Performance characteristics for measurement and instrumentation system Lecture 3 Performance characteristics for measurement and instrumentation system

3 classifications to define the performance of measurement system: operational, static, dynamic Operational characteristic Range Span Sensitivity Resolution Dead band/threshold

Range -will give the minimum and maximum range Span -the difference between the maximum and minimum range Eg: A specification of a thermometer reads as follows: Range and subdivision oC - -0.5 to +40.5 0.1 Min is –0.50C and max is 40.50C Span = 410C

Sensitivity -ratio of a change in output to the change in input which causes it at steady-states condition -Eg. A galvanometer has a sensitivity of 17mm/A -for a 1A input display, a light spot moving across the scale shows a movement of an index of 17 mm

Resolution The least incremental value of input or output that can be detected Dead band / Threshold The largest range of values of a measured variable to which the instrument does not respond

RULERS Normal - straight Folding ruler

VERNIER CALIPERS

Digital vernier caliper

HOW TO READ A VERNIER Scale reading = 3.70cm Vernier reading = (0.1/10) x 4 = 0.04 Caliper reading = 3.74cm

SCREW GAUGE

Static characteristic: Error Accuracy Precision Repeatability Linearity Hysteresis calibration

Error -Error is the difference between the true value Yn and instrument reading Xn e = Yn – Xn -Types of errors: systematic error (bias error) and random error (precision error) -Bias (systemic) error-consistent and repeatable error Bias error = average readings – true value

-Random error-the lack of repeatability in the output of the measuring system Random error = reading – average reading

Accuracy -Ability of the system to respond to a true value -Limit of error of a measuring device under certain operating conditions and can appear is several forms: 1. Measured variable: the accuracy is 0.2 of the measurement -If the temperature reading = 30.10C, the actual temperature lies between 29.90C and 30.30C 2. Percentage of full scale (FS), accuracy 1% f.s -If the full scale is 10 A, accuracy = 0.1 A

3. Percentage of instrument span, accuracy 3% span -If the span for pressure measurement is 20-50 psi, accuracy = 0.03 (50-20) = 0.9 psi 4. Given as percentage of actual reading, e.g. for a 2% -If the true value of the voltmeter is 2 V, accuracy = (2 0.02) = 0.04 V

Example 1.1 A temperature sensor has a span of 200C –2500C. A measurement results in a value of 550C for temperature. Specify the error if the accuracy is: a) 0.5%FS b) 0.75% of span c) 0.8% of reading What is the possible temperature in each case

Example 1.2 A temperature sensor has a transfer function of 5 mV/0C with an accuracy of 1%. Find the possible range of the transfer function?

Example 1.3 Suppose a reading of 27.5 mV results from the sensor used in previous example. Find the temperature that could provide this reading.

System accuracy Overall accuracy of many elements in a process-control loop to represent a process variable V V = (K K) (G G)C V = output voltage V = uncertainty in output voltage K,G = nominal transfer functions K, G = uncertainty in transfer functions C = dynamic variable

K K G G V V C The overall system accuracy as the root-mean-square (rms):

Example 1.4 Find the system accuracy of a flow process if the transducer transfer function is 10 mV/(m3/s) ±1.5% and the signal-conditioning system-transfer function is 1mA/mV ±0.05%

Precision -The degree of exactness of which an instrument is designed or intended to performed -Significant figures convey actual information regarding the magnitude and the measurement precision of a quantity -The more the significant the figure, the greater the precision of measurement

Repeatability -The ability of the system to display the same output for a series of applications of the same input signal, under the same operating conditions Linearity -The output reading of the measurement is linearly proportional to the quantity being measured

Hysteresis -different reading may be obtained if the variable was increasing prior to taking the reading if the variable was decreasing -causes: friction, mechanical flexure of internal part, electrical capacitance

Calibration -process of checking a measuring system against a standard reading -purposes: To ensure readings from an instrument are consistent with other measurements To determine the accuracy of the instrument readings To establish the reliability of the instrument i.e. that it can be trusted