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EE329 Linear Control Systems II Exam, Exams of Linear Control Systems

National Center For Biological Sciences Linear Control Systems

An exam for the ee329 linear control systems ii module, including instructions, requirements, and questions related to control systems, transfer functions, ziegler-nichols rules, and digital control systems. The exam consists of four questions, and students are required to answer any three of them. Each question carries equal marks (20 marks), and the duration of the exam is 2 hours.

Typology: Exams

2012/2013

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EE329 Linear Control Systems II Page 1 of 5

Autumn Examinations 2011/2012

Exam Code(s) 3BN, 3BSE (Electrical)

Exam(s) Third Year Electrical & Electronic Engineering

Third Year Energy Systems Engineering (Electrical)

Module Code(s) EE329

Module(s) Linear Control Systems II

Paper No.

Repeat Paper Yes

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

Internal Examiner(s) Prof. G. Ó Laighin

Dr. Maeve Duffy

Instructions:

Answer any three questions from four.

All questions carry equal marks (20 marks).

Duration

2 hours

No. of Pages

Discipline

Electrical & Electronic Engineering

Course Co-ordinator(s) Dr. Maeve Duffy

Requirements:

MCQ

Handout

Statistical Tables

Graph Paper

Log Graph Paper

Other Material

Partial preview of the text

Download EE329 Linear Control Systems II Exam and more Exams Linear Control Systems in PDF only on Docsity!

Autumn Examinations 2011/

Exam Code(s) 3BN, 3BSE (Electrical)

Exam(s) Third Year Electrical & Electronic Engineering

Third Year Energy Systems Engineering (Electrical)

Module Code(s) EE

Module(s) Linear Control Systems II

Paper No.

Repeat Paper Yes

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

Internal Examiner(s) Prof. G. Ó Laighin

Dr. Maeve Duffy

Instructions: Answer any three questions from four.

All questions carry equal marks (20 marks).

Duration 2 hours

No. of Pages 5

Discipline Electrical & Electronic Engineering

Course Co-ordinator(s) Dr. Maeve Duffy

Requirements :

MCQ

Handout

Statistical Tables

Graph Paper

Log Graph Paper

Other Material

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

Mp Mo

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

Tr ( 0 − 95 %) ≅ 3 / ω b ( ζ > 0. 4)

Tr (0 − 100%) =

π − sin−^1 1 − ζ 2

ω n 1 − ζ 2 ( ζ < 1)

Overshoot = 100 exp −

Ts (±2%) ≤

ζ ω n

^ ( ζ < 1)

Ts (±5%) ≤

ζ ω n

^ ( ζ < 1)

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

P+I control : K = 0.45 Kc , Ti = 0.83 Tc

PID control: K = 0.6 Kc , Ti = 0.5 Tc , Td = 0.125 Tc

Question 1

The P+I controller in a position control system was designed according to Ziegler-Nichols rules. It

has the transfer function

G (s)^4 (s^0.^5 ) c

(a) Identify the period of unstable oscillations, Tc, for the given system. Using Tc as a

reference, suggest a suitable sampling interval for a replacement digital controller.[ 5 marks]

(b) Explain how a D/A converter introduces a delay in a digital control system. Include a sketch

of typical input and output signals to support your answer. [5 marks]

(c) Given that the resonant frequency of the given system is ωr = 1.8 rad/s, and using a sampling

interval of T = 0.3 s, design a phase-lead compensator to offset the phase-lag of the D/A

converter at the resonant frequency. [10 marks]

Question 2

The block diagram of a digital control system which has a sampling interval, T = 0.2 s is shown in

Fig. 1. The computer algorithm is given as:

m(k) = m(k–1) + 1.7[e(k) – 0.4e(k–1)]

Fig. 1

(a) Represent the system of Fig. 4 in the z-domain, and write an expression for the closed-loop z-

transfer function. [ 11 marks ]

(b) Calculate the locations of the closed loop poles and zeros in the z-plane. [ 2 marks ]

(c) Determine the steady-state error of the system for a unit ramp input. [ 7 marks ]

Digital controller

D/A (s 2 )

A/D

r(kT) m(kT)^ m(t) c(t)

c(kT)

EE329 Linear Control Systems II Exam, Exams of Linear Control Systems

Related documents

Partial preview of the text

Download EE329 Linear Control Systems II Exam and more Exams Linear Control Systems in PDF only on Docsity!

Autumn Examinations 2011/

Exam Code(s) 3BN, 3BSE (Electrical)

Exam(s) Third Year Electrical & Electronic Engineering

Third Year Energy Systems Engineering (Electrical)

Module Code(s) EE

Module(s) Linear Control Systems II

Paper No.

Repeat Paper Yes

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

Internal Examiner(s) Prof. G. Ó Laighin

Dr. Maeve Duffy

Instructions: Answer any three questions from four.

All questions carry equal marks (20 marks).

Duration 2 hours

No. of Pages 5

Discipline Electrical & Electronic Engineering

Course Co-ordinator(s) Dr. Maeve Duffy

Requirements :

MCQ

Handout

Statistical Tables

Graph Paper

Log Graph Paper

Other Material

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

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

Tr ( 0 − 95 %) ≅ 3 / ω b ( ζ > 0. 4)

π − sin−^1 1 − ζ 2

ω n 1 − ζ 2 ( ζ < 1)

ζ ω n

^ ( ζ < 1)

ζ ω n

^ ( ζ < 1)

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

P+I control : K = 0.45 Kc , Ti = 0.83 Tc

PID control: K = 0.6 Kc , Ti = 0.5 Tc , Td = 0.125 Tc

Question 1

The P+I controller in a position control system was designed according to Ziegler-Nichols rules. It

has the transfer function

(a) Identify the period of unstable oscillations, Tc, for the given system. Using Tc as a

reference, suggest a suitable sampling interval for a replacement digital controller.[ 5 marks]

(b) Explain how a D/A converter introduces a delay in a digital control system. Include a sketch

of typical input and output signals to support your answer. [5 marks]

(c) Given that the resonant frequency of the given system is ωr = 1.8 rad/s, and using a sampling

interval of T = 0.3 s, design a phase-lead compensator to offset the phase-lag of the D/A

converter at the resonant frequency. [10 marks]

Question 2

The block diagram of a digital control system which has a sampling interval, T = 0.2 s is shown in

Fig. 1. The computer algorithm is given as:

m(k) = m(k–1) + 1.7[e(k) – 0.4e(k–1)]

Fig. 1

(a) Represent the system of Fig. 4 in the z-domain, and write an expression for the closed-loop z-

transfer function. [ 11 marks ]

(b) Calculate the locations of the closed loop poles and zeros in the z-plane. [ 2 marks ]

(c) Determine the steady-state error of the system for a unit ramp input. [ 7 marks ]

D/A (s 2 )

A/D

Question 3

The block diagram of a digital control system is given in Fig. 2.

Fig. 2

(a) Write an expression for the closed-loop z-transfer function of the system, C(z)/R(z). Given that

one of the poles is located at z = 0.235, complete a pole-zero diagram for the system. [ 8 marks ]

(b) Using a sampling interval, T = 0.5 s, map the poles and zeros onto the primary strip in the s-

plane. [ 8 marks ]

(c) Explain why you would be confident that predictions of the system response based on the

location of dominant s-plane poles would be accurate. [ 4 marks ]

Question 4

It is required to design a digital controller for a certain chemical process. Root locus analysis of the

system found that the gain at which the system becomes unstable is 18 dB, and the frequency of

unstable oscillations is ωc = 0.628 rad/s.

(a) Design an analogue PID controller for the process according to Ziegler-Nichols rules.

[ 7 marks ]

(b) Choosing a sampling interval of T = 1.5 s, directly apply the bilinear transformation to emulate

the analogue controller of part (a). Write the computer algorithm for the resulting digital