# Open Loop Transfer Function - System Engineering and Control - Exam, Exams for System Engineering. Acharya Nagarjuna University

## System Engineering

Description: The key points are:Open Loop Transfer Function, Time Constant, Transmitter Time Constant, Disturbance Stream, Block Diagram, Load Gain Constant, Load Time Constant, Tachometer Gain, Sampling Time, Cascade Control
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Cork Institute of Technology
Bachelor of Engineering (Honours) in Mechanical Engineering -
Award
(NFQ – Level 8)
Autumn 2006
Systems Engineering and Control
(Time: 3 Hours)
Answer any FIVE Questions Examiners: Prof. M. Gilchrist
ALL questions carry equal marks. Mr. J.E. Hegarty
Dr. M. J. O’Mahony
1. (a) A process control system has the following open loop transfer function;
GsHs Ke
ss s
s
() () ()( )
=
++
2
110
(i) Assuming initially K=5, plot the bode diagram and determine the gain margin
and phase margin for the system. Comment on its stability.
(10 marks)
(ii) What value of K will result in a phase margin of 60o and what would be the
corresponding gain margin?
(4 marks)
(b) Explain how dead-time compensation can be introduced to improve the
performance of control systems such as (a) above.
(6 marks)
2. A unit feedback position control system has the following open loop transfer
function:
GsHs s
ss
() () (. )
()
=
+
+
20 01 1
4
Determine the following closed loop frequency response parameters:
(i) Resonant Peak Mr
(ii) Resonant frequency ωr
(iii) System Bandwidth ωb (15 marks)
Comment on the values obtained and hence sketch the expected response to a unit
step input in the time domain? (5 marks)
3. (a) An automatic level control system for a effluent treatment plant is shown in
Fig. Q 3. Explain briefly the operation of the system and tune the controller to
give PI control of the tank level (ignore for the present the effects of the
disturbance flow Qd). The following parameters relate to the system block
diagram:
K
sp = Set point conversion factor = 4mA per m
K
v = Control valve coefficient = 0.028 m3/s per mA
τv = Control valve time constant = 20 s
A = Tank area = 10 m2
R = Outlet hydraulic resistance = 0.069 m3/s per m
τT = Transmitter time constant = 5 s
(12 marks)
(b) A disturbance flow stream Qd will on occasion enter the system. Suggest a
suitable control strategy that will minimise the effect of the disturbance flow on
the tank level Hact. The disturbance stream cannot be controlled but it can be
measured. Show the implementation of your proposed control strategy on a
modified block diagram of the system.
(8 marks)
4. Fig Q.4 shows the block diagram representation of the liquid level control system
in a steam boiler drum. Under certain conditions this system will exhibit an
“inverse response”. Explain what this means and determine the conditions under
which it will occur. (15 Marks)
How can the control system be modified to compensate for this effect?
(5 Marks)
5. Figure 5 shows a digital speed control system. Given that D(s)=KP transform
this diagram into the Z-domain and plot the root locus for the system. Hence
determine the limiting value of KP for stability and the value of KP that will
result in an underdamped response with a damping ratio of 0.5.
Data
K
τm = Motor/Load time constant = 0.4 s
K
t = Tachometer gain = 2.4 V per rad/s
T = Sampling Time = 0.01 s
6. (i) Outline the assumptions upon which the describing function method for
analysis of non-linear control systems is based. Show how it can be used to
predict the occurrence of limit cycles and how stable and unstable limit cycles can
be distinguished (8 marks)
(ii) Consider the system shown in Fig Q6 in which the non-linearity is an ideal
relay. Investigate the possibility of a limit cycle in this system. If a limit
cycle is predicted determine its amplitude and frequency and investigate its
stability. (12 marks)
7. Write detailed technical accounts on any TWO of the following:
(ii) Tuning PID Controllers
(iii) Feed Forward Control
(2 x 10 marks)
Ziegler Nichols tuning Parameters
Control Mode Proportional Gain
KP
Integral Time
Ti
Derivative Time
Td
P 0.5 KPU - -
PI 0.45 KPU 0.83 TU -
PID 0.6 KPU 0.5 TU 0.125 TU
KPU = Ultimate Gain
TU = Ultimate Period
Q2
Hact
Tank
Qd
LY
102
LIC
102
LT
102
Hset
Q1
LCV
102
+
-
+
+
Qd(s)
Hset(s)
Ksp Gc(s) Kv
τ
vs+1
1
As+R
Control
Valve
Controller
Set Point
conversion
1
τTs+1
Transmitter
Hact(s)
Tank
Dynamics
Q1(s)
Fig. Q3
HO(s)
+
- -
+
Swell
Hset(s)
Gc(s)
K1
s
K2
τ
2s+1
Controller
Boiler Drum Dynamics
Shrink
Fig. Q4