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Chapter 1

Measurement

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After you have read this chapter, you should be able to…

1. Explain the difference between analog and digital measurement systems.

2. Define accuracy, hysteresis, sensitivity.3. List the SI units for length, time, mass, and electric

current.4. Perform conversion from other units to Si units or

vice versa.5. Identify the standard transmission signal and its

P&ID symbols.6. Draw a typical first-order time response curve.

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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.

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Measurement System

A measurement system consists of :i. A sensor that performs the initial measurement

and energy conversion of a variable into analogues digital, electrical, or pneumatic information.

ii. 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.

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Figure 1.2 & fig 1.3 – example of measure

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.

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

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Analog Measurement System

Figure 1.14 (pg. 18)

An analog control system such as this allows continuous variation of some parameter, such as heat input, as a function of error.

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Digital Measurement System

• Figure 1.15 (pg. 19)

In supervisory control, the computer monitors measurements and updates set points, but the loops are still analog in nature.

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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.

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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.

1. SI units (International System on Units )2. 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.

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Examples:1. 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

?

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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 havem =??

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SI UnitsQUANTITY UNIT SYMBOL

BASE

-Length Meter m

-Mass Kilogram kg

-Time Second s

- Electric Current Ampere A

-Temperature Kelvin K

- Amount of substance Mole mol

- Luminuous intensity Candela cd

SUPPLEMENTARY

- Plane angle Radian rad

- Solid angle Steradian sr

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Analog Data Representation

Part of the specification in measurement system is the range of variables involved.

Example : slide 7A 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).

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Analog Data Representation

Two analog standards are in common use as a means of representing the range of variables.

1.Current signals : 4 – 20 mA2. 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.

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Analog Data Representation

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

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Analog Data Representation

Figure 1.6(a) pg 9

The physical diagram of a control loop and its corresponding block diagram look similar. Note the use of current- and pressure-transmission signals.

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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 mA and 250oC by 20 mA, with all temperatures in between represented by a proportional current.

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Why current is used for transmission instead of voltage?

One of the advantages of current as a transmission signal is that it is nearly independent of line resistance.

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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.

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Definitions

1. Error2. Accuracy3. Block Diagram4. Transfer function5. Sensitivity6. Hysteresis and Reproducibility7. Resolution8. Linearity

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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 1 0C.

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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 :1. Measured variable2. % of the instrument full-scale (FS) reading3. % of instrument span4. % of actual reading

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Accuracy

1. Measured variableExample : 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.

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Accuracy

2. % of the instrument full-scale (FS) readingExample :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.

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Accuracy

3. % of instrument spanPercentage 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.

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Accuracy

4. % of actual readingExample :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.

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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)

A transfer function shows how a system-block output variable varies in response to an input variable, as a function of both static input value and time.

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Transfer Function

T(x,y,t) describes the relationship between the input and output for the block.

A transfer function shows how a system-block output variable varies in response to an input variable, as a function of both static input value and time.

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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.

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Hysteresis and Reproducibility

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

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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.

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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.

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Linearity

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

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Drawings

- An electrical schematic is a drawing that employs a standard set of symbols and definitions so that anyone who knows the standards can understand the operation of the circuit.

-The standard was developed and approved by American National Standards Institute (ANSI) and Instrumentation, Systems, and Automation (ISA) society.

- Known as : ANSI/ISA S5.1-1984(R1992) Instrumentation Symbols and Identification.

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DrawingsPiping & Instrumentation Diagram (P&ID)

Computers and programmable logic controllers are included in the P&ID.

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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

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Sensor Time Response

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

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2.2.5 Sensor Time ResponseFirst Order Response and Time Constant

Characteristic first-order exponential time response of a sensor to a step change of input.

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Tutorial Problems – Chapter 11. Section 1.5 –

Q1.82. 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 -a. Describe what elements would be necessary to do (a) analog

measurement and (b) digital measurement system.

b. 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.