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Temperature Control System - Linear Control Systems I - Past Exam Paper, Exams of Linear Control Systems

National Center For Biological Sciences Linear Control Systems

Main points of this exam paper are: Phase Margin, Proportional Plus Integral, Respective Transfer Functions, Locations, Poles, Zeroes, Damping Ratio, Measurements, Open-Loop Conditions, Polar Plot

Typology: Exams

2012/2013

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EE318 Linear Control Systems I Page 1 of 5

Semester I Examinations 2011/2012

Exam Code(s)

3BEI, 3BN, 3BM, 3BSE, 4BEE

Exam(s)

Third Engineering Innovation – Electronic

Third Electronic Engineering

Third Mechanical Engineering

Third Energy Systems Engineering

Fourth Sports & Exercise Engineering

Module Code(s)

EE318, EE439

Module(s)

Linear Control Systems I

Paper No.

Repeat Paper

External Examiner(s)

Prof. G. W. Irwin

Internal Examiner(s)

Prof. G. Ó Laighin

Dr. M. Duffy

Instructions:

Answer any three questions from four.

All questions carry equal marks (20 marks).

Duration

2hrs

No. of Pages

Discipline

Electrical & Electronic Engineering

Course Co-ordinator(s)

Requirements:

MCQ

Handout

Statistical Tables

Graph Paper

Yes: mm graph paper

Log Graph Paper

Other Material

Nichols Chart Paper

Partial preview of the text

Download Temperature Control System - Linear Control Systems I - Past Exam Paper and more Exams Linear Control Systems in PDF only on Docsity!

Semester I Examinations 2011/

Exam Code(s) 3BEI, 3BN, 3BM, 3BSE, 4BEE

Exam(s) Third Engineering Innovation – Electronic

Third Electronic Engineering

Third Mechanical Engineering

Third Energy Systems Engineering

Fourth Sports & Exercise Engineering

Module Code(s) EE318, EE

Module(s) Linear Control Systems I

Paper No. 1

Repeat Paper No

External Examiner(s) Prof. G. W. Irwin

Internal Examiner(s) Prof. G. Ó Laighin

Dr. M. Duffy

Instructions: Answer any^ three^ questions from four.

All questions carry equal marks (20 marks).

Duration 2hrs

No. of Pages 5

Discipline Electrical & Electronic Engineering

Course Co-ordinator(s)

Requirements :

MCQ

Handout

Statistical Tables

Graph Paper Yes: mm graph paper

Log Graph Paper

Other Material Nichols Chart Paper

The following standard formulas are given and may be freely used:

Ziegler-Nichols Rules : Proportional control : K = 0.5 K c

P+I control : K = 0.45 K c , T i = 0.83 T c

PID control: K = 0.6 K c , T i = 0.5 T c , T d = 0.125 T c

M (^) p M (^) o

1 2 ζ 1 −ζ (^2) ( ζ ≤ 0. 707)

ω (^) r =ω (^) n 1 − 2 ζ (^2) ( ζ ≤ 0. 707)

ω (^) d =ω (^) n 1 −ζ 2

ω (^) b =ω (^) n (1− 2 ζ 2 ) + (1− 2 ζ 2 ) + 1

T (^) r (0 − 95%) ≅ 3 / ω (^) b ( ζ > 0. 4)

T (^) r (0 − 100%) =

π − sin−^1 1 −ζ 2

ω (^) n 1 −ζ (^2) ( ζ < 1)

Overshoot = 100 exp −

πζ

1 −ζ 2

( ζ < 1)

T (^) s (±2%) ≤

ζ ω (^) n

1 −ζ 2

^ ( ζ < 1)

T (^) s (±5%) ≤

ζ ω (^) n

1 −ζ 2

^ ( ζ < 1)

1. Results of the open-loop frequency response measured on a temperature control system as

shown in Figure 1 with K = 1, are given in Table 1.

Table 1

(a) Write an expression for the output signal you would expect to measure for an input

signal, r(t) = 0.1 sin(0.5t), applied to the open-loop system with K = 1. [ 4 marks ]

(b) Using mm graph paper, sketch the open-loop data of Table 1 on a polar plot.

[ 5 marks ]

(c) What value of gain, K, will result in a gain margin of 6 dB for the given system?

(Hint: the gain may be less than 1.) [ 3 marks ]

(d) With the gain set equal to the value found in part (c), sketch a new Polar Plot for the

system and determine the phase margin. [ 8 marks ]

Figure 1

2. The block diagram of a position control system used in a CD player is shown in Figure 2.

Figure 2

(a) Write the closed-loop transfer function for the given system in terms of the gain

parameter, K. [ 2 marks ]

(b) Sketch the root locus of the system for K, including a calculation for the location of

the breakpoint from the real axis. [ 12 marks ]

(c) Using the root locus of part (b), determine the maximum value of K that would

result in the system complex poles having a damping factor, ξ = 0.5. [ 6 marks ]

ω (rad/s) 0.2^ 0.3^ 0.5^ 0.7^ 1.0^ 1.

Gp(j ω ) –^5 –^ j 7.6^ –^4 –^ j 3.7^ –^ 2.4^ –^ j 0.8^ –^ 1.4^ –^ j 0^ –^ 0.6 + j 0.2^ –^ 0.15 + j 0.

_

R(s) C(s)

K^ Gp(s)

_

R(s)

(s 3 )

s(s 2 )

K(s 1 )

Temperature Control System - Linear Control Systems I - Past Exam Paper, Exams of Linear Control Systems

Related documents

Partial preview of the text

Download Temperature Control System - Linear Control Systems I - Past Exam Paper and more Exams Linear Control Systems in PDF only on Docsity!

Semester I Examinations 2011/

Exam Code(s) 3BEI, 3BN, 3BM, 3BSE, 4BEE

Exam(s) Third Engineering Innovation – Electronic

Third Electronic Engineering

Third Mechanical Engineering

Third Energy Systems Engineering

Fourth Sports & Exercise Engineering

Module Code(s) EE318, EE

Module(s) Linear Control Systems I

Paper No. 1

Repeat Paper No

External Examiner(s) Prof. G. W. Irwin

Internal Examiner(s) Prof. G. Ó Laighin

Dr. M. Duffy

Instructions: Answer any^ three^ questions from four.

All questions carry equal marks (20 marks).

Duration 2hrs

No. of Pages 5

Discipline Electrical & Electronic Engineering

Course Co-ordinator(s)

Requirements :

MCQ

Handout

Statistical Tables

Graph Paper Yes: mm graph paper

Log Graph Paper

Other Material Nichols Chart Paper

The following standard formulas are given and may be freely used:

Ziegler-Nichols Rules : Proportional control : K = 0.5 K c

P+I control : K = 0.45 K c , T i = 0.83 T c

PID control: K = 0.6 K c , T i = 0.5 T c , T d = 0.125 T c

1. Results of the open-loop frequency response measured on a temperature control system as

shown in Figure 1 with K = 1, are given in Table 1.

Table 1

(a) Write an expression for the output signal you would expect to measure for an input

signal, r(t) = 0.1 sin(0.5t), applied to the open-loop system with K = 1. [ 4 marks ]

(b) Using mm graph paper, sketch the open-loop data of Table 1 on a polar plot.

[ 5 marks ]

(c) What value of gain, K, will result in a gain margin of 6 dB for the given system?

(Hint: the gain may be less than 1.) [ 3 marks ]

(d) With the gain set equal to the value found in part (c), sketch a new Polar Plot for the

system and determine the phase margin. [ 8 marks ]

Figure 1

2. The block diagram of a position control system used in a CD player is shown in Figure 2.

Figure 2

(a) Write the closed-loop transfer function for the given system in terms of the gain

parameter, K. [ 2 marks ]

(b) Sketch the root locus of the system for K, including a calculation for the location of

the breakpoint from the real axis. [ 12 marks ]

(c) Using the root locus of part (b), determine the maximum value of K that would

result in the system complex poles having a damping factor, ξ = 0.5. [ 6 marks ]

ω (rad/s) 0.2^ 0.3^ 0.5^ 0.7^ 1.0^ 1.

Gp(j ω ) –^5 –^ j 7.6^ –^4 –^ j 3.7^ –^ 2.4^ –^ j 0.8^ –^ 1.4^ –^ j 0^ –^ 0.6 + j 0.2^ –^ 0.15 + j 0.

_

R(s) C(s)

K^ Gp(s)

_

R(s)

C(s)

3. Results of the open-loop frequency response of an industrial automation system using PID

control are given in Table 2.

Table 2

(a) Plot the results of Table 2 on a Nichols chart. Determine the bandwidth (BW) of

the closed loop system and use it to estimate the 0 – 95% rise time. [ 6 marks ]

(b) In order to reduce the system response time, the gain parameter is increased by 6

dB. Show how this increase in gain changes the Nichols chart for the system, and

use it to determine the new 0 – 95% rise time. [ 4 marks ]

(c) Using the Nichols chart of part (b), calculate (i) the percentage step response

overshoot and (ii) the ±5% settling time. [ 8 marks ]

(d) Suggest an alternative method for reducing the system response time which would

have greater stability than that proposed in part (b). [ 2 marks ]

4. A DC motor is connected into the tachometric feedback loop shown in Figure 3, and the

gain of the power amplifier is set at K = 3.6.

Figure 3

(a) Confirm that without tachometric feedback, i.e. with β = 0, the system of Figure 3

has closed-loop poles located at s = − 0.5 ± j 0.975. [ 3 marks ]