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CORK INSTITUTE OF TECHNOLOGY
INSTITIÚID TEICNEOLAÍOCHTA CHORCAÍ
Semester 1 Examinations 2009/
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. Neil Kingston, Mr. Joe Phelan Internal Examiner(s): Dr. Marcin Cychowski Mr. Conor O’Farrell
Instructions: Answer any 4 from 6. All questions carry equal marks. 25 Marks per question
Duration: 2 Hours
Sitting: Winter 2009
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) Many processes employ a three term (PID) controller. Explain what is meant by
proportional (P), Integral (I) and Derivative (D) action. (6 Marks)
b) The following open-loop response data was recorded when the input volumetric flow rate on a level control system was changed from 0.02m^3 /min to 0.05m^3 /min. Using the
Ziegler-Nichols process reaction method (and the table provided), determine the optimal P, PI and PID controller settings for this application.
(13 Marks)
Time (min)
Output Height h(t) (cm) 0 16. 1 16. 2 16. 3 28. 4 34. 5 37. 6 39. 7 40. 8 41. 9 41. 10 41. 11 41. 12 41.
c) Sketch the output of the controller having proportional, integral and derivative action
(each considered in isolation) for the error signal (controller input) depicted in Figure
(6 Marks)
Time
Error
0
Figure 1
Question 3:
a) Calculate the closed-loop transfer function Y ( s )/ R ( s ) for the block diagram in Figure 3. (9 Marks)
Figure 3
b) In general terms, a second order system is defined by the transfer function
2 2
2
2
n n
n s s
K
Gs
Define each of the terms K , ω n and ζ and briefly explain the effect that each of these
parameters would have on the step response of the system. (7 Marks)
c) A process is described by the second order transfer function with K = 2 , ω n = 0. 5 and
ζ = 0. 4. If the process is controlled by a proportional only controller with gain
K (^) p = 1. 5 using negative feedback, calculate the closed loop transfer function.
(9 Marks)
Page 5 of 11
Question 4:
(a) Draw a clear and labelled block diagram representing a complete single negative feedback
loop.
[7 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.
[7 Marks]
(c) For a proportional controller
1) What gain corresponds to a PB% of 20%
2) What PB corresponds to a gain of 5?
[4 Marks]
(d) In a heat exchange process, steam is transported through a pipe of length d = 132m with
uniform cross-sectional area of A = 0.27 m^2. If the dead time in transporting the steam
through the pipe is τD = 1.75 s, calculate the flow rate.
[7 marks]
Page 7 of 11
Question 6:
(a) Using the PID algorithm ( ) ( ) ( )
t p d i
p
p C
dt
det
etdt K
K
ct K et
0
0 show that its transfer
function is given by ( )
= + s
s
G s K d
i
c p
1. State clearly any assumptions made and
explain the terms Kp, Ti and Td.
[10 Marks]
(b) Figure 4 shows the response of a second order under-damped system. Determine the transfer
function parameters for this second order system.
Figure 4
[15 Marks]
Page 8 of 11
Ziegler Nichols Tuning Parameters
Process Reaction Curve Method (Open loop)
Controller Type K^ p Ti^ Td
Proportional-only
d K
Proportional + Integral 0.^
d K
3.33 τ d
PID 1.^
d K
2 τ d 0.5 τ d
τ d = Dead time (Estimate)
τ = Process time constant
K = Steady State Gain =
Process Output
Controller Output
