# Bode Plot Control Engineering and Automation Systems - Exam, Exams for Engineering Materials. Chhattisgarh Swami Vivekanand Technical University

## Engineering Materials

Description: Main points of this past exam are: Bode Plot, Represents, Phase Margin, Gain Margin, Comment, Unit Step Input, Damping Ratio
Showing pages  1  -  4  of  13
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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.
Page 2 of 13
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;
12
() () (1)( 1)()
K
GsHs Ts 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:
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
(15 marks)
Page 3 of 13
(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:
GsHs s
ss
() () (. )
()
=
+
+
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)
Page 4 of 13
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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