Subject Code: BEE502
Subject Name: Control System
Course: B.Tech (Semester V)
Maximum Marks: 70
Time: 3 Hours
Exam Year: 2024–25
Structure: Three Sections – A, B, C
BEE502-CONTROL-SYSTEM
🧩 SECTION A – Short Questions (2 × 7 = 14 Marks)
Attempt all questions briefly.
Classification of control systems (open-loop, closed-loop).
Torque–speed characteristics of an AC servo motor and effect of X/R ratio.
For T(s)=K(s+6)s(s+2)(s+5)(s2+7s+12)T(s) = \frac{K(s+6)}{s(s+2)(s+5)(s^2 + 7s + 12)}T(s)=s(s+2)(s+5)(s2+7s+12)K(s+6): find poles, zeros, characteristic equation, and pole-zero plot.
Define absolute stability and conditional stability.
Define phase margin, gain margin, gain crossover frequency, and phase crossover frequency.
Draw Lag and Lead networks using passive elements (R, C).
Discuss Kalman’s test for state controllability.
SECTION B – Medium-Length Questions (7 × 3 = 21 Marks)
Attempt any three.
Simplify the block diagram (Fig. a, page 1) using reduction rules to obtain the overall transfer function Y(s)F(s)\frac{Y(s)}{F(s)}F(s)Y(s).
Draw and explain the time response curve of a second-order system for a unit step input and define key specifications (rise time, settling time, overshoot, etc.).
For unity feedback system G(s)=Ks(s2+10s+36)G(s) = \frac{K}{s(s^2 + 10s + 36)}G(s)=s(s2+10s+36)K:
Find range of KKK for stability.
Find KKK for which response is oscillatory and corresponding frequency of oscillation.
For G(s)=10(s+4)(s2+4s+8)G(s) = \frac{10}{(s+4)(s^2 + 4s + 8)}G(s)=(s+4)(s2+4s+8)10: sketch polar plot and find intersections with real and imaginary axes.
Given system matrix A=[−110−1]A = \begin{bmatrix} -1 & 1 \\ 0 & -1 \end{bmatrix}A=[−101−1]:
Find state transition matrix using power series method and verify by Laplace transform.
SECTION C – Long / Analytical Questions (7 × 5 = 35 Marks)
Attempt one part from each question.
Q3. Feedback and Mechanical Systems
a. Explain effect of feedback on (i) Overall gain (ii) Bandwidth.
b. Obtain transfer function Y1(s)F(s)\frac{Y_1(s)}{F(s)}F(s)Y1(s) for the mechanical system (Fig. b, page 2).
Q4. Transient Response and PD Controller
a. (i) Derive rise time for C(s)R(s)=as+a\frac{C(s)}{R(s)} = \frac{a}{s+a}R(s)C(s)=s+aa.
(ii) Explain steady-state error and methods to reduce it.
b. Discuss Proportional–Derivative (PD) controller and its impact on second-order system performance.
Q5. Stability Criteria and Root Locus
a. Explain Hurwitz and Routh criteria and their special cases.
b. Derive three rules for root locus construction.
Determine angle of departure for G(s)H(s)=Ks(s2+6s+12)G(s)H(s) = \frac{K}{s(s^2 + 6s + 12)}G(s)H(s)=s(s2+6s+12)K.
Q6. Frequency Response and Nyquist Plot
a. Derive resonant peak and resonant frequency for a standard second-order system.
b. Sketch Nyquist plot for G(s)H(s)=(s−z1)s(s+p1)G(s)H(s) = \frac{(s - z_1)}{s(s + p_1)}G(s)H(s)=s(s+p1)(s−z1) where z1,p1>0z_1, p_1 > 0z1,p1>0.
Q7. Compensators and State Model
a. Explain effects and limitations of Lead, Lag, and Lead–Lag compensators.
b. Derive state-space model using (i) Companion form (Bush form) and (ii) Jordan’s form.
Key Topics for Study
Classification: Open-loop & Closed-loop systems
Block diagram reduction & Signal flow graph
Time response specifications (rise, delay, settling time)
Stability tests: Routh–Hurwitz, Root locus, Polar, Nyquist
Controllers: P, PI, PD, PID and effects on system behavior
Frequency response analysis: Bode, Polar, Nyquist
State-space representation & controllability tests
Preparation Tips
Revise control system types and their real-world examples.
Practice block diagram and transfer function derivations.
Solve numericals on stability using Routh–Hurwitz and root locus.
Understand Nyquist criterion and frequency response curves.
Memorize key formulas (steady-state error, rise time, resonant frequency).
