(SEM VI) THEORY EXAMINATION 2024-25 CONTROL SYSTEM

BEC602 – CONTROL SYSTEM

Time: 3 Hours | Max Marks: 70

SECTION A – Short Answer Questions

(2 × 7 = 14 marks | Attempt ALL)
Write definition + formula / key comparison

a. Open Loop vs Closed Loop System

b. Transient Response & Steady State Response

Transient response: System behavior immediately after input is applied

Steady state response: System behavior after transients die out

c. Kalman’s Test

Kalman’s test is used to determine controllability and observability of a system using state-space 
matrices.

d. Find KpK_pKp​ and KvK_vKv​

Given:

G(s)=50(1+0.1s)(s+10)G(s)=\frac{50}{(1+0.1s)(s+10)}G(s)=(1+0.1s)(s+10)50​ Kp=lim⁡s→0G(s)=5K_p=\lim_{s→0}G(s)=5Kp​=s→0lim​G(s)=5 Kv=lim⁡s→0sG(s)=0K_v=\lim_{s→0}sG(s)=0Kv​=s→0lim​sG(s)=0 

e. Stability Using Routh Criterion

Characteristic equation:

2s4+2s3+s2+3s+2=02s^4+2s^3+s^2+3s+2=02s4+2s3+s2+3s+2=0

Routh array shows no sign change ⇒ Stable system

f. Asymptotes & Centroid (Root Locus)

Asymptotes: Indicate path of roots at infinity         Centroid: Intersection point of asymptotes

Centroid=∑poles−∑zerosP−Z\text{Centroid}=\frac{\sum poles-\sum zeros}{P-Z}Centroid=P−Z∑poles−∑zeros​ 

g. Relative & Absolute Stability                                Absolute stability: Stable or unstable

Relative stability: Degree of stability (how far poles are from imaginary axis)

SECTION B – Medium Answer Questions

(7 × 3 = 21 marks | Attempt ANY THREE)

a. Armature Controlled DC Motor                            Electrical equation

Mechanical equation                                                Derive transfer function

Draw block diagram

θ(s)V(s)=Ks(Ls+R)(Js+B)\frac{\theta(s)}{V(s)}=\frac{K}{s(Ls+R)(Js+B)}V(s)θ(s)​=s(Ls+R)(Js+B)K​ 

b. Transfer Function from State Model                     Given matrices A, B, C

G(s)=C(sI−A)−1BG(s)=C(sI-A)^{-1}BG(s)=C(sI−A)−1B

 Compute inverse and substitute values.

c. Steady State Error for Ramp Input

Given:

C(s)R(s)=Ks+bs2+as+b\frac{C(s)}{R(s)}=\frac{Ks+b}{s^2+as+b}R(s)C(s)​=s2+as+bKs+b​

Open loop:

G(s)=Ks+bs(s+a)G(s)=\frac{Ks+b}{s(s+a)}G(s)=s(s+a)Ks+b​ ess=a−kbe_{ss}=\frac{a-k}{b}ess​=ba−k​ 

d. Stability & Location of Poles                              LHP → Stable

RHP → Unstable                                                     Imaginary axis → Marginally stable

Farther left poles ⇒ better damping & faster response.

e. Bode Plot of

G(s)=1000s(1+0.1s)(1+0.001s)G(s)=\frac{1000}{s(1+0.1s)(1+0.001s)}G(s)=s(1+0.1s)(1+0.001s)1000​

Steps:

Find corner frequencies                                        Draw magnitude plot

Draw phase plot on semi-log paper

SECTION C – Attempt ANY ONE

(7 marks)

a. Block Diagram Reduction

Find:                                                                       C(s)R(s)\frac{C(s)}{R(s)}R(s)C(s)​

Use:                                                                        Series rule

Parallel rule                                                            Feedback rule

Simplify step-by-step.

b. Signal Flow Graph

Use Mason’s Gain Formula:                                CR=∑PkΔkΔ\frac{C}{R}=\frac{\sum P_kΔ_k}{Δ}RC​=Δ∑Pk​Δk​​