Sample Question Paper for 9210-136
Graduate Diploma in Engineering
Control systems
Duration: three hours
You should have the
following for this examination
• one answer book
• non-programmable calculator
• pen, pencil, drawing
instruments
General instructions
• This paper consists of nine questions.
• Answer any five questions.
• A non-programmable electronic calculator may be used but candidates must show
sufficient steps to justify their answers.
• Drawings should be clear, in good proportion and in pencil. Do not use red ink.
• All questions carry equal marks. The maximum marks for each section within a
question are shown.
1
a)
A motor cycle shock-absorber is shown in Figure Q1,
Figure Q1
b)
c)
2
a)
where k and b are spring constant and daming coefficient. Draw the free-body
diagram and derive the ordinary differential equation of the shock-absorber
dynamic model.
Derive the transfer function G(s)=Y(s)/F(s) of the shock-absorber, where Y(s)
and F(s) are the Laplace transforms of response y(t) and External force f(t).
Determine the characteristic equation of the shock-absorber for k=125 N/cm,
b=700 Ns/cm, and m=50 kg, and determine the poles of the shock-absorber model.
(6 marks)
(8 marks)
(6 marks)
A feedback control system through a single feedback gain is shown below.
Figure Q2
b)
c)
Derive the closed loop transfer function Gc(s)=G(s)/(1+KG(s)) and show that closed
loop poles can be positioned using feedback gain K.
For G(s)=3/(s2+4s+3), determine the value of K for closed loop system to be
critically damped.
Show that an additional gain of K+1 is needed to maintain zero steady state error.
2
(6 marks)
(6 marks)
(8 marks)
3
a)
A robot arm open loop control system is shown below with the transfer function.
Figure Q3
kτ/n
Θ(s) =
[(R+Ls)(Jeqs+beq)+kτkBs]s
V(s)
b)
c)
4
a)
b)
c)
d)
5
a)
b)
c)
d)
Draw the unity gain negative feedback control block diagram and determine the
closed loop transfer function of the robot arm.
Determine the closed loop transfer function assuming following parameters:
L = 0.062 H, R = 2.5 Ω, n = 20, kτ = 0.026 Nm/A,
kB = 0.02 Vs/rad, Jeq = 0.00004 kg/m2, beq = 0.001 Nms/rad.
Determine the steady state error of the robot arm for a unit step input.
The root locus design method is used to locate poles at desired locations.
However, it is not possible to locate poles arbitrarily. Provide reasons for
this statement.
Derive the gain and phase criteria of the root locus design method.
For the open loop plant G(s)=1/(s+3)(s2+6s+20), determine the following:
i)
parts of the root locus on the real axis
ii) asymptote angles
iii) asymptote intersection point.
Sketch the root locus.
Determine the maximum stable feedback gain using the Routh array method.
A second order control system is given by the transfer function G(s)=24/(s2+3s+43).
Determine the natural undamped frequency ωn and damping ratio ζ.
Determine the followings for unit step input.
i)
Rise time and settling time.
ii) 1% settling time.
iii) Peak overshoot.
Derive the state space model of the system.
Check the controllability and observability of the system.
3
(6 marks)
(8 marks)
(6 marks)
(4 marks)
(4 marks)
(3 marks)
(3 marks)
(2 marks)
(4 marks)
(5 marks)
(1 mark)
(2 marks)
(2 marks)
(5 marks)
(5 marks)
See next page
6
a)
b)
Describe phase margin and gain margin referring to frequency domain
controller design.
The Bode plots of the plant represented by (s+5)(s+6)/{(s3+14s2+13s+2)(s2+13s+2)}
are shown below in Figure Q6.
A phase lag of -180° is observed at 0.6 rad/s and 0 dB gain is observed at 0.4 rad/s
(4 marks)
Figure Q6
c)
d)
7
a)
b)
8
a)
b)
c)
Determine the gain margin and phase margin.
What is the gain required to improve the control bandwidth to 3 rad/s?
Propose a method to keep the system stable after the bandwidth adjustment.
(8 marks)
(4 marks)
(4 marks)
i)
Explain the term PID controller. Illustrate it with an aid of a block diagram.
ii) For what type of system is a PID controller suitable?
iii) Give a practical example of a PID controller.
Define the following terms explaining their differences.
i)
Precision and accuracy.
ii) Repeatability and reproducibility.
(8 marks)
(2 marks)
(2 marks)
State an advantage and a limitation of using thermistors over thermocouples.
If a work piece is to be moved by applying a constant force of 100 kN through
a distance of 60 cm with a duration of 12 sec.
i)
Calculate the energy required and the average power.
ii) Assuming that a hydraulic cylinder is to be used that has a diameter of 1 m,
find the required pressure and the average flow rate.
An incremental encoder is used to calculate the speed of a D.C.
(Direct Current) motor.
i)
Explain the disadvantage of using this method when the motor speed is not
a constant.
ii) Name a transducer that can overcome the disadvantage mentioned above
in part c) i).
iii) Sketch outputs from the encoder for a unit time interval, when the motor
is running at high speed as well as at low speed to illustrate the difference.
(2 marks)
4
(4 marks)
(4 marks)
(4 marks)
(4 marks)
(4 marks)
(2 marks)
(4 marks)
9
A pressure transducer gives 2 V at 0.5 bar and 6 V at 1.5 bar and assume that it linearly
varies between pressure values. It is required to measure the atmospheric pressure
that is expected to vary between 0.95 bar and 1.05 bar.
a) Find the measuring range of the transducer and the expected voltage generated
at 0.95 bar and 1.05 bar.
b) The output from the pressure transducer has to be conditioned in such a way that
when the pressure is lowest (0.95 bar) it should give 0 V output and when the
pressure is highest (1.05 bar) it should give 10 V output.
i)
Find the amplification and the level shifting required to conduct this task.
ii) Sketch a circuit with operational amplifiers and resistors that satisfy the
requirement of an inverting amplifier.
iii) After the amplification and level shifting, it is to be supplied to an analogue
to digital converter (ADC). Find the minimum number of bits that should be
used in ADC, if the required resolution is 0.001 bar.
5
(4 marks)
(4 marks)
(8 marks)
(4 marks)