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CORK INSTITUTE OF TECHNOLOGY
INSTITIÚID TEICNEOLAÍOCHTA CHORCAÍ
Semester 1 Examinations 200 11 / 12
Module Title: Process Automation & Control
Module Code: MECH
School: Engineering (Mechanical Engineering Department)
Programme Title: Bachelor of Science (Honours) in Process Plant Technology – Year 4
Programme Code: EPPTE_8_Y
External Examiner(s): Mr Kevin McCarthy, Mr Ger Reilly 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 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) 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 voltage on a DC motor control system was changed from 6V to 24V. 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 (sec)
Motor Speed (t) (rpm) 0 450 0.05 452 0.10 830 0.15 1100 0.20 1300 0.25 1450 0.30 1600 0.55 1750 0.80 1790 1.00 1800 1.25 1800 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 1.
Time
Error
0 Figure 1 (6 Marks)
Question 3: a) A unit feedback system has the following open-loop transfer function G s ( ) = (^) s s ( K +^ p 10)
Determine the value of Kp so that the system will have a damping factor of 0.7. (12 Marks)
b) 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)
c) A process is described by the second order transfer function with K 5 , n 2 and 0. 7
. If the process is controlled by a proportional only controller with gain Kp 0. 5 using negative feedback, calculate the closed loop transfer function. (6 Marks)
Question 4:
(a) Draw a clear and labelled block diagram representing a complete single negative feedback loop. (7 Marks)
(b) Explain what is meant by the Transfer Function of a System with respect to process control. Illustrate your answer with an appropriate diagram. (3 Marks)
(c) Derive the transfer function for the process described by the differential equation
y t u t dudt t^ u tdt
t
Where u t and y t are the process input and output respectively
(3 Marks)
(d) What is the order of the transfer function derived in (c) (2 Marks)
(e) 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)
(f) 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. (5 Marks)
Question 6:
(a) Using the PID algorithm
t p (^) ip p d dt C ct K et K etdt K det 0 0
show that its transfer
function is given by
G (^) c s Kp is ds 1 1. State clearly any assumptions made and
explain the terms Kp, Ti and Td. (10 Marks)
(b) Figure 3 shows the response of a second order under-damped system. Determine the transfer function parameters for this second order system.
Figure 3 (15 Marks)
Ziegler Nichols Tuning Parameters Process Reaction Curve Method (Open loop) Controller Type Kp Ti Td
Proportional-only d^ K
Proportional + Integral 0.9^ d^ K 3.33^ ^ d
PID 1.2^ d^ K 2 d 0.5 d
d = Dead time (Estimate)
= Process time constant
K = Steady State Gain =Controller OutputProcess Output
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 1 e ( 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
