# Open Loop Transfer Function - System Engineering and Control - Exam, Exams for Systems Engineering. Acharya Nagarjuna University

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The key points are:Open Loop Transfer Function, Time Constant, Transmitter Time Constant, Disturbance Stream, Block Diagram, Load Gain Constant, Load Time Constant, Tachometer Gain, Sampling Time, Cascade Control
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Cork Institute of Technology

Bachelor of Engineering (Honours) in Mechanical Engineering - Award

(NFQ – Level 8)

Autumn 2006

Systems Engineering and Control

(Time: 3 Hours)

Answer any FIVE Questions Examiners: Prof. M. Gilchrist ALL questions carry equal marks. Mr. J.E. Hegarty Dr. M. J. O’Mahony 1. (a) A process control system has the following open loop transfer function;

G s H s Ke

s s s

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)

2. A unit feedback position control system has the following open loop transfer

function:

G s H s s

s s ( ) ( )

( . ) ( )

= + +

20 01 1 4

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? (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 (12 marks) (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.

(8 marks)

4. Fig Q.4 shows the block diagram representation of the liquid level control system in a steam boiler drum. Under certain conditions this system will exhibit an “inverse response”. Explain what this means and determine the conditions under which it will occur. (15 Marks)

How can the control system be modified to compensate for this effect?

(5 Marks)

5. Figure 5 shows a digital speed control system. Given that D(s)=KP transform this diagram into the Z-domain and plot the root locus for the system. Hence determine the limiting value of KP for stability and the value of KP that will result in an underdamped response with a damping ratio of 0.5.

Data

τm = Motor/Load time constant = 0.4 s

Kt = Tachometer gain = 2.4 V per rad/s

T = Sampling Time = 0.01 s

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 (8 marks)

(ii) Consider the system shown in Fig 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. (12 marks)

7. Write detailed technical accounts on any TWO of the following:

(ii) Tuning PID Controllers

(iii) Feed Forward Control

(2 x 10 marks)

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

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)

Fig. Q3

HO(s) +- -

+

Swell

Hset(s) Gc(s)

K1 s

K2 τ2s+1

Controller

Boiler Drum Dynamics

Shrink

Fig. Q4

Fig. Q5

2

-2 )110 )(1(

10)( ++

= sss

sG - +

R(s) C(s)

Fig Q6

- 1− −e s

Ts

VC(s)

T = 0.01 s

ZOH

+ D(s)

Digital Filter

1 m

m

K sτ +

Kt

Tacho