Under the action of unit step input, the output response of the system is c(t) = 1-2e-2t+e-t under zero initial condition. The transfer function r(t)= 1(t) of the system is laplace transformed to obtain R(S)= 1/s, c (.

In order to solve the integral of Dirac Delta function, the unit step function is introduced, and in the response problem of the system excited by the input signal, in order to distinguish the two time points before and after the signal is applied to the system.

The time when the signal enters the system and starts to work is called "time 0" falling edge, which is recorded as 0+, and t=0+, then t>0; The point where the input signals are to be added but not added is called the 0- moment frontier, which is denoted as 0-,t=0-, t < 0.

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It is generally believed that the step signal is a very bad working state for the system, because there are jumping points (discontinuous points) in the step signal. The response of zero initial state system under unit step input is studied.

A series of dynamic performance indexes are defined to judge the dynamic performance of the system, such as overshoot, attenuation ratio, rise time, regulation time and peak time.

Baidu Encyclopedia-Unit Step Function