MCQs on Control Systems

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

Characteristic 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 = 0.9

08․ A unity feedback control system has forward loop transfer function as e^-Ts/s(s+1). Its phase value will be zero at frequency ω₁. Which of the following equations should be satisfied by ω₁?

Given transfer function = e^-Ts/s(s+1) G(jω) = e^-Tjω/jω(jω+1) ∠G(jω) = -ωT - π/2 - tan^-1ω At ω = ω₁;∠G(jω) = 0 -ω₁T - π/2 - tan^-1ω₁ = 0 - tan^-1ω₁ = ω₁T + π/2 - ω₁ = -cot(Tω₁) ω₁ = cot(Tω₁)

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