现代控制理论及应用考试题--2010春A试题

姓

线 号 学

封

级

班

卷 试 密学

大 峡

三

2010─2011学年 第1学期

2009级《现代控制理论及应用》课程试卷（A卷）

注意：1、本试卷共 1 页； 2、考试时间: 120 分钟 3、姓名、学号必须写在指定地方 题号 一 二 三 四 五 六 七 总分 得分 一．(4 ×5‘=20‘) SAQs. (1) Briefly highlight the history of automatic control theory. (2) Briefly highlight the differences between the mathmatical model of the classical control theory and the ones of the modern control theory.

(3) Briefly highlight the concepts of controllability and observability. (4) Briefly highlight the contents and methods of optimal control problem.

二．(12’)A m-k-c system is shown in Figure 2. (1)Identify a suitable set of state variables and K1Coutput vaiables; m1 (2)Obtain the set of differential equations in terms of u1the state variables; uK2x12 (3)Write the state equation and output equation.

m2

x2 Figure 2三．(10’)Determine a state space representation for a system with the following transfer function

G(s)s10s412s323s234s40

四．(10’)Determine a state space representation for a system with the following differential equation

 y9y26y14yu

名

姓 线

号 学

封

级

班

卷

试 密学 大

峡

三

五．(12’)A system has the following state equation and intial condition

x13x1x1(0)x025x0u0221x(0)0 2Caculate the response for a unit step input u1 for the system.

六．(12’)A system is described by the state equation and the output equation

0100X0014X0u56

4y292X0uDetermine whether the system is controllable and observable.

七．(12’)A system is described by the following state equation

x101x10u(t)

x200x21Determine the optimal control law u0pt(t) such that the performance index

J120x2t)7x221(2(t)u(t)dt is minimized.

八．(12’)A large antenna is used to receive satellite signals and must

accurately track the satellite as it moves across the sky. The control system uses an armature-controlled motor and a controller to be selected, as showed in

Figure 8. The system specifications require a steady-state error for a ramp input, r(t)Bt,less than or equal to 0.01B.We also seek an overshoot to a step input less than 5% with a settling time (with a 2% criterion) less than 3 seconds. (a)

Design a controller Gc(s) and plot the resulting time response.(b) Determine the effect of the disturbance D(s)Qs on the output Y(s).(For ease, let R(s)0.)

ControllerD(s)Motor and antennaR(s)G10Y(s)c(s)ss5s10PositionAntenna position control