Dynamic Characteristics

Dynamic Characteristic -Output Response of an instrumentation is a function of time when input applied is changed. - Relation btw input and output for nth order is represented as: -3 types of dynamic: Zero order system response, first order system and second order system.

Zeroth Order System -Zero Order is represented by the following equation :- a0y=b0u, y=Ku y= output, u=input, K=b0/a0= static sensitivity / gain -output is obtained as soon as input is applied -Eg: potentiometer

First Order System Response -divide with ao -T=a1/a0=time constant, K=b0/a0=static sensitivity

First Order System general equation: Sensor u(t) y(t)

-eq : thermocouple T= time constant time when the output is 63% of the steady state output.

General equation as a function of time: bi = initial value output bf = final value output T = time constant

Example 1 A sensor measures temperature linearly with a static transfer function of 33 mV/0C and has a 1.5-s time constant. Find the output 0.75 s after input changes from 200C to 410C. Find the error in temperature this represents.

Second Order Time Response Applying D operator

Rearranging where: =damping ratio, n=natural frequency

The time response is given as q0(t)  qe-atsin(nt) where q=amplitude and a= n is output damping ratio -eg:accelerometer

Tutorial 1 A pressure sensor has a resistance that changes with pressure according to R = (0.15 k/psi)p +2.5 k. This resistance is then converted to a voltage with the transfer function

The sensor time constant is 350 ms The sensor time constant is 350 ms. At t = 0, the pressure changes suddenly from 40 psi to 150 psi a) What is the voltage output at 0.5 s? What is the indicated pressure at this time? b) At what time does the output reach 5.0V

Tutorial 2 At t = 0, a temperature sensor was suddenly changed from 250C to 1000C. The sensor outputs voltage given by the expression V = (0.06 V/0C)[T-200C]. The following table gives the voltages measured and the times. Determine the average time constant of the sensor. t(s) 0.1 0.2 0.3 0.4 0.5 V 1.8 2.8 3.4 3.9 4.2