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Seat No.: Enrolment
GUJARAT TECHNOLOGICAL UNIVERSITY
PDDC- SEMESTER-IV EXAMINATION SUMMER 2017
Subject Code: X41102 Date:29/05/2017
Subject Name: Control Theory
Time: 10:30 AM TO 01:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1

Define the following terms.
1. Peak Overshoot
2. Settling time
3. Rise time
4. Steady state error
5. Self loop
6. Forward path
7. Characteristics equation
07

Classify the control system and explain close loop control system with suitable example also give the advantages of close loop system over open loop system.
07
Q.2

What is transfer function? List and explain the different steps for deriving the transfer function using Mason's gain formula.
07

Explain the different steps for block diagram reduction technique using appropriate example.
07
OR

Explain the analogous quantities of mechanical and electrical systems using
force voltage analogy and
force current analogy
07
Q.3

Explain the modeling of thermal system with appropriate example.
07

What is state space? Derive the relationship between state space and transfer function.
07
OR
Q.3

What do you mean by Stability? Determine the stability of the system described by characteristic equation: S5 7S4+ 6S3+42S2+8S+56 0 using Routh's criterion.
07

Derive the steady state error in terms of static error coefficients Kp, Kv and Ka and discuss for type 0 system.
07
Q.4

What is the significance of root locus in system stability? Draw the root locus for unity feedback control systems has open loop transfer function

07

Derive the relationship between transient response and frequency response of the control system.
07
OR
Q.4

Define the following terms.
1. Asymptote
2. Angel of aperture
3. Angel of departure
4. Real axis loci
5. Break away point
6. Centroid
7. Angel of asymptote
07
2

A unity feedback system is characterized by the open loop transfer function 361 (s2+16s+361). Determine rise time, peak time, peak overshoot and settling time.
07
Q.5

Draw the response of system having following location of roots.
1. Roots on negative real axis
2. Roots on positive real axis
3. Complex conjugate roots on left-half of the s-plane
4. Complex conjugate roots on right-half of the s-plane
5. Single pair of roots on imaginary axis
6. Double pair of roots on imaginary axis
7. Single root at origin
07

Explain the Nyquist Stability Criterion with suitable example.
07
OR
Q.5

List the general steps for constructing the Bode Plot and draw the bode plot using appropriate example.
07

Explain the transfer function of simple liquid level pressure difference system with appropriate example.
07