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Cork Institute of Technology
Bachelor of Engineering (Honours) in Mechanical Engineering- Award
(NFQ Level 8)
Summer 2007
Systems Engineering and Control
(Time: 3 Hours)
Answer any FIVE Questions Examiners: Prof. M. Gilchrist ALL questions carry equal marks. Mr. P. Clarke Dr. M. J. O’Mahony
Q1. (a) A process control system has the following open loop transfer function;
G s H s (^) s s Kes
s ( ) ( ) = (^) ( + )( + )
− 2 1 10 (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)
Q2. A unit feedback control system has the following open loop transfer function:
G s H s( ) ( ) = (^) ( s + K s ( 2^ )( + s^8 − ) 2 )
(a) Construct the Nyquist plot for the system (assume initially K=1). (15 marks) (b) Determine how the system stability is influenced by the value of K. (5 marks)
Q3. (a) An automatic level control system for an effluent treatment plant is shown in Fig. Q3. 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 Q (^) d ). 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 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 (12 marks) (b) A disturbance flow stream Q (^) d will on occasion enter the system. Suggest a suitable control strategy that will minimise the effect of the disturbance flow on the tank level H (^) act. 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)
Q4. (a) What are the underlying assumptions when using describing function analysis to model the behaviour of non-linear systems? How can these assumptions be verified in practice? (5 marks) (b) Investigate the behaviour of the non-linear servo system shown in Fig. Q4 as the process gain K 1 varies from 0 to ∞. If K 1 = 50 determine the output c(t) of the system if the input r(t) = 0. (15 marks)
Q5. (a) A digital speed control system is shown in Figure 5. Transform this diagram to the z-domain and obtain the transfer function R(z)/C(z). (14 marks) (b) Determine the closed loop response to a step input R z ( ) = (^) z − z 1 for the first six sampling instants. (6 marks)
Fig Q
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 T (^) U = Ultimate Period
M
m
K τ
Q 2
H (^) act
Tank
LY Q^ d 102
H (^) set LIC 102 LT 102
Q 1
LCV 102
Q (^) d (s) H (^) set (s) K (^) sp G (^) c(s) K^ v τv s+
As+R
Control Valve
Set Point Controller conversion
τTs+
Transmitter
H (^) act (s)
Tank Dynamics Q 1 (s)
Fig Q
Fig Q
Fig Q
1 − e − s
R(s) Ts C(s)
T = 0.5 s ZOH
Motor/Load 1 s + 1
K
s s s
1
R(s) K=3 C(s)
Amplifier G (^) p (s) Process
