PYQs Based test 14: Control Systems

Consider the following asymptotic Bode magnitude plot ( $\omega$ is in rad/s).



Which one of the following transfer functions is best represented by the above Bode magnitude plot?

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 ________

For the system governed by the set of equations:

$\begin{array}{l}\frac{d{x}_1}{dt}=2x_1+x_2+u\\ \frac{d{x}_2}{dt}=-2x_1+u\\ y=3x_1\end{array}$

the transfer function $Y\left(s\right)/U\left(s\right)$ is given by

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 ______.

The range of K for which all the roots of the equation s³ + 3s² + 2s + K = 0 are in the left half of the complex s-plane is