01․ The transfer function of a plant is T(s) = 5/(s+5)(s² + 5 + 1). The second order approximation of T(s) using dominant pole concept is

Using dominant pole concept,
T(s) = 5/(s+5)(s² + 5 + 1)
T(s) = 5/5(s/5+1)(s² + 5 + 1)
T(s) = 1/(s² + 5 + 1)

02․ The phase margin of a system having the loop transfer function G(s)H(s) = 2√3/s(s+1) is

The characteristic equation for given system is
s² + s + 3.46 = 0
Phase margin ≈ 100*ζ
Damping ratio = 0.27
Phase margin = 27° ≈ 30°

03․ A system has poles at 0.01 Hz, 1 Hz and 80 Hz; zeros at 5 Hz, 100 Hz and 200 Hz. The approximate phase of the system response at 20 Hz is

Using dominant pole technique, all the pole and zeros are insignificant except a pole at 0.01 Hz. Therefore, given system consists of only a pole at 0.01 Hz.
Therefore, the approximate phase of the system is -90°.

04․ The Laplace transform of a transportation lag of 5 seconds is

Dead time in real system is also known as transportation lag.
Transfer function of transportation lag = e

^{-Ts}Therefore, transportation lag of 5 seconds can be written as e^{-5s}.05․ A property of phase lead compensation is that the

Lead compensator characteristics:

- 1. For sinusoidal input, the phase of controller output leads by tan
^{-1}(ωT_{d}). - 2. In terms of filtering property it acts as high pass filter.
- 3. It reduces rise time.
- 4. It increases bandwidth.
- 5. It increases stability of the system.
- 6. It reduces peak over shoot.

06․ Which of the following is the correct expression for the transfer function of an electrical RC phase lag compensating network?

Phase lag compensator acts as a low pass filter.
Therefore transfer function for lag compensator = 1/(1+RCS).

07․ The value of 'a' in to give phase margin = 45

^{o}will beCharacteristic equation is
Natural frequency ω

_{n}= 1 rad/s Phase margin = 100*ζ Damping ratio ζ = 45/100 = 0.45 2ζω_{n}= a Therefore, a = 0.908․ A unity feedback control system has forward loop transfer function as
e

^{-Ts}/s(s+1). Its phase value will be zero at frequency ω_{1}. Which of the following equations should be satisfied by ω_{1}?Given transfer function = e

^{-Ts}/s(s+1) G(jω) = e^{-Tjω}/jω(jω+1) ∠G(jω) = -ωT - π/2 - tan^{-1}ω At ω = ω_{1};∠G(jω) = 0 -ω_{1}T - π/2 - tan^{-1}ω_{1}= 0 - tan^{-1}ω_{1}= ω_{1}T + π/2 - ω_{1}= -cot(Tω_{1}) ω_{1}= cot(Tω_{1})09․ In polar plots if the critical point '-1+j0' is enclosed then the system is --------

A point is said to be enclosed by a contour if it lies to the right side of the direction of the contour.
A point is said to be encircled if the contour is a closed path.
In polar plots if the critical point '-1+j0' is enclosed then the system is said to be unstable and if it not enclosed then the system is said to be stable.

10․ Resonant peak of a marginally stable system is

Resonant peak is the maximum value of magnitude occurring at resonant frequency ω

_{r}. Resonant peak µ_{r}_{}= 1/(2ζ√(1-ζ²)) For marginally stable system, damping ratio ζ = 0 Therefore, resonant peak = Infinity<<<1920212223>>>