Control System Questions Ias Mains

7/31/2019 Control System Questions Ias Mains

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CONTROL SYSTEM2009

1)

2)

3)


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4)

2007

x x u

Given that the above is a linear time-invariant (LTI) system, how would you check the

stability of the system ? If there is an unstable mode in the system, is it controllable? If the

unstable mode is controllable shift it to a stable position, say =0.5, by state feedback.

(20)

2005

1)Point out the advantages of frequency response studies of a system. Explain the Bode plots

for the log magnitude versus frequency and phase angle versus frequency for the complex

conjugate poles or zeros.

(20)

2)State and explain the Masons Gain formula. Determine all input-output relationships of thesystem represented by the set of following linear equations using the Masons Gain formula:

x1 = a11 x1 + a12x2 + b1u1, and

x2 = a21 x1 + a22 x2 + b2u2

where u1 and u2 are the inputs and x1 and x2 are the states of the system.(20)

3) Select any three of the following statements, read them carefully and identify the correct and the

incorrect ones. Justify your answer using not more than 200 words in each case.

3 20 = 60

(a) Jury stability test states that if the first element of descending order polynomial, viz, a0 > 0,

then all roots of the polynomial Q(z) are inside the unit circle if and only if the first element

in each odd-numbered row is positive in the derived array.


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2004

1) Write the discrete forms of P, PI and PID controllers. What are various methods of tuning

them?

Discuss in brief.

20

2) What do you understand by lead compensator? Draw the approximate Bode plot for a typical

lead compensator. Design a suitable control system for a missile to introduce a lead of 35

and gain of 6.5 db at 2.8 rad/s. What will be the transfer function of this lead compensator

that will satisfy the above requirement?

(20)

3) Select any THREE of the following statements, read them carefully and identify the correct and

the

incorrect ones. Justify your answer using not more than 200 words in each case

(a) At any point on the root locus with angle condition satisfied, the value of K-variable

parameter (for this point to be a root) is obtained asproduct of lengths of vectors from poles

product of lengths of vectors from zero

K

2003

1) Explain the following

(i) Gain margin (ii) Phase margin

How are they determined from Nyquist plot and Bode plot?

(20)

2) Discuss the performances of proportional plus derivative and proportional plus integral

controllers.

(20)

3) Select any three of the following statements, read them carefully and identity the correct and the

incorrect ones. Justify your answer using not more than 200 words in each case:

20 3 = 60

(a) Routh-Hurwitz criterion is an algebraic method that provides information on the absolute

stability of linear time invariant system that has a characteristic equation with constant coefficient

4)Explain the effects of negative feedback in control systems on the following

20(i) Stability (ii) External disturbances

2002

1) Show that the feedback reduces the effect of parameter variation on the performance of the

control system, but adversely affects the gain of the systems Also discuss briefly the effect of

feedback on the transient performance of the control system. .

(20)


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2)Select any three of the following statements, read them carefully and identify the correct and the

incorrect ones. Justify your answer using not more than 200 words in each case

20 3 = 60

(a) The steady - state errors for unit step input to type-0, type-1 and type-2, unity feedback

systems are finite non-zero, zero and infinite respectively

3) A system is represented by state equation X = AX.

If for

1

0 3

2

X

the response is

2

3 2

2t

t

e

X t

e

And for 1

0

1

X

t

t

e

X t

e


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Determine the state transition matrix (NOTE:SEE ORIGINAL PAPER FOR MISSING

MATRIX)4) Select any three of the following statements read them carefully and identify the correct and theincorrect ones. Justify your answer using not more than 200 words in each case

20 3 = 60

(a) The magnitude of a transfer function whose poles are only in the left half of s plane andwhose zeros are mirror images of the poles about the jw axis increases with increase in

frequency.

2001


the

incorrect ones. Justify your answer using not more than 200 words in each case. .20 3 = 60

(a) Routh-Hurwitz and continuous fraction stability criteria tell whether the system is stable or

unstable. They do not tell anything about the relative stability of the system.


the


20 3 = 60

(a) While a lead compensator reduces system bandwidth, a lag compensator on the other hand

increases the system bandwidth.

2000

1) A system is described by the following state and output equations

0 1 0

2 3 1

X X U

(NOTE:SEE ORIGINAL PAPER FOR MISSING

MATRIX)And Y = [1 0]X

where u(t) is a unit step input and the initial conditions X1(0) = 0, X2(0) = 0. Obtain the timeresponse of the system.

(20)



20 3 = 60

(a) Feedback provides same control on the steady state error to standard inputs by adjustment of


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open-loop gain.

3) The open hop transfer function of a unity feedback system is given by

1 2 1 1

G s k

s st st

(NOTE:SEE ORIGINAL PAPER FOR MISSING TRANSFER FUNCTION G(s))(i) Using the RouthHutwitz method, determine the necessary conditions for the systemto be stable.

(ii) Sketch the root locus diagram for the system described for positive values of k, t1 and

t2. Show how the root locus gets modified with addition of a zero.

(20)



20 3 = 60

(a) State variable approach for analysis is applicable only to linear time invariant systems.

1999

1) Describe the constructional features and working of a 2-phase, 4/6 pole hybrid stepping

motor.

Discuss its torque-displacement characteristics also.

(20)

2) (i) The pole-zero configuration of a closed-loop control system is given by (s1, s2) =2

j2. Calculate the undamped resonance frequency and the damping ratio.

(10)

(ii) Explain Hurwitz stability criteria.

The characteristic equation of a system is represented by

4s3 + 3s2 + 2s + 3 = 0.

Verify the stability of the system through expansion by confined fraction.

(10)

3) Enumerate states and state variable representation of a dynamic system.

Determine, by Routh array, whether a system represented by characteristic equation.

s3 + 4s2 + 8s + 11 = 0

is stable or not.

(20)

4) What is Bode-plot? Discuss how a Bode-plot can be drawn.


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Derive the step response of a second order system expressed by:

2 a d b d c F i

dt dt

(NOTE:SEE ORIGINAL PAPER FOR MISSING EQUAION).

(20)

5) Select any three of the following statements, read them carefully and identify correct and incorrect

ones. Justify your answer using not more than 200 words in each case:

(20 x 3 = 60)

Case

(a) For a stable system, the gain margin and phase margin should be positive.

1998

1) Describe with the help of a neat diagram the operation of a reluctance-type stepper motoralong with its characteristics. What are its possible applications ?(20)

2) Select any Three of the following statements, read them carefully and identify correct and

incorrect

ones. Justify your answer using not more than 200 words in each case:

(20 x 3 = 60)

a) Phase lead compensation decreases the band width of a system.

3) The roots of a second order system are located at1+j2 and1j2. Determine the followingsif the system is excited by unit step input:

(i) Damping ratio

(ii) Maximum % overshoot

(iii) Natural frequency of oscillation

(iv) Damped frequency of oscillation(20)

4) The unity feedback system has forward path transfer function

1 2 G s K

s s s

(NOTE:SEE ORIGINAL PAPER FOR MISSING EQUAION)Sketch the Nyquist diagram. If K = 4, determine whether the given system is stable or not. If

the system is stable, determine its gain margin. What is the maximum value of K that willmake its gain margin zero ?

(20)

5) Obtain the transfer function of phase lead network. Show that

sin 1

m 1

a

a


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and 1

m aT (NOTE:SEE ORIGINAL PAPER FOR MISSING EQUAION)

where m, w, a and T have usual meanings.

(20)

6) The unity feedback system has forward path transfer function

2

1

2 4G s S

s s s

(NOTE:SEE ORIGINAL PAPER FOR MISSING EQUAION)Determine steady state error coefficients Kp, Kv and Ka.

Hence find the steady state error in output if

(i) unit step input,

(ii) nit ramp input and

(iii) nit parabolic input are given.7) The state equations for a system are given by

X AX Bu

Y CX Du

where

1 0 0

0 2 0

0 0 3

A

,

1

2

1

B


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,C

1 1 1and

0

0

0

D

(NOTE:SEE ORIGINAL PAPER FOR MISSING EQUAION)Determine the output response of a system to unit step input.

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Control System Questions Ias Mains