Correlation between frequency and transient responses of feedback control systems

The performance of a feedback control system is often evaluated on the basis of the transient response, for which the step function is used as the input. The abrupt change of input or disturbance may represent important actual operating conditions that the system may be subjected to. However, synthesis or design on this basis is mathematically difficult to carry out when the system has a characteristic equation of high order. As a result, synthesis on the sinusoidal or frequency basis has been developed and widely used. It is obviously most desirable to know the correlation between the frequency and transient responses so that a criterion for the frequency response method may be properly established.