課程名稱︰自動控制
課程性質︰工科系光機電組必修
課程教師︰江茂雄
開課學院：工學院
開課系所︰工科海洋系
考試日期（年月日）︰2009.05.12
考試時限（分鐘）：120
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1.(a) Please explain the following terms using a differential equation
(i) linear and nonlinear (5%)
(ii) time invariant and time-variant (5%)
(iii) causal and noncausal (5%)
(b) what's the difference of the initial condition between transfer function
and state equation? (5%)
2. A control system with state equation as
. -2 0 1 1
x = [ ]x + [ ]u(t) , X(0)=[ ]
-1 -1 1 0
y=[0 1]x
Solve the output y(t) as the input is the unit step by Laplace transform (20%)
3. A rotational system is shown below. A step input of torque T(t) is given at
θ1
(a) Find the transfer function G(s)=θ2/T(S) (10%)
(b) Solve the percent overshoot, settling time and peak time for θ2 (10%)
T(t) θ1(t) θ2(t)
───(───(────1 kg‧m^2──1 N‧m‧s/rad──(───1 N‧m/rad──│
4.A control system transfer function is
s+3
G(s)=─────
s^2+2s+7
(a) Represent it in state-space in phase variable form by drawing signal
graph. (10%)
(b) Represent it in state-space in controller canonical form by drawing
signal graph. (10%)
5.A control system is shown below.
(a) Find the closed-loop transfer function (5%)
(b) Find the value of gain K for stability (5%)
(c) Find the value of gain K that will make the system oscillate. (5%)
(d) Find the oscillation frequency in (c) (5%)
┌──────┐
R(s) + ┌────┐ + │ 1 │ C(s)
──→○──→│ K │──→○─→│──────│─┬→
-↑ └────┘ -↑ │ s(s+2)(s+3)│ │
│ │ └──────┘ │
│ │ ┌───┐ │
│ └────│ s │←─┤
│ └───┘ │
│ │
└────────────────────────┘
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※ 編輯: miracle0722 來自: 59.104.84.53 (05/22 13:04)