Question 35.PE.NAQ.1: A control system is described by following differential equa......

The given differential equation can be written as

\begin{aligned}& \frac{d^2 y}{d t^2}+\frac{2 d y}{d t}+4 y=4 x \\or \qquad\qquad & \frac{d^2 y}{d t^2}+\frac{2 d y}{d t}+(2)^2 y=(2)^2 x\end{aligned}

Comparing the above equation with the generalized second-order control system differential equation,

\frac{d^2 y}{d t^2}+2 \zeta \omega_n \frac{d y}{d t}+\omega_n^2 y=\omega_n^2 x

we get, 2ζω_n = and ω_n = 2 . The time constant is

\tau=\frac{1}{\zeta \omega_n}=\frac{1}{1}=1