Step response and transient response

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Step Response and transient response

In control theory, the step response of the system is the time response of the outputs of a system when its inputs are Heaviside step functions. The concept can be extended to the abstract mathematical notion of a dynamical system using an evolution parameter. From a practical viewpoint, to know how a system responds to a sudden input is important because large and fast deviations from long term steady state may have extreme effects on the component and on other portion of the system dependent on this component. Also, the overall system cannot act until the output of the component settles down to some vicinity of its final state, thereby delaying the overall system response. System performance may be specified in terms of parameters describing time-dependence of response, instead of frequency response. Also, the step response of the dynamical system gives information on stability of such a system and on its ability to reach one stationary state when starting from another. The step response can be described by the following quantities related to its time behaviour: overshoot, ringing, settling time and rise time. In the case of linear dynamic systems, these characteristics help in inferring much about the systems.

Fig (1): Typical Step response of a second order system.

Transient response is also known as natural response of a system. In electrical engineering and mechanical engineering, the transient response of the system is the response of the system to a change from equilibrium. Transient response pertains to any event that affects the equilibrium of the systems and not only “on/off” events. Impulse response and Step response are transient responses to a specific input (an impulse and a step, respectively).

Fig (2): Damping oscillations, typical transient response.

Step Response Example

Following is an example of step response of first order system: