Unit Parabolic Signal

Unit Parabolic Signal

A unit parabolic signal, p(t) is defined as,

p(t)=t22;t≥0p(t)=t22;t≥0

=0;t<0=0;t<0>

We can write unit parabolic signal, p(t)p(t) in terms of the unit step signal, u(t)u(t)as,

p(t)=t22u(t)p(t)=t22u(t)

The following figure shows the unit parabolic signal.

So, the unit parabolic signal exists for all the positive values of ‘t’ including zero. And its value increases non-linearly with respect to ‘t’ during this interval. The value of the unit parabolic signal is zero for all the negative values of ‘t’.

Time Response Analysis & Design

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<![endif]> <![endif]--><!--[if !vml]--><!--[endif]-->Two types of inputs can be applied to a control system

Command Input or Reference Input yr(t)

Disturbance Input w(t) (External disturbances w(t) are typically uncontrolled variations in the load on a controlsystem)

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<![endif]> <![endif]--><!--[if !vml]--><!--[endif]-->In systems controlling mechanical motions, load disturbances may represent forces.

In voltage regulating systems, variations in electrical load area major source of disturbances.

First-order system time   response

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   Second-order system time response

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<!--[if !supportLists]-->v  <!--[endif]-->Steady-state