Find Response

This page demonstrates how to find the response of a motor on its own or in speed control (first order), or a mass spring system or motor position control (second order).

The response is to a step, where it moves from zero to a final steady value, or to an impulse, where it starts at 0, is given a kick, and returns to 0.

The different models are depicted and the user can click on model parameters to change them, and the user can select step or impulse. The user is then guided through a series of questions to allow them to deduce the response. which will be a function of exponentials, whose constants are associated with the roots of the 'auxilliary equation' which itself comes from the system differential equation.

First order systems have one root of the auxilliary equation, so that root and the associated constant must be found.

Second order systems have two roots, which can be two real or imaginary roots or one repeated root. Again two constants must be found.

Click on the relevant blocks in the diagram to change their parameters and see the effect.