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RK INSTITUTE OF TECHNOLOGY
INSTITIÚID TEICNEOLAÍOCHTA CHORCAÍ
Semester 2 Examinations 2010
Module Title: Control Engineering and Automation Systems
Module Code: MECH
School: Mechanical and Process Engineering
Programme Title: Bachelor of Engineering (Honours) in Mechanical Engineering
Programme Code: EMECH_8_Y
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:
- 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.
- 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)
- (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)( )
G s H s K T s T S s
=
Comment on the stability of the system. (10 marks)
If T 1 = 0.2, T 2 = 0.5 determine the value of K that will give a Gain Margin of 20 dB. (5 marks)
- (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 m^3 /s per mA
τv = Control valve time constant = 20 s A = Tank area = 10 m^2 R = Outlet hydraulic resistance = 0.069 m^3 /s per m
τT = Transmitter time constant = 5 s (15 marks)
- (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)
Figure Q
Fig. Q
Q 2
Hact
Tank
Qd LY 102
LIC 102
LT 102
Hset
Q 1
LCV 102
Qd (s)
Hset (s)
Ksp Gc(s) Kv τv s+
As+R
Control Valve
Set Point Controller conversion
τT s+
Transmitter
Hact(s)
Tank Dynamics Q 1 (s)
2(s+5) s
2 e − sT
s + 2
Actual blood pressure
Desired blood pressure
Anaesthetic Controller
Body dynamics
Sensor
Figure Q
-2 (^1 )( 10 1 )
s s s
+- G s
R(s) C(s)
Figure Q
