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The step response of a system in a given initial state consists of the time evolution of its outputs when its control inputs are Heaviside step functions. In electronic engineering and control theory , step response is the time behaviour of the outputs of a general system when its inputs change from zero to one in a very short time.
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 ...
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. The transient response is not necessarily tied to abrupt ...
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.
The step response can be interpreted as the convolution with the impulse response, which is a sinc function. The overshoot and undershoot can be understood in this way: kernels are generally normalized to have integral 1, so they send constant functions to constant functions – otherwise they have gain .
For example, the time interval graphically corresponding to the intercept points of the tangent drawn through the 50% point of the step function response is occasionally used. [12] Another definition, introduced by Elmore (1948 , p. 57), [ 13 ] uses concepts from statistics and probability theory .
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The total response of the circuit is the superposition of the ZSR and the ZIR, or Zero Input Response. The ZIR results only from the initial state of the circuit and not from any external drive. The ZIR is also called the natural response, and the resonant frequencies of the ZIR are called the natural frequencies. Given a description of a ...