1. Dynamic Characteristics

2. 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.

3. 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

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

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

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

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

8. 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.

9. Second Order Time Response
Applying D operator

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

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

13. 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

14. 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

15. 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