About this previous year paper
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
| Open Loop | Closed Loop |
|---|---|
| No feedback | Feedback present |
| Less accurate | High accuracy |
| Simple & cheap | Complex & costly |
| Less stable | More stable |
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=lims→0G(s)=5K_p=\lim_{s→0}G(s)=5Kp=s→0limG(s)=5 Kv=lims→0sG(s)=0K_v=\lim_{s→0}sG(s)=0Kv=s→0limsG(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∑PkΔk