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RK INSTITUTE OF TECHNOLOGY
INSTITIÚID TEICNEOLAÍOCHTA CHORCAÍ
Autumn Examinations 2009/
Module Title: System Dynamics and Control Engineering
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. Robin Clarke, Mr. Peter Clarke Internal Examiner(s): Dr. Michael J. O’Mahony
Instructions: Attempt 3 questions All questions carry equal marks
Duration: 2 hours
Sitting: Autumn 2010
Requirements for this examination:
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.
- Describe an experiment to investigate the response of a DC motor position control system. Discuss the parameters involved and show how you would optimise the system response.
Illustrate your answer with suitable sketches and block diagrams.
(33 marks)
- (a) The transient response of a control system is determined by the location in the s-plane of the roots of the characteristic equation. Discuss the various root configurations that can occur and illustrate the resulting system response for each case. (15 marks)
(b) What is meant by the dominant root response and under what conditions can it be assumed to occur? (6 marks)
(c) Consider the case of rabbits and foxes in Australia. The number of rabbits is x 1 and if left alone would grow indefinitely (until the food supply is exhausted) so that 1 1
dx kx dt
However, with foxes present on the continent, we have 1 1 2
dx kx ax dt
where x 2 is the number of foxes. Now if the foxes must have rabbits to exist, we have 2 2 1
dx hx bx dt
Determine if this system is stable and thus decays to the condition x 1 (t)=x 2 (t)=0 at t=∞. What are the requirements on a, b, h and k for a stable system? What is the result when k is greater than h? (12 marks)
- On/Off control Proportional Integral Derivative
Discuss the above control actions in relation to industrial control systems. State where these are applicable, describe the effects they have on system response and comment on their practical limitations. (18 marks)
In the absence of velocity feedback (i.e. Switch S open) determine the natural frequency n and the damping ratio of the position control system in Fig. Q.5 given the following parameters:
Kp = Proportional gain = 10 Km = Motor/Load Gain Constant = 15 rad/s per V Kpot = Potentiometer Sensitivity = 1.5 V per rad m = Motor/Load Time Constant = 0.2s
Determine the value of tachometer constant Kt which will result in a damping ratio of 0.7 when the switch S is closed. (15 marks)
Fig Q
Percent overshoot and normalized peak time versus damping ratio for a second-order
system
C(s) 1 9
s 6
s^1
R(s)
