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RK INSTITUTE OF TECHNOLOGY INSTITIÚID TEICNEOLAÍOCHTA CHORCAÍ
Semester 2 Examinations 2010
Module Title: Control Engineering and Automation Systems Module Code: MECH8001
School: Mechanical and Process Engineering Programme Title: Bachelor of Engineering (Honours) in Mechanical Engineering Programme Code: EMECH_8_Y4 External Examiner(s): Prof. R. Clarke, Mr. J.T. Hayes Internal Examiner(s): Dr. Michael J. O’Mahony Instructions: Attempt 4 questions All questions carry equal marks Duration: 2 hours Sitting: Summer 2010
Requirements for this examination: 1. Nichols Chart Chartwell Graph data ref. 7514 (copy attached) 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.
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1. Fig Q.1 relates to the control of drug-induced unconsciousness associated with anaesthetics used in surgery. Problems are encountered with large differences in patient response. The block diagram represents a model for the control of arterial blood pressure
(a) Construct the Bode plot for the system as ω varies from 0.01 to 100 rad/s and hence
obtain the gain margin and phase margin when T = 0.05 sec. (15 marks)
(b) Repeat the above for the case where T = 0.1 sec and comment on the results obtained.
(5 marks) (c) Predict the damping ratio and the expected response to a unit step input for both cases (a)
and (b) above. (5 marks)
2. (a) State and discuss the Nyquist Stability Criterion. (10 marks)
(b) Plot the Nyquist Contour for the system with the following open loop transfer function;
1 2 ( ) ( )
( 1)( 1)( ) KG s H s
T s T S s =
+ +
Comment on the stability of the system.
(10 marks)
If T1 = 0.2, T2 = 0.5 determine the value of K that will give a Gain Margin of 20 dB. (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:
Ksp = Set point conversion factor = 4mA per m
Kv = 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
(15 marks)
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(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.
(10 marks)
4. Consider the digital control system show in Figure 4. A proportional control algorithm is used giving D(s)=2. The sampling period T=0.1s.
(i) Determine the closed loop transfer function
Θ Θ
L
R
z z
( ) ( )
(15 marks)
(ii) Obtain the output response to a unit step input at the first three sampling instants. What will be steady state response to this input?
(10 marks) 5. A unit feedback position control system has the following open loop transfer function:
G s H s s
s s ( ) ( )
( . ) ( )
= + +
20 01 1 4
The open loop Bode Diagram for this system is shown in Figure Q5.
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. (10 marks)
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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.
(15 marks)
(ii) Consider the system shown in Figure 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. (10 marks)
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Figure Q1
Fig. Q3
Q2
Hact Tank
Qd LY 102
LIC 102
LT 102
Hset
Q1
LCV 102
+- + +
Qd(s) Hset(s)
Ksp Gc(s) Kv τvs+1
1 As+R
Control Valve
Controller Set Point conversion
1 τTs+1
Transmitter
Hact(s)
Tank Dynamics
Q1(s)
- 2(s+5)
s e sT−2
2 2s +
Actual blood pressure
Desired blood pressure
Anaesthetic Controller
Body dynamics
Sensor
+
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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
Figure Q4
- D(s) 1− −e
s
Ts 10 0 4 1s s( . )+
ΘL(sΘR(s) Digital ZOH
+
Plant
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Figure Q5
2
-2 )110 )(1(
10)( ++
= sss
sG - +
R(s) C(s)
Figure Q6
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