Time Response:
Time Response is the output which is given as a function of time when an input signal is applied. Time Response of a system can be split into two different parts:

  1. Transient Response

  2. Steady State Response

Time Response of a control system can be represented as:

Mathematically Time response can be depicted as:

\small \;\;c(t)\;=\;c_t(t)\;+\;c_{ss}(t)

\small c_t(t)= transient response 
\small c_{ss}(t)= steady state response

Transient Response:
Transient response is the part of the response in the transient state. It is ideally 0 and practically decreases with increasing time.
I.e \small lim_{t\rightarrow\infty}c_t(t)=0

Transient response can be exponential or oscillatory in nature.

Steady State Response:
Steady State response is the part of the response in the steady state. It is the response that is remaining even at larger values of t i.e when there is almost no transient response remaining.

Steady State Error:
If the steady state response of the output does not match with the desired theoretical value then the system is said to have steady state error.