Draw and explain the response of first order and second order instruments to the step input.

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First order instrument response to step input:

The time equation for the step response of a first order instrument is exponential in nature and is given by the equation,

c(t) = 1- −/

Where, is called the time constant of the system.

It shows that, the value of the unit step response, c(t) is zero at t = 0 and for all negative values of t. It is gradually increasing from zero value and finally reaches steady state. The steady state value depends on the magnitude of the input. Second order instrument response to step input: The step response of the second order instrument is oscillatory in nature. Depending upon the value of damping ratio, it may be over, under or critically damped or even un- damped.

Fig. below shows the response for an under- damped case. The response up to the settling time is known as transient response and the response after the settling time is known as steady state response. Analysis of such a system is done by calculating different parameters called time response specifications. 