課程名稱︰自動控制
課程性質︰系定必修(大三)
課程教師︰陽毅平
開課學院：工學院
開課系所︰機械系
考試日期（年月日）︰2009/11/03
考試時限（分鐘）：120min
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1.A spring-mass-damper system is oscillating in oil. The equation of motion is
expressed as mx''+bx'+kx=u , where m is the mass, b is the viscous coeffici-
ent, k is the spring constant, u is the external force, and x' is measured
as the output.
───┬───
┌──┼──┐
│ ︴ │air (中間那個是彈簧..XD)
│ ︴ │
├──┼──┤
│ ┌┴┐ │
│ └─┘ │oil
└─────┘
(a)Find the transfer function between the control input u and the output x' .
(b)If the states are defined as x1=kx , x2=mx' , write the two state-space
equations for the system, and indicate your new input variable, system
matrix, input matrix and output matrix. (a,b各5%)
Vout s^2 +1
2. The transfer function of a notch filter is expressed as ── = ──────
Vin s^2 + 4s + 1
(a)What is the order of the system?(2%)
(b)What are system poles and zeros?(3%)
(c)What is the corresponding differential equation or governing equation?(3%)
(d)If a constant voltage is applied, Vin = 10 , what is the steady state
output voltage? (4%)
(e)Find the steady-state response to the sinusoidal input Vin=sint+10sin2t.
(You don't have to calculate the square root or arctan value.) (8%)
(f)Let y=Vout, u=Vin, y(0)=0, y'(0)=1, u(0)=u0, u'(0)=u'0, the Laplace
transfer of system response is expresses as Y(s)=Yn(s)+Yf(s), where Yn is
the natural response and Yf is the forced response. Calculate Yn and Yf.
(10%)
3.A control engineer applied an impulse δ(t) to a structure of a space shuttle
and created a model y''+4y'+3y = u'-2u .
(a)What are the modes and their amplitudes of the structure excited by the
impulse? (Hint: find out the impulse response by transfer function)(10%)
(b)Is it a minimum phase or non-minimum phase system? Why? (5%)
(c)If the system transfer function is H(s), design a feedback integral
controller so that the closed-loop system is stable. What is the proper
range of a? (Hint: use Routh's array)(10%)
┌─┐
r + │１│ u ┌──┐ y
──→○─→│─│─→│H(s)│─┬→
-↑ │as│ └──┘ │
│ └─┘ │
└────────────┘
4.A rim motor is invented by the Propulsion Control Laboratory at NTU, and is
modeled as G(s) = 1/s(s+2)
R + ┌──┐ ┌──┐ Y
──→○─→│D(s)│─→│G(s)│─┬→
-↑ └──┘ └──┘ │
└─────────────┘
A proportion controller is designed in the form of D(s)=K.
(a)Specify a range of K so the rise time of the closed-loop system is no
more than 0.18 second according to the equation tr = 1.8/ωn (10%~90%
criterion). (10%)
(b)If one chooses K at 100, what is the maximum overshoot Mp of the closed-
loop system? (10%)
(題目有附 Mp(%) 對應 ζ 的曲線圖)
(圖在 Pearson 第五版的自控課本 P.96 Figure 3.21)
5.Determine C/R for system (a) (10%) and C/W for system (b) (10%).
┌─┐
┌─────→│G2├───┐
│ + ┌─┐└─┘ ↓+
R──┴─○→│G1├────┬→○→ C
+↑ └─┘┌─┐ │ +
└────┤H1│←┘
└─┘ (a)
┌─┐ ｗ
┌─┤H3│←────┐ │+
+ ┌─┐ ↓- └─┘┌─┐ + │+ ↓ ┌─┐
R →○→│G1│→○───→│G2│→○┴→○→│G3├─┬┬→ C
-↑ └─┘ + └─┘ -↑┌─┐ └─┘ ││
│ └┤H2│←────┘│
│ ┌─┐ └─┘ │
└───────┤H1│←─────────────┘ (b)
└─┘
6. "Was Einstein right? NASA is gathering proof 88 years later." To test this
claim in a way never done before, NASA launched the Gravity Probe B (GP-B)
mission in April 2004. If all goes well with this satellite experiment, we
should know by mid-2006 whether Einstein's theory of curved space time is a
true description of our universe. Engineers in NASA cooperate with
intelligent students in automatic control course at NTU to control the
pointing direction, or attitude, of the Gravity Probe B spacecraft in orbit
about the Earth. The transfer function between the pointing angle and input
torque of the satellite is modeled as G(s).
Ｗ
│+ ┌───────────┐
+ ┌─┐+ ↓ │ 1 │
R ──→○→│Ｋ│→○→│G(s)= ────────├┬→ Y
-↑ └─┘ │ (s-1)(s+2)(s+100)││
│ └───────────┘│
└────────────────────┘
(a)Students are anxious whether they could reduce the order of the plant. Do
you have an approximate closed-loop transfer function after you reduce the
order of G(s)? (5%)
(b)For W=0, without reducing the plant order, determine K so that the closed-
loop system is stable. (10%)
考卷最後面有附Laplace轉換表
.
題目裡面打成 x' 表示是 x ，因為分兩行很佔空間，而且兩點不好打..所以用x'表示~
希望對學弟妹有幫助~
XD
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