作者yaujack (大头)
看板NTU-Exam
标题[试题] 96下 陈明新 数位控制系统 期中考
时间Thu May 1 23:35:55 2008
课程名称︰ 数位控制系统
课程性质︰ 选修
课程教师︰ 陈明新
开课学院: 工学院
开课系所︰ 机械系
考试日期(年月日)︰ 2008/05/01
考试时限(分钟): 180
是否需发放奖励金: 是
试题 :
Digital Control, Midterm Term, 2008
[1]
(a) For a continuous time system G(s) with satisfactory performance,
the poles of G(s) should be in the good region as shown in Figure 1.
What is the corresponding good region in the unit circle for a
discrete time system H(z) ?
(b) What is the discrete time PID controller ?
(c) What should be the corner frequency of an anti_alising filter if the
sampling time is T seconds.
[2]
(a) Find the closed-loop characteristic polynomials of the block diagram in
Figure 2.
(b) Use the bilinear transformation and the Routh stability test to find out
if the closed-loop system can be stabilized by a positive constant K. If
the answer is yes, find out the range of positive constant K > 0 so that
the closed-loop system is stable.
[3]
(a) If the frequency spectrum of a continuous signal r(t) is R(ω), what is
the relationship between the sampled spectrum R*(ω) and the original
spectrum R(ω)?
(b) Let the sampling time be T. What is the condition on the spectrum R(ω)
of a continuous signal so that after sampling, the sampling spectrum
R*(ω) remains un-distorted ?
(c) What is the frequency observed when a signal f(t) = sin(10t) is sampled
with a sampling time T = 0.3π second.
[4]
(a) What is the discretized transfer function y(k) = H(z)u(k) of continuous
plant y(t) = G(s)u(t) = (1/s)u(t) when using a zero-order hold with a
sampling time T = 0.1 second, where u(t) = u(k), t 属於 [kT,(k + 1)T).
(b) Repeat problem (a) using a predicative first order hold, where u(t) = u(k)
+ (t-kT)×[u(k+1) - u(k)]/T, t 属於 [kT,(k+1)T).
Hint: substitute the control u(t) into the following equation
kT+T
y(k+1) = y(k) + ∫ u(t)dt = …
kT
(c) Use the root locus technique to design an implementable digital feedback
controller C(z) to stabilize the discretized system in (b).
[5]
(a) Let the Z-transform of a sequence f(k) be F(z) = Σf(k)z^-k. Please prove
that -z(dF(z)/dz) is the Z-transform of sequence kf(k).
(b) What is the Z-transform of the sequence (k^2)f(k) in terms of F(z)?
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