# Describe the theory and use of Time Responses

QuestionsCategory: QuestionsDescribe the theory and use of Time Responses

Describe the theory and use of Time Responses

• If output of q control system is varies with respect to time for an input, then it is called as time – response of the control system.

• Transient response and steady state response are two parts of time-response
• The response of control system in the time-domain is shown in the following figure: Here, both the transient and the steady states are indicated in the above figure. The responses corresponding to these states are known as transient and steady state reponses.

Mathematically: C(t) = Ctr(t) + Css(t)

Ctr(t) = Transient response
c(t) = Time respons (Total)

Transient Response:
After applying input to the control system, output takes certain time to reach steady state. So, the output will be transient state till it goes to the steady state. the response of control system during transient state is known as transient – response.

transient response will be zero for lakge values of “t”. Ideally the value of “t” is infinity and practically, it is s * time constant.

Mathematically:
lim Ctr(t) = 0
t -> infinity

The part of the time response that remains even after the transient response has zero value for lasge value of “t” is known as steady-state response. This means, the transient response will be zero, even during the steady state.

Example:
Let us find the transient and steady state terms of the time response of the control system.

C(t) = 10+5.e^-t

Here the second term (5e^-t) wil be zero, at t denotes infinity so this is the transient-term. And the first term (10) remain even as t approaches infinity, so this is the steady state system.

Use of time response:

1. The transient part of time response reveals the nature of response (i.e oscillatory or nature of damping) also giving an indication about its speed.
2. The steady state part of time response reveals the accuracy or steady state error of a control system.