Cork Institute of Technology

Bachelor of Engineering (Honours) in Mechanical Engineering - Award

(NFQ – Level 8)

Autumn 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

1. Fig Q.1 shows a block diagram of chemical reactor system.

(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.

(8 marks) (b) Represent the system response on the Nichols chart and hence determine

the following system parameters:

(i) Gain and Phase Margins (ii) Resonant Peak Mr (iii) Resonant Frequency ωr

(iv) Bandwidth ωb. (8 marks)

(c) Comment on the results obtained and sketch the system response to a unit-step input in the time domain.

(4 marks)

2. (a) State the Nyquist Stability Criterion. (4 marks)

(b) Plot the Nyquist Contour for the system with the following open loop transfer

function;

1 2

( ) ( )( )( 1)( 1)

KG s H ss T s T s

=+ +

Comment on the stability of the system. (8 marks)

(c) If T1 = 0.05, T2 = 0.2 and K =1

i. Find the GM for the system. ii. Determine the value of K that will give a phase margin of 40o.

(8 marks)

3. An automatic temperature control loop for heating methanol using low

pressure steam plant is shown in Fig. Q3. The following parameters relate to the system block diagram:

Kd = Kh= Input/Feedback gain factors = 0.16 mA/oC

Kv = Control valve coefficient = 0.1 Kg/s per mA Ke = Heat Exchange gain = 100 oC per Kg/s (of steam) KT = Sensitivity of TPO to TPi = 1oC/oC τv = Control valve time constant = 5 s τe = Heat Exchanger time constant= 20 s Gc(s) is initially set as a proportional controller. (a)

(i) Determine the closed loop gain (∆TPO(s)/ ∆TP(set)(s)) (ii) Determine the response of the system output to process inlet temperature

disturbance (∆TPO(s)/∆TPi(s)), in the static case only. (iii) Analyse the effect of varying the proportional gain on the methanol outlet

temperature. Assume that TP(set) = 100oC (iv) Analyse the effect of varying the proportional gain on the methanol outlet

temperature due to a disturbance input due to variations in the input temperature of the methanol (∆TPi(s)). Assume that ∆TPi = 10oC (10 marks)

(b) A disturbance due to variations in the input temperature of the methanol (∆TPi(s)) will on occasion enter the system. Suggest a suitable control strategy that will minimise the effect of the disturbance on the process output temperature (TPO(s)). The temperature disturbance cannot be controlled but it can be measured. Show the implementation of your proposed control strategy on a modified block diagram of the system.

How would full dynamic compensation be achieved?

(8 marks) Discuss the factors that would influence the choice of a particular controller configuration. (2 marks)

4. (a) Investigate the behaviour of the relay operated motor control system shown in Figure Q4. Is the system stable? (12 marks)

(b) Assuming r(t)=0 sketch the waveforms corresponding to n(t) and c(t). Comment on the frequency spectrum of these signals. (8 marks)

5. (a) Consider the temperature control system for the large test chamber shown in Figure Q5. Given that D(z)=6, transform this diagram into the Z-domain and hence obtain the open loop transfer function GH(z) and the closed loop transfer function Y(z)/R(z). (14 marks)

(b) Plot the root locus for the system in the z-plane and describe the expected response to a unit step input. (6 marks)

6. (a) In the analysis of digital control systems discuss the relationships between the s-plane, the z-plane and the w-plane. (10 marks)

(b) A microprocessor-based control system with a sampling time T of 0.01 sec. has the following open loop transfer function:

G z H zz

( ) ( ).

.=

−12

08

Determine the gain and phase margins of the system and comment on its stability. (10 marks)

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

(i) Cascade Control (ii) ISA-5.1-1984 (R1992) Symbols and Identification

(iii) Smith predictor (dead time compensation)

(10 marks x 2)

Fig Q1: Chemical reactor system

Fig. Q3

Fig Q4

-

0.12 ses

−C(s) R(s)

Sensor

+

40( 4)( 10)s s+ +

1

24

-24

100( )( 1)( 10)s s s+ +-

r(t) c(t)

Power Amplifier

Gp(s) Plant

+ m(t) n(t)

TPO (s) Actual Temperature

∆TPi(s)

Control Valve Controller

Heat exchanger Dynamics

TP(set)(s)

Kh

Gc(s) Kv

τvs+1

Ke

τes +1

Temp Sensor/Transmitter

Set Point Temperature

+-

Kd

Signal conversion

+

KT

Fig. Q5

- D(z) 1− −e

s

Ts 0 . 51 0 1s +

Y(s) oC

R(s) Compensator ZOH

+

Test chamber

T=2s

2

( )M s