Elements of metrology in measurements of process variables

As we mentioned above, the more accurate a measuring instrument can measure the value of a process variable the more accurate a control system can control this variable. As a result, we can achieve the objective of a particular process (the desired quality of the product, the minimum consumption of energy, etc). What do we mean under the term of an accuracy?

It is not possible to measure any variable without an error.

An error of the measurement is the difference between a measured value and a true value of a measured variable. Since we cannot determine the true value of a measured variable then, instead of it, we can use its actual value, which can be measured by a reference measuring instrument with a high degree of accuracy. Thus, an absolute error is equal to the absolute value of the difference between a measured value and an actual value of a process variable, as follows:

,                                                         (1.2)

where:             Am      - the value determined by a measuring device;

                       Aa      - the actual value of a process variable.

This error is expressed by the units of the measured variable (or quantity), ie, m, A, V, m/s, K, Pa, kg/m³, Pa*s, kg/s, m³/s, etc.

In order to determine errors of instruments and corrections to values of measured variables, all measuring instruments are regularly subjected to verification according to standard or reference instruments.

Accuracy is an agreement of a measurement with the true value of a measured quantity. We should know how accurate the measuring device can measure a process parameter. In general form accuracy is usually expressed as a percentage of the instrument span (the range of instrument measurement capability) or full-scale

,                                                  (1.3)

where:

            A_max  and A_min  - maximum and minimum values of a process variable  respectively, which can be measured by a measuring instrument;

            A_max  - A_min- a span or full-scale of a measuring instrument.

There is another characteristic of a measurement process.

Repeatability, according to a British Standard definition, "is the ability of a measuring instrument to give identical indications, or responses, for repeated applications of the same value of the measured quantity under stated conditions of use. If an accuracy is the ability of the device or an instrument to tell the truth about the process parameters, the repeatability is the ability of an instrument to stick the same story. Instruments as well as people are sometimes capable to tell the same lie over and over again. Good repeatability is no guarantee of good accuracy, although poor repeatability is a sure sign of poor accuracy. In other words, good repeatability is a necessary, but not sufficient condition of good accuracy." (Hayward A.T.J., Repeatability and Accuracy, 1977).

Sensitivity is a measure of the change in output of an instrument for a change in input. In other words, it is the ability of a measuring device to detect small differences in a quantity being measured. High sensitivity is desirable in an instrument because a large change in output for a small change in input implies that a measurement may be taken easily.

Example: if a very small change in pressure applied to two pressure gages results a perceptible change in the indications of one instrument and not in the other, it is said that the former is more sensitive instrument. The most sensitive instrument equipment may not always lead to the most precise or the most accurate results. The sensitivity of a measuring device with a linear static characteristic is equal to the ratio between the variation of the output signal of the measuring instrument and the variation of its input signal which causes that variation of the output signal

,                                                        (1.4)

where:                     S- the sensitivity of an instrument;

                             ΔX - the variation of an input signal;

                             ΔY - the variation of an output signal.

If in the temperature range from 0 to 50 °C temperature variation in one degree Celsius causes the change in an output signal of a temperature transducer in 4 mV, it is said that the sensitivity of this transducer is equal to 4 mV/°C in the above temperature range. Why we say “in the above temperature range”? It is known that static behaviour of a system or a measuring instrument can be expressed graphically (see Fig. 1.5). It is not correct to say that thermocouple, which correlation of thermoelectromotive force vs temperature is graphically shown in this figure, has the same sensitivity in the entire temperature range. Sensitivity of a mesuring instrument (or sensor, or transducer) has different values when its static characteristic is non-linear, and it is constant in the case of a linear static characteristic.

Article Source: Dr. Alexander Badalyan, University of South Australia