PYQs Based test 15: Control Systems

A second-order real system has the following properties:

The damping ratio $\xi =0.5$ and undamped natural frequency ${\omega }_n=10rad/s$, the steady state value at zero is 1.02.

The transfer function of the system is

When a unit ramp input is applied to the unity feedback system having closed loop transfer function

$\frac{C\left(s\right)}{R\left(s\right)}=\frac{Ks+b}{s^2+as+b},(a>0,b>0,K>0)$, The steady state error will be

For the given system, it is desired that the system be stable. The minimum value of α for this condition is _______________.

A closed loop system has the characteristic equation given by s³ + Ks² + (K + 2)s + 3 = 0. For this system to be stable, which one of the following conditions should be satisfied?

The transfer function of a system is given by,

$\frac{V_0\left(s\right)}{V_i\left(s\right)}=\frac{1-s}{1+s}$

Let the output of the system be $v_0\left(t\right)=V_m\sin \left(\omega t+\varphi \right)$ for the input, $v_i\left(t\right)=V_m\sin \left(\omega t\right)$. Then the minimum and maximum values of ϕ (in radians) are respectively