推 ketsu1109 :已收入精華區 04/20 20:49
課程名稱︰控制系統
課程性質︰選修
課程教師︰陳永耀
開課學院：電機系
開課系所︰電資學院
考試日期（年月日）︰2009/04/16
考試時限（分鐘）：180min
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
Note:
(1)Exam starts at 2:20PM, end at 5:20PM (2)NO turn-in after 5:05PM
(3)Calculator allowed
1.There are many biological feedback systems in human bodies.For the
controlled variables below, please draw the graph showing the process being
controlled, the sensor that measured the variable, the actuator that causes it
to increase and/or decrease, the information path that completes the feedback
path, and the disturbance that upset the variable.(In case you do not know the
exact biological mechanisms, you are free to make resonable assumptions.)
(a) heart rate (8%)
(b) eye pupil diameter (8%)
2.An op-amp model is given by the following equation and is shown in Figure 1.
R_f
┌─^^^^^─┐
⒎ R_in │ ︵ │
10 ─^^^^^^^─┴┤-╲ │
V_out= ───[V﹢- V-] │ ）─┴─
s+1 V_in ┌┤+╱ V_out
│ ︶ ╮
┌─────┴──┴───
┴
i﹢= i- = 0 ≡ Figure 1.
┌─────┐
v+ │ ︵ │
└┤+╲ ﹨
│ ）──┴
V_in ────┤-╱ V_out
v- ︶ ╮
┌────────┴───
┴
≡ Figure 2.
(a)Please find the transfer function of the system in Figure 1.(8%)
(b)Show that, for the non-ideal model of the op-amp above, the circuits in
Figure 2 is un stable.(8%)
3.For the unity-feedback system in Figure 3, please find K, z, and p such that
the closed-loop system has a 10% overshoot to a step-input, a setting time
of 1.5 sec (1% criterion) (15%)
1 K(s+z)
G(s)= ─── and D(s)= ────
s(s+3) s+p
+ ︵ ┌──┐ ┌──┐
R(s) ─→（Σ）─→│D(s)│─→│G(s)│─┬─Y(s)
︶ └──┘ └──┘ │
↑- │
└──────────────┘
Figure 3
4. For the system with integral control in Figure 4,
(a)Please find the transfer function F_1 from V_c to V (with W=0) and the
transfer function F_2 from W to V (with V_c=0 ).(10%)
(b)What are the system types for F_1 anf F_2?(6%)
(c)What is the steady-state error of v when there is a unit-ramp disturbance
w? (5%)
W
┌──┐ ↓+ ┌──┐
┌──┐ + ︵ k1E │k_2 │ F ︵ │ m │
V_c─┤ k_1├─→（Σ）─→│──│─→（Σ）─→│──│─┬──┬─V
└──┘ ︶ │ s │ + ︶ │ s │ │ │
↑- └──┘ ↑- └──┘ │ │
│ │ ┌──┐ │ │
│ └───│k_3 │─┘ │
│ └──┘ │
│ │
│ ┌──┐ │
└────────────── │k_1 │ ───┘
└──┘
Figure 4.
┌───┐
+ ︵ │ A │
R ─→（Σ）─→│───│─→───┬─Y(s)
︶ │s(s+2)│ │
↑- └───┘ │
│ ┌────┐ │
└───│1+k_t*s │─←──┘
└────┘
Figure 5.
5. Given the PD control system in Figure 5 to be designed with the following
specifications:(1)steady-state error of less than 10% to a ramp reference
input, (2)maximum overshoot for a unit-step input of less than 5%, (3)1%
setting time if less than 3 sec.
(a)Please find the transfer function of the closed system.(5%)
(b)To satisfy the specifications, please indicate the region in the complex
plane that the closed-loop poles should lie.(15%)
(c)What does spec.(1) imply about the value of A?(5%)
(d)Suppose A=32. Please find the value of k_t that yields closed-loop poles
on the right-hand boundary of the feasible region.(10%)
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