PYQs Based Test - 06 : Control Systems

Given the following polynomial equation

$s^3+5.5s^2+8.5s+3=0,$

the number of roots of the polynomial, which have real parts strictly less than $-1$, is ________

Consider a closed-loop control system with unity negative feedback and KG(s) in the forward path, where the gain K = 2. The complete Nyquist plot of the transfer function G(s) is shown in the figure. Note that the Nyquist contour has been chosen to have the clockwise sense. Assume G(s) has no poles on the closed right-half of the complex plane. The number of poles of the closed-loop transfer function in the closed right-half of the complex plane is ___________.

Two linear time-invariant systems with transfer functions

${\mathrm{G}}_1(\mathrm{s})=\frac{10}{{\mathrm{s}}^2+\mathrm{s}+1}$ and ${\mathrm{G}}_2(\mathrm{s})=\frac{10}{{\mathrm{s}}^2+\mathrm{s}\sqrt{10}+10}$

have unit step responses y₁(t) and y₂(t), respectively. Which of the following statements is/are true?

Consider a negative unity feedback system with forward path transfer function $G\left(s\right)=\frac{K}{\left(s+a\right)\left(s-b\right)\left(s+c\right)}$, where K, a, b, c are positive real numbers. For a Nyquist path enclosing the entire imaginary axis and right half of the s-plane is the clockwise direction, the Nyquist plot of (1 + G(s)), encircles the origin (1 + G(s)) –plane once in the clockwise direction and never passes through this origin for a certain value of K. then, the number of poles of $\frac{G\left(s\right)}{1+G\left(s\right)}$ lying in the open right half of the s-plane is ______.

Which of the options is an equivalent representation of the signal flow graph shown here?