ELEC4632 : Computer Control Systems - S2 2012
Mid-term Test
Question 1 (6marks)
Find discrete time pulse transfer function of the following sampled system for sampling interval
h = 0.1 and a = 1
Figure 1: Sampled system
Solution:
K
K(1 ehs )
1 ehs
= 2
s
s
8 CONTROLLER DESIGN USING OPTIMAL CON-
TROL TECHNIQUES
8.1 Introduction
The subject of this chapter is the use of optimal control techniques for design of digital
controllers. Optimal control design tools have a number of important advantages:
1. They eas
Tutorial 2 (Elec 4632)
Question 1: Determine the characteristic equation of the following matrix:
1 2
.
A=
3 5
Also, show that the matrix A satisfies its own characteristic equation.
Question 2: Consider the discrete-time dynamic system
x(k + 1) = Ax(k)
Tutorial 1 (Elec 4632)
Question 1: Find the rank of the following
1
1 1 1
2
A = 1 2 2 ; B =
2
1
1 2 3
3
matrices:
2 3
1
2
1
1
6 8
6 0
; C = 2 4 2 2
3 6 3 4
2 5
8 6
Do they have full rank?
Question 2: Find the rank, the range and the null space of the m
7H El Que-ITIOIl/J
%
/Question 1 (6 marks)
Explain what is sampling creates new frequencies phenomenon in digital control.
/Question 2 (7 marks)
Given the system
2.5 7.0 2
k+1 = k k,
x( ) (417 0.85 )d (0%
Design deadbeat output feedback-feedback controlle
Question 6 ('7 marks)
Consider a linear discretetime system and a quadratic cost function. Assume that the control
input is required to satisfy a constraint of the form:
luch 5 A. Show that if, in the solution to
the optimal control problem, only the rst
ELEC4632 : Computer Control Systems - S2 2012
Mid-term Test
QUESTION 1
(6 marks)
Find discrete time pulse transfer function of the following sampled system for sampling interval
h = 0.1 and a = 1
Figure 1: Sampled system
QUESTION 2
(4 marks)
Check the sta
QUESTION 1
(12 marks)
a) Derive the discrete time system corresponding to the following continuous time system
when a zero-order-hold circuit is used:
du
d2 y dy
6y = 12
6u
2
dt
dt
dt
(4 marks)
b) Derive the discrete time state space model if the follow
School of EE& Telecommunications, University of New South Wales (UNSW), Sydney, Australia
Chapter 7:Case Study 1
Non-invasive estimation
and deadbeat control of
pulsatile flow in an
implantable
p a tab e rotary
ota y b
blood
ood
pump for heart failure
pat