(SEM-V) THEORY EXAMINATION 2022-23 CONTROL SYSTEM

Course: B.Tech (Semester V)                                                         Subject Code: KEE-502

Subject Name: Control System                                                    Time: 3 Hours

Total Marks: 100                                           

Note: Attempt all sections. Choose missing data suitably. 

Section A – Short Answer Questions (2 × 10 = 20 Marks)

Answer all briefly:

Define transfer function of a control system.        Explain Mason’s Gain Formula.

A unity feedback system with G(s)=2s(s+p)G(s) = \frac{2}{s(s+p)}G(s)=s(s+p)2​ is critically damped. Find ppp.

Effects of PD and PI control actions on a second-order system.

Explain special cases of Routh–Hurwitz criterion. Define Centroid and Breakaway point.

Define Relative Stability.                        Explain Gain Margin and Phase Margin in Bode Plot terms.

Define State Variable and State Vector.

Mention any four properties of the State Transition Matrix. 

Section B – Descriptive Questions (10 × 3 = 30 Marks)

Attempt any three:
 

Find C(s)R(s)\frac{C(s)}{R(s)}R(s)C(s)​ using Mason’s Gain Formula for the given signal flow graph.

With a neat sketch, explain time-domain specifications of a second-order system and derive the formula for Peak Time.

Define Root Locus and explain steps for plotting it.

Sketch Polar Plot and determine gain crossover, phase crossover, gain margin, and phase margin for
G(s)=1(1+s)(1+2s)G(s) = \frac{1}{(1+s)(1+2s)}G(s)=(1+s)(1+2s)1​.

Find the State Transition Matrix for
A=[−2−301]A = \begin{bmatrix} -2 & -3 \\ 0 & 1 \end{bmatrix}A=[−20​−31​]. 

CONTROL-SYSTEM-KEE502

Section C – Long Answer Questions (10 × 5 = 50 Marks)

Question 3

(a) Explain open-loop and closed-loop control systems with examples.
or
(b) Find the transfer function of the given block diagram using Block Reduction Technique.

Question 4

(a) Derive time response of a second-order system for unit step input.
or
(b) For the open-loop system G(s)=K(1+sT)G(s) = \frac{K}{(1+sT)}G(s)=(1+sT)K​:

(i) Find the factor to multiply KKK to change damping ratio from 0.3 to 0.9.

(ii) Find the factor to multiply TTT to reduce damping ratio from 0.8 to 0.2.

Question 5

(a) Sketch the Root Locus for G(s)H(s)=Ks(s+1)(s+2)(s+3)G(s)H(s) = \frac{K}{s(s+1)(s+2)(s+3)}G(s)H(s)=s(s+1)(s+2)(s+3)K​ and state stability conditions.
or
(b) For G(s)=K(s−1)(s+6)(s+1)G(s) = \frac{K(s-1)(s+6)}{(s+1)}G(s)=(s+1)K(s−1)(s+6)​, determine

(i) Range of KKK for stability

(ii) Marginal value of KKK

(iii) Root locations for marginal stability

Question 6

(a) Define Resonant Peak (Mₙ) and Resonant Frequency (ωᵣ), and derive their formulas.
or
(b) Draw Bode Plot for
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​
and determine

(i) Gain Crossover Frequency

(ii) Phase Crossover Frequency

(iii) Gain Margin

(iv) Phase Margin

(v) Stability

Question 7

(a) List types of Compensators. Explain Lead Compensator and derive the relation between maximum lead angle (Φₘ) and α.
or
(b) Examine Controllability and Observability for
A=[−6−11−6001010]A = \begin{bmatrix} -6 & -11 & -6 \\ 0 & 0 & 1 \\ 0 & 1 & 0 \end{bmatrix}A=​−600​−1101​−610​​,
B=[101]B = \begin{bmatrix} 1 \\ 0 \\ 1 \end{bmatrix}B=​101​​,
C=[10 5 1]C = [10\ 5\ 1]C=[10 5 1].