现代控制理论及应用考试题--2010春A试题

名

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

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

output vaiables;

(2)Obtain the set of differential equations in terms of

the state variables;

(3)Write the state equation and output equation.

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

432

10

()

12233440

s

G s

s s s s

+

=

++++

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

92614

y y y y u

∙∙∙∙∙∙

+++=

1

2

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

111

22

2

(0)

0300

251(0)0

x x x

u

x x

x

∙

∙

⎡⎤

⎡⎤⎡⎤

⎡⎤⎡⎤⎡⎤

⎢⎥=+=

⎢⎥⎢⎥

⎢⎥⎢⎥⎢⎥

⎢⎥--

⎣⎦⎣⎦⎣⎦

⎣⎦⎣⎦

⎣⎦

Caculate the response for a unit step input 1

u=for the system.

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

[][]

0100

0010

4564

2920

X X u

y X u

∙

⎡⎤⎡⎤

⎢⎥⎢⎥

=+

⎢⎥⎢⎥

⎢⎥⎢⎥

---

⎣⎦⎣⎦

=-+

Determine whether the system is controllable and observable.

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

11

2

2

010

()

001

x x

u t

x

x

∙

∙

⎡⎤

⎡⎤

⎡⎤⎡⎤

⎢⎥=+

⎢⎥

⎢⎥⎢⎥

⎢⎥⎣⎦⎣⎦

⎣⎦

⎣⎦

Determine the optimal control law

()

pt

u t such that the performance index

222

12

1

()7()()

2

J x t x 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 ()

c

G s and plot the resulting time response.(b) Determine the effect of the disturbance ()

D s Q s

=on the output ()

Y s.(For ease, let ()0

R s=.)

()

Y s

Antenna position control