题满分10分）如图所示为一个摆杆系统，两摆杆长度均为，摆杆的质量忽略不计，摆杆末端两个质量块（质量均为）视为质点，两摆杆中点处连接一条弹簧，与分别为两摆杆与竖直方向的夹角。当时，弹簧没有伸长和压缩。水平向右的外力作用在左杆中点处，假设摆杆与支点之间没有摩擦与阻尼，而且位移足够小，满足近似式，。（1）写出系统的运动微分方程；（2）写出系统的状态方程。【解】（1）对左边的质量块，有对右边的质量块，
12、有在位移足够小的条件下，近似写成： 即（2）定义状态变量，则或写成二（本题满分10分）设一个线性定常系统的状态方程为，其中。若时，状态响应为；时，状态响应为。试求当时的状态响应。【解答】系统的状态转移矩阵为，根据题意有合并得求得状态转移矩阵为当时的状态响应为三（本题满分10分）已知某系统的方块图如下，回答下列问题：（1）按照上图指定的状态变量建立状态空间表达式；（2）确定使系统状态完全能控且完全能观时，参数的取值范围。【解答】（1）系统的状态空间表达式为（2）使系统状态完全能控且完全能观时，参数且。四（本题满分10分）离散系统的状态方程为（1）是否存在一个有限控制序列，使得系统由已知的初始状态
13、，转移到，？试给出判断依据和判断过程。（2）若存在，求的最小值及控制序列。【解答】（1）由题意，由系统能控性的定义可知：存在有限控制序列，使得在有限时间内由状态初值转移到零。（2）由系统状态完全能控的性质可知，此系统为二阶系统，可用适当的，使得，即的最小值为1。 根据状态方程进行递推如下：，由上面最后一步可得即即，。五（本题满分10分）对下列系统试设计一个状态反馈控制器，满足以下要求：闭环系统的阻尼系数；阶跃响应的峰值时间等于3.14秒。【解答】假设状态反馈控制律为，代入状态方程得闭环系统闭环特征多项式为根据题意的要求，期望特征多项式为根据多项式恒等的条件可得：解得状态反馈控制律为。六（本题满
14、分10分）设系统的状态空间表达式为若该系统的状态不可测量，试设计一个降维状态观测器，使降维观测器的极点为，要求写出降维观测器动态方程，并写出状态的估计方程。【解答】将状态空间表达式写成：进一步写成设降维观测器方程为引入中间变量，两边求导数得根据题意，降维观测器的极点为-10，即，解得。 最终得到降维观测器的动态方程为状态估计的表达式为。七. （本题满分10分）证明对于线性定常系统的线性变换，其传递函数（矩阵）保持不变。【证明】设原线性系统为其传递函数矩阵为 设线性变换为，变换后的线性系统为该系统的传递函数矩阵为显然，即其传递函数（矩阵）保持不变。 证毕八. （本题满分10分）某2阶非线性系统的
15、状态方程为，证明该系统在坐标原点处渐近稳定。【证明】取李雅普诺夫函数，显然是正定函数；此外，沿着状态轨线的导数为：令函数，则，关于的二次方程的根的判别式为，。则有，所以表达式恒小于零，因此，为负定。所以该系统在坐标原点处渐近稳定。采购的食品原料及成品必须色、香、味、形正常，不采购腐败、变质、有毒有害、霉变生虫、过期、混有异物或感官性状异常及其他不符合卫生标准要求的食品。plenary session, each session of the Central Committee of national institutions and personnel problems have been arranged, you can concentrate on national development and reforms. Previous plenary session is often branded with a cen
