DUBLIN INSTITUTE OF TECHNOLOGY
Kevin Street, Dublin 8.
SCHOOL OF CONTROL SYSTEMS AND ELECTRICAL ENGINEERING
Solution Sheet
Course/Year
Subject
Examiner
DT009 Year 3
Control and Automation Minor
Gavin Duffy
Question No.
1
Examination
Sitting
Page 1 of 7
Semester 1
2005/2006
(i) Open loop - simple, inexpensive. Result of output not measured. Good knowledge of system
required
[2]
Suitable example
[2]
Closed loop - more complicated but better. Output is measured and compared against setpoint to
give an error.
[2]
Suitable example
[2]
Output 
(ii) Integral control -
1
edt
Ti 
[2]
Remembers past history of the error and is used to remove the offset of a proportional controller [2]
Integral windup – a very large cumulative integral result occurs when the error cannot be corrected
(e.g. faulty instrument, valve).
[4]
(iii) Ultimate cycle - set controller to P control only; increase gain until oscillations develop; stop
increasing gain when system becomes unstable
[3]
Process reaction curve - place controller in manual mode; set output to a constant value and allow
system to reach a steady state; make a step change in the output and record the process variable
response with time
[3]
Disadvantage of ultimate cycle is that operates on the borderline of instability - this could cause
damage to plant and/or personnel
[2]
(iv) Step 1 is Self Test – check for errors in hardware/software
Step 2 is Input Scan – Reads input values from input cards to the memory
Step 3 is Execute Logic – each ladder in program is executed and outputs are updated
Step 4 is Output Scan – Writes output values from memory to output cards
[8]
(v) Types of pushbuttons: Start is normally open or press to close switch – done this way so that if
wire breaks motor can’t start. Stop is normally closed or press to open switch – done this way so
that if wire breaks the motor stops (it’s the same as pressing stop button).
[4]
Ladder logic – two ways of doing this.
Option 1 is as follows:
DUBLIN INSTITUTE OF TECHNOLOGY
Kevin Street, Dublin 8.
SCHOOL OF CONTROL SYSTEMS AND ELECTRICAL ENGINEERING
Solution Sheet
Course/Year
Subject
Examiner
DT009 Year 3
Control and Automation Minor
Gavin Duffy
Examination
Sitting
Page 2 of 7
Semester 1
2005/2006
Option 2:
Option 1 or 2
[4]
DUBLIN INSTITUTE OF TECHNOLOGY
Kevin Street, Dublin 8.
SCHOOL OF CONTROL SYSTEMS AND ELECTRICAL ENGINEERING
Solution Sheet
Course/Year
Subject
Examiner
DT009 Year 3
Control and Automation Minor
Gavin Duffy
Examination
Sitting
Page 3 of 7
Semester 1
2005/2006
Question No. 2
(a)
(i) Convert to frequency domain as follows: Starting with:

dTR
 TR  TJ
dt
Applying the Laplace transform to this equation gives:
sTR s   TR s   TJ s 
[2]
The transfer function which is the output over the input is now easily determined:
sTR s   TR s   TJ s 
 TR s 1  s   TJ s 

T R s 
1

TJ s  1  s 
[3]
(ii) We can replace the input TJ(s) in the Laplace transformed equation above with a/s, the Laplace
transform of a step input of magnitude a. The equation now becomes:
T R s  T R s 

T J s 
a s
 T R s  
a 1
1
a
s 1  s 
s 1  s 
1
1
 T R s   a
a
s 1   s 
s s  1  
[5]
(iii) Check the tables to find
 b 
  1  e bt
L1 
 ss  b  
In the above equation, b = 1/ and Ka is a constant so remains unchanged. Therefore:
[2]
DUBLIN INSTITUTE OF TECHNOLOGY
Kevin Street, Dublin 8.
SCHOOL OF CONTROL SYSTEMS AND ELECTRICAL ENGINEERING
Solution Sheet
Course/Year
Subject
Examiner
DT009 Year 3
Control and Automation Minor
Gavin Duffy
Examination
Sitting
 a 
  1  e  at
L1 
 ss  a  
  o  a 1  e t 1  

  o  a1  e


t

Page 4 of 7
Semester 1
2005/2006
[3]


(b)
Above code
Comments
[6]
[4]
Noise is reduced by using the averaged value from the card instead of the present value.
[3]
This requires changing the buffer memory address to read the data from the averaged value and also
requires sending down a number of averages to the buffer memory address for this information. [2]
DUBLIN INSTITUTE OF TECHNOLOGY
Kevin Street, Dublin 8.
SCHOOL OF CONTROL SYSTEMS AND ELECTRICAL ENGINEERING
Solution Sheet
Course/Year
Subject
Examiner
DT009 Year 3
Control and Automation Minor
Gavin Duffy
Question No.
3
Page 5 of 7
Examination
Sitting
Semester 1
2005/2006
(i) Convert the system into a single block to give the equation below:
the overall output over input = transfer function
the static gain is above the line
the time constant is the constant in the s term
[4]
[4]
[4]
KpK
KpK
KpK
1 K pK
 o s 
 s  1 

K p K s  1  K p K

 i s 
1 s
1
1 K pK
s  1
(ii)
 new 
1


10
1 K pK
 10  1  K p K
 KpK  9
 Kp 
9
3
3
i.e. proportional gain = 3
[5]
At steady state we have:
KpK
 o s 
9


 0.9
 i s  1  K p K 1  9
  o s   0.9 i s 
E ( s) steadystate   i s    o s    i s   0.9 i s   0.1 i s 
Therefore, the error is 10% of the input.
[5]
(iii) Proportional offset is the steady state error observed when using proportional control.
[2]
It can be removed by adding integral action. The integral term acts on the integral of the error and
removes any steady state error.
[2]
(iv) Yes. A high gain may result in overshoot and undershoot oscillations which may not die off.
This causes instability.
[4]
DUBLIN INSTITUTE OF TECHNOLOGY
Kevin Street, Dublin 8.
SCHOOL OF CONTROL SYSTEMS AND ELECTRICAL ENGINEERING
Solution Sheet
Course/Year
Subject
Examiner
DT009 Year 3
Control and Automation Minor
Gavin Duffy
Question No.
4
Page 6 of 7
Examination
Sitting
Semester 1
2005/2006
(i) Block Diagram
[9]
PLC
Error SPPV
i
SP +
o Temp
Controller
On-Off
Process
Water Tank
-
A/D card
Transmitter
RTD
(ii) Error = SP – PV (PV = Temp in this case).
When error is positive, heater is On. When error is negative, heater is Off.
[2]
[2]
(iii) Advantages – cheap, easy to implement, simple, digital output instead of analog
Disadvantages – can’t have PV exactly at setpoint. Frequent switching of output
[2]
[2]
(iii) Add a deadband or hysteresis. Reduces frequency of switching on and off.
[4]
DUBLIN INSTITUTE OF TECHNOLOGY
Kevin Street, Dublin 8.
SCHOOL OF CONTROL SYSTEMS AND ELECTRICAL ENGINEERING
Solution Sheet
Course/Year
Subject
Examiner
(iv)
DT009 Year 3
Control and Automation Minor
Gavin Duffy
Semester 1
2005/2006
Temperature
Temp
off
28ºC
25ºC
22ºC
Examination
Sitting
Page 7 of 7
off
on
on
Power
Time
[6]
Error
+ve
0
-ve
Time
[3]