1. Introduction
Many applications of control theory are to servomechanisms which are systems using the feedback principle designed so that the output will follow the input. Hence there is a need for studying the time response of the system. The time response of a system may be considered in two parts:
2. Response of the first order systems
3. Response of second order systems
overdamped system:
critically damped system:
underdamped system:
In this case, the poles p_{1} and p_{2} are complex conjugate having the form p_{1,2} = α + iβ where α = a_{1}/2 and
The three cases discussed above are plotted as:
There are two important constants associated with each second order system:
Some definitions:
4. Steady state error
step input: r(t) = ku(t)
Ramp input: r(t) = ktu(t)
Parabolic input: r(t) = 1/2 kt^{2} u(t)
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