(1) Perform product search on the Internet to find a gauge pressure transducer with input range 0-1 bar, current output from 4-20 mA with overall accuracy ± 0.5% FS or better and response time < 2 ms. Provide the datasheet and highlight these specifications on it.
(2) A force sensor has an output range of 1 to 5 V corresponding to an input range of 0 to 2 x 105 N. Find the equation of the ideal straight line.
(3) A pressure transducer has an input range of 0 to 104 Pa and an output range of 4 to 20 mA at a standard ambient temperature of 20°C. If the ambient temperature is increased to 30°C, the range changes to 4.2 to 20.8 mA. Find the values of the environmental sensitivities K1 and KM.
(4) The results reported in the following table were obtained when a pressure transducer was tested in a laboratory under the following conditions:
|
Input
Pressure
(barg)
|
Output Current (mA)
|
|
Conditions
I
|
Conditions
II
|
Conditions
III
|
|
0
|
4
|
4
|
6
|
|
2
|
7.2
|
8.4
|
9.2
|
|
4
|
10.4
|
12.8
|
12.4
|
|
6
|
13.6
|
17.2
|
15.6
|
|
8
|
16.8
|
21.6
|
18.8
|
|
10
|
20
|
28
|
22
|
Conditions I: Ambient temperature 20 °C, supply voltage 10 V (standard conditions) Conditions II: Ambient temperature 20 °C, supply voltage 12 V
Conditions III: Ambient temperature 25 °C, supply voltage 10 V
(a) On one figure, plot the output versus input for conditions I and II. On another figure plot the output versus input for conditions I and III. Which input (temperature or power supply) causes zero bias drift (interfering input), and which input causes sensitivity drift (modifying input)?.
(b) Determine the values of K1, KM, a and K associated with the generalized model equation 0 = (K + KmIm)I + a + KIII.
(c) Predict an output value when the input is 5 barg, the power supply is 12 V and the ambient temperature is 25 °C.
(5) A measurement system consists of a thermocouple, emf-to-current converter and a recorder. The model of each element is given in the table below.
|
|
Thermocouple
|
e.m.f to Current Converter
|
Recorder
|
|
Model
|
E = 0.04T
|
i = 3.9E + 0.0002EΔTa + 0.002ΔTa- 3.8
|
TM = 6.25i + 25
|
|
Standard
deviations
|
σT = 0
|
σΔTa = 10
|
σi = ?
|
Assuming that all probability distributions are normal, calculate the mean and standard deviation of the error probability distribution, when the input temperature is 117 °C and the ambient temperature variation from standard temperature is ΔTa = -10.
(6) A force sensor (similar to the one considered in Example 4 of Lecture 3) has a mass of 0.5 kg, stiffness of 200 N/m and a damping constant of 6.0 N.s/m.
(a) Calculate the steady-state sensitivity, natural frequency and damping ratio for the sensor.
(b) Calculate the displacement of the sensor for a steady input force of 2 N.
(c) If the input force is suddenly increased from 2 to 3 N, derive an expression for the resulting displacement of the sensor.
(d) Express the dynamic error as a function of time using the result you obtained above.
(7) A measurement system consists of two cascaded low-pass first order elements with time constants Τ1 = 1 ms and Τ2 = 0.025 ms.
(a) Find the overall transfer function of the system.
(b) Plot the amplitude frequency response of both systems and the overall amplitude frequency response on the same figure.
(c) Find the bandwidth of each element and the overall system bandwidth
(d) Approximate the rise time of the overall system.