Download Advanced Control Exam for Electronic Engineering Students and more Exams Advanced Control Systems in PDF only on Docsity!
Cork Institute of Technology
Bachelor of Engineering (Honours) in Electronic Engineering - Award
(NFQ – level 8)
Autumn 2006
ADVANCED CONTROL
(Time: 2 Hours)
INSTRUCTIONS: Answer any FOUR questions. All questions carry 25 marks.
Examiners: Dr. T O' Mahony Prof. G. Hurley Dr. S. Foley
Q1. (a) Given the model ( ) ( )^ ( ) ( ) ( ) ( ) ( )
y k B z^ u k d C z k A z A z
= − + ξ
derive the minimum variance predictor i.e. the control law that minimises
J k ( ) = E { y k ( + d )^2 }.
[15 marks]
(b) Calculate the minimum variance control law for the system 3 1 1 1 ( ) 0.4^ ( ) 1 0.2 ( ) 1 0.9 1 0.
y k z^ u k z k z z
ξ
− − − − = + + − −
[10 marks]
Q2. Design a digital cascade controller for the system illustrated in Figure Q2. You may assume that the inner controller is a simple proportional controller while the outer controller is to be designed using the method of (Diophantine) pole-placement. The system is sampled every 0.01sec and the process gain is K = 1.5. The design objective is that the overall system should have a bandwidth of approximately 1rad/s.
z −
K
Y 2 (z)
( 0. 998 )
- 5 z^2 z −
D(z)
D(z): unmeasurable disturbance Y 1 (z): primary process variable, measurable Y 2 (z): secondary process variable, measurable
++ Y 1 (z) U(z)
Figure Q2: Block diagram of process model [25 marks]
Q3. Table Q3 records the input, u(k) and output, y(k) data of a system identification experiment. Identify a first-order model from the data and hence design a Diophantine pole-placement controller to yield dead-beat closed-loop dynamics. The controller should be designed to reject step-like disturbances.
k u k y k
Table Q3: Recorded data [25 marks]
Q5. (a) Derive the least squares algorithm. [17 marks]
(b) A recursive least squares algorithm is to be used to identify a servo-motor on-line. An initial step test was applied to the servo-motor and the response of Figure Q5(b) recorded. By considering this data, explain how you would initialise the recursive least squares algorithm.
Time (sec.)
Amplitude
0 0.5 1 1.5 2 2.5 3 0
1
2
3
u(t)
y(t)
Figure Q5(b): Open-loop step response of servo-motor [8 marks]
USEFUL FORMULAS
- damping factor, (^)
=
= 100 2 2 ln
(^2) PO β β π
β ζ
- settling-time, n
ts ζω
