# 程序代写案例-ELEC4632

The University of New South Wales
School of Electrical Engineering and
Telecommunications
ELEC4632 Computer Control Systems
Final Examination,
Term 3, 2020
1. Time allowed : 2 hours
2. Reading time : 10 minutes
3. Scanning time : 15 minutes
4. Total exam duration: 9:30am – 11:55am (Sydney time).
5. The paper contains 6 questions (60 marks in total).
6. Each question has the value indicated.
7. This exam contributes 60% to the course final mark.
8. Candidates should attempt all questions.
9. This is an open book examination.
10. This paper contains 4 pages.
11. Please combine answers in one pdf file, name the file by zID first
name family name, and click the submit button before the due
time.
1
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NO collaborations allowed and the work submitted must be
your own. During the exam you may NOT be in contact with
anyone else via any form of communication media (email, messag-
ing, phone, video conferencing, etc). Violating this will be consid-
ered an academic misconduct and disciplinary action will be taken
against anyone who is proven to have violated this rule.
ANSWERS MUST BE WRITTEN IN INK. EXCEPT WHERE THEY
ARE EXPRESSLY REQUIRED, PENCILS MAY ONLY BE USED FOR
DRAWING, SKETCHING OR GRAPHICAL WORK.
2
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Question 1 (10 marks)
Sample the continuous-time system
x˙(t) =
(
0 4
0 −1
)
x(t) +
(
0
1
)
u(t− 1.35),
y(t) =
(
1 −2
)
x(t)
using the sampling interval h = 0.3.
Question 2 (10 marks)
A discrete-time control system is described by
x(k + 1) =
 1.5 0 3a1− a −2a2 19
−3.0 0 1.7
x(k), y(k) =
 0.5 + a
2 0 3.1
8− a a− 10 1
0.4 0 3− a
x(k).
where the parameter a varies from −∞ to∞. Determine for which values of
a this system is observable.
Question 3 (10 marks)
Given the system
x(k + 1) =
(
1.2 0.4
0.6 0.3
)
x(k) +
(
2
0
)
u(k),
y(k) =
(
−2 3
)
x(k).
Design
(b) state estimator with the poles 0.0 and −0.25.
3
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Question 4 (10 marks)
(a) The characteristic equation of a discrete-time control system is
given by
z2 + (3K − 1)z +K = 0
where K varies from −∞ to ∞. Determine the range of K for stability.
(b) The characteristic equation of a discrete-time control system is
given by
z3 + 1.4z2 + 0.75z + 1.05 = 0.
Determine the number of characteristic roots outside the unit disk without
calculating them. Is this system stable?
Question 5 (10 marks)
Consider the following nonlinear discrete-time system of the form
x1(k + 1) = x1(k) + x2(k)
2 − 1, x2(k + 1) = 3x1(k)2 + sin(pix2(k)) + x2(k).
Find all singular points of this system and study their stability.
Question 6 (10 marks)
Consider the optimal control problem for the system
x(k + 1) = −3x(k) + u(k)
with initial condition x(0) = 0.8, the cost function
J =
∞∑
k=0
x2(k)→ min
and the constraint
|u(k)| ≤ 2.
Determine the optimal control strategy and the optimal value of the cost
function.
4
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