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CORK INSTITUTE OF TECHNOLOGY
INSTITIÚID TEICNEOLAÍOCHTA CHORCAÍ
Semester 7 Examinations 200 10 / 11
Module Title: Process Automation & Control
Module Code: MECH
School: Engineering (Mechanical Engineering Department)
Programme Title: Bachelor of Science (Honours) in Process Plant Technology
Programme Code: CR_EPPTE_
External Examiner(s): Mr. Ger Reilly, Mr. Pat Ryan 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: Winter 2010
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 ^ u tdt dt yt ut dut^ t 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) Show that the RC electrical system in figure 2 obeys first order dynamics and calculate its
transfer function. The input voltage is vi t , vo t is the voltage across the capacitor C
and i t is the current in the circuit.
vo t
Figure 2 [5 Marks]
(b) Consider a first order process represented by the transfer function
s
G s kss (^) p. What
do the symbols kss and represent? Sketch the typical response curve obtained from a
first order process given that kss 0. 95 and 1. 2 s
[5 Marks]
(c) A critically damped second order process has a steady state gain of 1 and a natural radiancy of 20 rad/s. It is controlled by a P-Only controller with gain kp using negative feedback. Derive the closed loop transfer function for the system. [7 Marks] (d) Determine the value of kp if the closed-loop response is to have a maximum percentage overshoot of 10% [8 Marks]
R
i(t) C
Question 4
(a) Reduce the block diagram in figure 3 to canonical form.
Figure 3 [12 Marks]
(b) If a process described by the transfer function (^22)
2 (^2) p np np
np
Gp s s s
is controlled
by a proportional only controller using negative feedback, show that n np 1 kp ,
p
p ss (^) k
k k
and p
p k
[13 Marks]
R +
G 3
H 1
G 4
H 2
G 2
Page 7 of 10
Question 6
a) In general terms, a second order system is defined by the transfer function
2 2
2 2
n n
n s s
Gs K
Define each of the terms K , n and and briefly explain the effect that each of these
parameters would have on the step response of the system. (7 Marks)
b) Write a brief but concise technical description of
- Settling Time
- Rise Time
(6 Marks)
c) A process is described by the second order transfer function with K 2 , n 0. 5
and 0. 4. If the process is controlled by a proportional only controller with gain
Kp 1. 5 using negative feedback, calculate the steady-state error for a unit-step input. (12 Marks)
Page 10 of 10
Laplace Transform of common functions
Time-domain function Laplace domain function f(t) F(s)
0 0 ( )^10 t ut t s
1
C s
C
f ( t d ) e s^ dF ( s ) t 2
1 s
dt
df sF^ (^ s ) f (^0 )
0
( )
t ^ f^^ ^ d ^1 s^ F s ( ) e at s a
1
te at ( )^2
1 s a t (^) e at 2
2 ( )^3
1 s a
t e
1 ( 1 )
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
