04 - Second Order Systems

Second order system is also called quadratic lag system. The dynamics of the system in time-domain is given by a second order differential equation, as below: \[\tau^2\frac{d^2Y}{dt^2} + 2\zeta\tau\frac{dY}{dt} + y = K_p\,X(t)\] The corresponding transfer function is given by

Note: \(\tau, \ \zeta > 0\). They can’t take \(-\)ve values.