Download Exam Paper: Energy Systems Control (MECH8003) for BSc (Hons) in Sustainable Energy Tech and more Exams Energy Efficiency in PDF only on Docsity!
CORK INSTITUTE OF TECHNOLOGY
INSTITIÚID TEICNEOLAÍOCHTA CHORCAÍ
Semester 7 Examinations 20 10 / 11
Module Title: Energy Systems Control
Module Code: MECH80 03
School: Engineering (Mechanical Engineering Department)
Programme Title: Bachelor of Science (Honours) in Sustainable Energy Technology
Programme Code: ESENT_8_Y
External Examiner(s): Prof. E. Coyle, Mr. R. Linger Internal Examiner(s): Mr. Conor O’Farrell
Instructions: Answer any 4 from 6. All questions carry equal marks. 25 Marks per question
Duration: 2 Hours
Sitting: Autumn 2011
Requirements for this examination:
Note to Candidates: Please check the Programme Title and the Module Title to ensure that you have received the correct examination paper. If in doubt please contact an Invigilator.
Question 1:
(a) Explain what is meant by the Transfer Function of a System with respect to process control. Illustrate your answer with an appropriate diagram. [5 Marks]
(b) Derive the transfer function for the process described by the differential equation y t u t dudt t^ u tdt
t 11 (^28) 0 Where u t and y t are the process input and output respectively. [5 Marks] (c) Determine the process poles and zeros for the transfer function derived in (b). [2 Marks]
(d) If a proportional controller with gain Kp now controls the process described in (b) above using
positive feedback, derive (1) The Forward Path Transfer Function (2) The Closed Loop Transfer Function Illustrate your answers with appropriate sketches. [8 Marks] (e) Describe what is meant by the terms Open Loop Control and Closed Loop Control when applied to a controller. [5 Marks]
Question 3:
(a) Reduce the block diagram in figure 2 to canonical form.
F
Figure 2 [12 Marks]
(b) Explain how one would calculate the effect load disturbances have on systems. Calculate the relationship between the output C, the input R and the loads disturbances N for the system shown in figure 3.
Figure 3 [13 Marks]
C
R G 1 G 2 G 3
+^ +
N 1 N 2 N^3
R +
G 3
H 1
G 4
H 2
G 2
Question 4:
(a) Write down the transfer function for a second order system, explaining clearly all symbols used. [5 Marks]
(b) Show on one sketch the second order response curves for the following four cases. i. ζ = 0 ii. ζ = iii. 0 ζ 1 iv. ζ 1
[4 Marks]
(c) If a process described by the transfer function (^22)
2
2 p np np
p np
G s s s
is controlled by a
proportional only controller using negative feedback, show that n np 1 kp ,
p ss p
k
k k
1 ^ and p
p
k
^ .
[16 Marks]
Question 6: (a) Draw a clear and labelled block diagram representing a complete single negative feedback loop. [5 Marks] (b) Define the term process lag in relation to process control. Illustrate process lag on a fully labelled diagram for a process which experiences a step input change. On the same illustration show a process that experiences the same step input change but also suffers from dead time. [5 Marks] (c) For a proportional controller i. What gain corresponds to a PB% of 20% ii. What PB corresponds to a gain of 5? [5 Marks] (d) Figure 4 shows the response of a second order under-damped system. Determine the transfer function parameters for this second order system.
Figure 4 [10 Marks]
Laplace Transform of common functions
Time-domain function Laplace domain function f(t) F(s)
( )^10
t ut t s
C
s
C
f ( t d ) e s^ dF ( s ) t 2
s
dt
df sF (^^ s ) f (^0 )
0
( )
t ^ f^^ ^ d ^1 s^ F s ( ) e at s a
te at ( )^2
s a t (^) e at 2
2 ( )^3
s a
t 1 e ( 1 )
s s sin t (^2) 2
s cos t s^2 ^2
s
e at sin t ( )^2 ^2
s a e at cos^ t ( )^2 ^2
s a
s a
