The GATE Grind

GATE 2020 EE – Question 45

Control Systems · Stability analysis using Routh-Hurwitz and Nyquist criteria, Bode plots, Root loci · 2 marks · Multiple choice

Which of the following options is correct for the system shown below?

Diagram for GATE 2020 EE question 45
  1. $4^{th}$ order and stable
  2. $3^{rd}$ order and stable
  3. $4^{th}$ order and unstable
  4. $3^{rd}$ order and unstable

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (C) $4^{th}$ order and unstable

Explanation

The forward path is $\frac{1}{s+1}\cdot\frac{1}{s^2}$ and the feedback is $\frac{20}{s+20}$, so the characteristic equation is $s^2(s+1)(s+20)+20=s^4+21s^3+20s^2+20=0$. It is 4th order, and the missing $s^1$ term means that some coefficient is zero, so the system cannot be stable.