课程名称︰自动控制
课程性质︰必修
课程教师︰王富正
开课学院：工学院
开课系所︰机械系
考试日期（年月日）︰2014/11/4
考试时限（分钟）：101分钟
是否需发放奖励金：是
（如未明确表示，则不予发放）
试题:
1.(10%)Find the Laplace Transform F(s) of the following function:
f(t)= ｛ e^at sin(ω(t-2)), t＞=2
｛ 0, otherwise
2.Consider Fig.2,
(1)5%-Draw the free-body diagram of Mv, and write its dynamics equation.
(2)5%-Draw the free-body diagram of Mt, and write its dynamics equation.
(3)15%-Find the transfer function from F to x1 and x2 by taking Laplace
transform of the above dynamic equations.
F↓
[ Mv ] ＿ 　　　Ｌ L
| | ↓x1 Ｏ－－→＊＊＊－﹁→＊＊＊－－﹁－←－Ｏ
b1 = ︴k1 + ｜ ｜　　　+
| | ＝C C＝
[ Mt ] ˍ - ｜ ｜ -
| | ↓x2 Ｏ－－－－－－－ ”－－－－－－｣－－－Ｏ
b2 = ︴k2
___|__|___
Fig.2 Fig.3
3.(20%)Refer to Fig.3, where V1 is input and V2 is output.
(1)10%-PLease find the transfer function from V1 to V2.
(2)10%-Find the Controller Canonical Form of tje system in (1), and draw the
corresponding block diagram.
4.(20%)Consider the followint state-space model:
{ 0 1 0 1
{ xdot= ［ 0 0 -1 ］ x + ［ 0 ］u
{ 0 1 2 1
{
{ y = ［ 1 1 0 ］ x
(1)10%-Please find the trandfer function of the model Tu→y
(2)10%-Find the state response x(t), when given an input u(t)=1 with an
initial condition x(0)= [1 0 0]^T.
5.(25%)Refer to the system shown in Fig.5, where G(s)=10/[(s+1)(s+2)],
K=2+Ki/s:
(1)5%-Find the transfer functoin Tr→y.
(2)5%-Find the system sensitivity to Ki.
(3)5%-Find the steady-state error to a unit step input R(s)=1/s. If 0<Ki<3.
(4)10%-Find the response y(t), to a step disturbance, i.e. Td(s)=1/s and
R(s)=0. Set Ki=0.
Td(s)
　　　　　+ controller　　 +↓ Process
R(s)－→Ｏ－－－→[ K ]－－→Ｏ－－→[ G ]－－－﹁－－－→Y(s)
Desired -↑ + ｜ Actual
thickness ｜ ｜ thickness
｜ ｜
﹂－－－－－－－－－－－－－－－－－－－－－－－”
Fig.5