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Damped oscillation is a typical transient response, where the output value oscillates until finally reaching a steady-state value.. In electrical engineering and mechanical engineering, a transient response is the response of a system to a change from an equilibrium or a steady state.
Steady state is also used as an approximation in systems with on-going transient signals, such as audio systems, to allow simplified analysis of first order performance. Sinusoidal Steady State Analysis is a method for analyzing alternating current circuits using the same techniques as for solving DC circuits. [1]
This period of time is known as the transient state. A capacitor acts as a short circuit immediately after the switch is closed, increasing its impedance during the transient state until it acts as an open circuit in its steady state. An inductor is the opposite, behaving as an open circuit until reaching a short circuit steady state.
Steady state is reached (attained) after transient (initial, oscillating or turbulent) state has subsided. During steady state, a system is in relative stability. Steady state determination is an important topic, because many design specifications of electronic systems are given in terms of the steady-state characteristics. Periodic steady ...
In AI, an example might be a chatbot modelling the discourse state of humans: the more accurately it can model the human state (e.g. on a telephone voice-support hotline), the better it can manipulate the human (e.g. into performing the corrective actions to resolve the problem that caused the phone call to the help-line).
The steady-state response is the output of the system in the limit of infinite time, and the transient response is the difference between the response and the steady-state response; it corresponds to the homogeneous solution of the differential equation. The transfer function for an LTI system may be written as the product:
First order LTI systems are characterized by the differential equation + = where τ represents the exponential decay constant and V is a function of time t = (). The right-hand side is the forcing function f(t) describing an external driving function of time, which can be regarded as the system input, to which V(t) is the response, or system output.
Settling time depends on the system response and natural frequency. The settling time for a second order , underdamped system responding to a step response can be approximated if the damping ratio ζ ≪ 1 {\displaystyle \zeta \ll 1} by T s = − ln ( tolerance fraction ) damping ratio × natural freq {\displaystyle T_{s}=-{\frac {\ln ...