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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.
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.
The impulse response and step response are transient responses to a specific input (an impulse and a step, respectively). In electrical engineering specifically, the transient response is the circuit’s temporary response that will die out with time. [1]
Step response of system for two different initial values V 0, one above the final value and one at zero. Long-time response is a constant, V ∞. Time axis in units of the time constant . Suppose the forcing function is chosen as a step input so: + = = (),
Turning to step response, the step response is the integral of the impulse response; formally, the value of the step response at time a is the integral of the impulse response. Thus values of the step response can be understood in terms of tail integrals of the impulse response. Assume that the overall integral of the impulse response is 1, so ...
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 ...
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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.