1) The document discusses measurement systems and provides definitions for key terms like accuracy, sensitivity, hysteresis, and resolution. It describes analog and digital measurement systems and the components that make them up, including sensors, signal conditioning, and controllers. 2) Common units for physical quantities like length, time, mass and current are discussed as well as standards for measurement. Analog signals like 4-20 mA and 3-15 psi are described for representing variable ranges. 3) Drawings like P&IDs (piping and instrumentation diagrams) and electrical schematics are addressed along with the standards that define their symbols. Sensor response curves are examined, including first-order exponential curves. Tutorial problems are presented at the

1. Chapter 1 Measurement 1

2. After you have read this chapter, you should be able to… Explain the difference between analog and digital measurement systems. Define accuracy, hysteresis, sensitivity. List the SI units for length, time, mass, and electric current. Perform conversion from other units to Si units or vice versa. Identify the standard transmission signal and its P&ID symbols. Draw a typical first-order time response curve. 2

3. Introduction A measurement refers to the conversion of the variable into some corresponding analog of the variable, such as pneumatic pressure, an electrical voltage or current, or a digitally encoded signal. 3

4. Measurement System A measurement system consists of : A sensor that performs the initial measurement and energy conversion of a variable into analogues digital, electrical, or pneumatic information. A signal conditioning for further transformation to complete the measurement function. The sensor is also called a “transducer” -a device that converts any signal from one form to another. 4

5. Figure 1.2 & fig 1.3 – example of measure 5 A human can regulate the level using a sight tube, S, to compare the level, h, to the objective, H, and adjust a valve to change the level.

6. 6 An automatic level-control system replaces the human with a controller and uses a sensor to measure the level.

7. Analog Measurement System Figure 1.14 (pg. 18) 7 An analog control system such as this allows continuous variation of some parameter, such as heat input, as a function of error.

8. Digital Measurement System Figure 1.15 (pg. 19) 8 In supervisory control, the computer monitors measurements and updates set points, but the loops are still analog in nature.

9. Units, Standards, and Definitions The field of measurement has many sets of units, standards, and definitions to describe its characteristics. In this section, we will go through common units, standards and definitions used in the measurement technology. 9

10. Units To ensure precise technical communication among individuals employed in technological disciplines, it is essential to use a well-defined set of units of measurement. SI units (International System on Units ) Other units (CGS, English system) In United States, the English system of units is still common in use. We should be able to translate between the SI unit to other unit or vice versa. Refer Appendix 1. 10

11. Examples: Express a pressure of p =2.1x103 dyne/cm2 in pascals. 1 Pa=1 N/m2 Solution : 100cm= 1 m and 105 dyne = 1 newton; thus p = ? N/m2 =? pascals (Pa) 2. Express 6.00 ft in meters. Solution : Using 39.37 in./m and 12 in./ft; thus ? 11

12. 3. Find the number of feet in 5.7m. Solution : 1 m=39.37in and 1 ft=12 in; thus ? 4. Express 6.00 ft in meters. Solution : Using 39.37 in./m and 12 in./ft; thus ? 5. Find the mass in kilograms of a 2-lb object. Solution : The conversion factor between mass in kilograms and pounds to be 0.454 kg/lb. Therefore, we have m =?? 12

13. SI Units 13

14. Analog Data Representation Part of the specification in measurement system is the range of variables involved. Example : slide 7 A thermistor sensor is used to measure temperature in an oven. The range of temperature inside the oven is from 0oC to 250oC. - 0oC to 250oC is the range of variables in the process (in this case oven). 14

15. Analog Data Representation Two analog standards are in common use as a means of representing the range of variables. 1.Current signals : 4 – 20 mA 2. Pneumatic signals : 3 – 15 psi These signals are used to transmit variable information over some distance, such as to and from the control room and plant. 15

16. Analog Data Representation Electric current and pneumatic pressures are the most common means of information transmission in the industrial environment. 16

17. Analog Data Representation Figure 1.6(a) pg 9 17 The physical diagram of a control loop and its corresponding block diagram look similar. Note the use of current- and pressure-transmission signals.

18. Current Signal : 4-20 mA The common current transmission signal is 4 to 20 mA. In the previous example, range of temperature inside the oven is from 0oC to 250oC. 0oC might be represented by 4 mAand 250oC by 20 mA, with all temperatures in between represented by a proportional current. 18

19. Why current is used for transmission instead of voltage? 19 One of the advantages of current as a transmission signal is that it is nearly independent of line resistance.

20. Pneumatic Signal : 3 – 15 psi The common pneumatic transmission signal is 3 to 15 psi. When a sensor measures some variable in a range (for example, temperature in oven 0oC to 250oC), it is converted into proportional pressure of gas in pipe. The gas is usually dry air. The English system standard is still widely used in the United States, despite the move to the SI units. The equivalent SI range is 20 to 100 kPa. 20

21. Definitions Error Accuracy Block Diagram Transfer function Sensitivity Hysteresis and Reproducibility Resolution Linearity 21

22. Error Error is the difference between the actual value of a variable and the measured indication of its value. Example : The current temperature inside the oven is 900C. However, the measurement from temperature sensor inside the oven is 890C.Therefore, the error is 10C. 22

23. Accuracy To specify the maximum overall error to be expected from a device, such as measurement of a variable. Can appear in several forms such as : Measured variable % of the instrument full-scale (FS) reading % of instrument span % of actual reading 23

24. Accuracy Measured variable Example : The accuracy of temperature sensor used to measure the oven temperature is ± 1oC. Thus, if the current temperature inside the oven is 90oC, a reading between 89oC to 91oC is acceptable. 24

25. Accuracy 2. % of the instrument full-scale (FS) reading Example : An analog multimeter with 5-V full-scale range gives an accuracy of ± 00.5% FS. This means the uncertainty in any measurement is ±0.025V. If we want to measure a 5-V voltage using this analog multimeter, the measurement between (5 -0.025)V and (5+0.025)V is acceptable. 25

26. Accuracy 3. % of instrument span Percentage of the range of instrument measurement capability. Example : A pressure sensor device is measuring ±3% of span for a 3 to 15 psi range of pressure. Thus, the accuracy of the device is (±0.03)(15-3)=±0.36 psi. 26

27. Accuracy 4. % of actual reading Example : For a 2% of reading voltmeter, we will have an inaccuracy of ±0.04V for a reading of 2V. Please look into Example 1.8, 1.9,1.10 for further understanding about accuracy. 27

28. Block Diagram A block has an input of some variable, x(t) and an output of another variable y(t). Figure 1.21 (pg. 27) 28 A transfer function shows how a system-block output variable varies in response to an input variable, as a function of both static inputvalue and time.

29. Transfer Function T(x,y,t) describes the relationship between the input and output for the block. 29 A transfer function shows how a system-block output variable varies in response to an input variable, as a function of both static inputvalue and time.

30. Sensitivity A measure of change in output of an instrument for a change in input. High sensitivity is desirable in an instrument. Sensitivity must be evaluated together with other parameters, such as linearity of output to input, range, and accuracy. The value of sensitivity is indicated by transfer function. Example : when temperature transducer outputs 5 mV per degree Celcius, the sensitivity is 5 mV/oC. 30

31. Hysteresis and Reproducibility 31 Hysteresis is a predictable error resulting from differences in the transfer function as the input variable increases or decreases.

32. Resolution Resolution of a device is a minimum measurable value of the input variable. This characteristic of the instrument can be changed only by redesign. Example 1.12 : A force sensor measures a range of 0 to 150N with a resolution of 0.1% FS. Find the smallest change in force that can be measured. Solution : Because the resolution is 0.1% FS, we have a resolution of (0.001)(150N) = 0.15N, which is the smallest measurable change in force. 32

33. Linearity In both sensor and signal conditioning, a linear relationship between input and output is highly desirable. Example : Consider a sensor that outputs a voltage as a function of pressure from 0 to 100 psi with a linearity of 5% FS. This means, at some point on the curve of voltage versus pressure, the deviation between actual pressure and linearly indicated pressure for a given voltage deviates by 5% of 100psi, or 5 psi. 33

34. Linearity Comparison of an actual curve and its best-fit straight line, where the maximum deviation is 5% FS. 34

36. DrawingsPiping & Instrumentation Diagram (P&ID) 36 Computers and programmable logic controllers are included in the P&ID.

37. Sensor Time Response The sensing element inside the sensor has a time dependence that specifies how the output changes in time when the input is changing in time. Time response analysis is always applied to the output of the sensor. Figure 1.27 37

38. Sensor Time Response Figure 1.27 38 The dynamic transfer function specifies how a sensor output varies when the input changes instantaneously in time (i.e., a step change).

39. 2.2.5 Sensor Time ResponseFirst Order Response and Time Constant 39 Characteristic first-order exponential time response of a sensor to a step change of input.

40. Tutorial Problems – Chapter 1 Section 1.5 – Q1.8 Section 1.6 – Q 1.15, 1.16, 1,17, 1.18,1.19,1.20,1.21,1.23, 1.24 3. Additional questions - Describe what elements would be necessary to do (a) analog measurement and (b) digital measurement system. By referring to Figure 1.36 (Supplementary Problems QS1.8), identify all the sensors available in the drawing and the type of signals that connect the sensors (4-20 mA or 3-15 psi). Refer to Appendix 5 for P&ID symbols. 40