The first improved measurement unit was a unit of length (the metre) defined as 107 times the polar quadrant of the earth. A platinum bar made to this length was established as a standard of length in the early part of the nineteenth century. This was superseded by a superior quality standard bar in 1889, manufactured from a platinum–iridium alloy. Since that time, technological research has enabled further improvements to be made in the standard used for defining length. Firstly, in 1960, a standard metre was redefined in terms of 1.65076373 ð 106 wavelengths of the radiation from krypton-86 in vacuum. More recently, in 1983, the metre was redefined yet again as the length of path travelled by light in an interval of 1/299 792 458 seconds. In a similar fashion, standard units for the measurement of other physical quantities have been defined and progressively improved over the years. The latest standards for defining the units used for measuring a range of physical variables are given in Table 1.1. The early establishment of standards for the measurement of physical quantities proceeded in several countries at broadly parallel times, and in consequence, several sets of units emerged for measuring the same physical variable. For instance, length can be measured in yards, metres, or several other units. Apart from the major units of length, subdivisions of standard units exist such as feet, inches, centimetres and millimetres, with a fixed relationship between each fundamental unit and its subdivisions. Table 1.1 Definitions of standard units Physical quantity Standard unit Definition Length metre Mass kilogram The length of path travelled by light in an interval of 1/299 792 458 seconds The mass of a platinum–iridium cylinder kept in the International Bureau of Weights and Measures, S`evres, Paris Time second Temperature kelvin Current ampere Luminous intensity candela Matter mole 9.192631770 ð 109 cycles of radiation from vaporized caesium-133 (an accuracy of 1 in 1012 or 1 second in 36 000 years) The temperature difference between absolute zero and the triple point of water is defined as 273.16 kelvin One ampere is the current flowing through two infinitely long parallel conductors of negligible cross-section placed 1 metre apart in a vacuum and producing a force of 2 ð 107 newtons per metre length of conductor One candela is the luminous intensity in a given direction from a source emitting monochromatic radiation at a frequency of 540 terahertz (Hz ð 1012 ) and with a radiant density in that direction of 1.4641 mW/steradian. (1 steradian is the solid angle which, having its vertex at the centre of a sphere, cuts off an area of the sphere surface equal to that of a square with sides of length equal to the sphere radius) The number of atoms in a 0.012 kg mass of carbon-12
Table 1.2 Fundamental and derived SI units (a) Fundamental units Quantity Standard unit Symbol Length Mass Time Electric current Temperature Luminous intensity Matter metre kilogram second ampere kelvin candela mole m kg s A K cd mol Quantity Standard unit Symbol Plane angle Solid angle radian steradian rad sr (b) Supplementary fundamental units (c) Derived units Quantity Standard unit Symbol Area Volume Velocity Acceleration Angular velocity Angular acceleration Density Specific volume Mass flow rate Volume flow rate Force Pressure Torque Momentum Moment of inertia Kinematic viscosity Dynamic viscosity Work, energy, heat Specific energy Power Thermal conductivity Electric charge Voltage, e.m.f., pot. diff. Electric field strength Electric resistance Electric capacitance Electric inductance Electric conductance Resistivity Permittivity Permeability Current density square metre cubic metre metre per second metre per second squared radian per second radian per second squared kilogram per cubic metre cubic metre per kilogram kilogram per second cubic metre per second newton newton per square metre newton metre kilogram metre per second kilogram metre squared square metre per second newton second per square metre joule joule per cubic metre watt watt per metre kelvin coulomb volt volt per metre ohm farad henry siemen ohm metre farad per metre henry per metre ampere per square metre m2 m3 m/s m/s2 rad/s rad/s2 kg/m3 m3 /kg kg/s m3 /s N N/m2 Nm kg m/s kg m2 m2 /s N s/m2 J J/m3 W W/m K C V V/m F H S m F/m H/m A/m2 Derivation formula kg m/s2 Nm J/s As W/A V/A A s/V V s/A A/V (continued overleaf )
Table 1.2 (continued) (c) Derived units Quantity Standard unit Symbol Magnetic flux Magnetic flux density Magnetic field strength Frequency Luminous flux Luminance Illumination Molar volume Molarity Molar energy weber tesla ampere per metre hertz lumen candela per square metre lux cubic metre per mole mole per kilogram joule per mole Wb T A/m Hz lm cd/m2 lx m3 /mol mol/kg J/mol Derivation formula Vs Wb/m2 s1 cd sr lm/m2 Yards, feet and inches belong to the Imperial System of units, which is characterized by having varying and cumbersome multiplication factors relating fundamental units to subdivisions such as 1760 (miles to yards), 3 (yards to feet) and 12 (feet to inches). The metric system is an alternative set of units, which includes for instance the unit of the metre and its centimetre and millimetre subdivisions for measuring length. All multiples and subdivisions of basic metric units are related to the base by factors of ten and such units are therefore much easier to use than Imperial units. However, in the case of derived units such as velocity, the number of alternative ways in which these can be expressed in the metric system can lead to confusion. As a result of this, an internationally agreed set of standard units (SI units or Syst`emes Internationales d’Unit´es) has been defined, and strong efforts are being made to encourage the adoption of this system throughout the world. In support of this effort, the SI system of units will be used exclusively in this book. However, it should be noted that the Imperial system is still widely used, particularly in America and Britain. The European Union has just deferred planned legislation to ban the use of Imperial units in Europe in the near future, and the latest proposal is to introduce such legislation to take effect from the year 2010. The full range of fundamental SI measuring units and the further set of units derived from them are given in Table 1.2. Conversion tables relating common Imperial and metric units to their equivalent SI units can also be found in Appendix 1. 1.2 Measurement system applications Today, the techniques of measurement are of immense importance in most facets of human civilization. Present-day applications of measuring instruments can be classified into three major areas. The first of these is their use in regulating trade, applying instruments that measure physical quantities such as length, volume and mass in terms of standard units. The particular instruments and transducers employed in such applications are included in the general description of instruments presented in Part 2 of this book.
The second application area of measuring instruments is in monitoring functions. These provide information that enables human beings to take some prescribed action accordingly. The gardener uses a thermometer to determine whether he should turn the heat on in his greenhouse or open the windows if it is too hot. Regular study of a barometer allows us to decide whether we should take our umbrellas if we are planning to go out for a few hours. Whilst there are thus many uses of instrumentation in our normal domestic lives, the majority of monitoring functions exist to provide the information necessary to allow a human being to control some industrial operation or process. In a chemical process for instance, the progress of chemical reactions is indicated by the measurement of temperatures and pressures at various points, and such measurements allow the operator to take correct decisions regarding the electrical supply to heaters, cooling water flows, valve positions etc. One other important use of monitoring instruments is in calibrating the instruments used in the automatic process control systems described below. Use as part of automatic feedback control systems forms the third application area of measurement systems. Figure 1.1 shows a functional block diagram of a simple temperature control system in which the temperature Ta of a room is maintained at a reference value Td . The value of the controlled variable Ta , as determined by a temperature-measuring device, is compared with the reference value Td , and the difference e is applied as an error signal to the heater. The heater then modifies the room temperature until Ta D Td . The characteristics of the measuring instruments used in any feedback control system are of fundamental importance to the quality of control achieved. The accuracy and resolution with which an output variable of a process is controlled can never be better than the accuracy and resolution of the measuring instruments used. This is a very important principle, but one that is often inadequately discussed in many texts on automatic control systems. Such texts explore the theoretical aspects of control system design in considerable depth, but fail to give sufficient emphasis to the fact that all gain and phase margin performance calculations etc. are entirely dependent on the quality of the process measurements obtained. Comparator Reference value Td Error signal Heater (Td−Ta) Room Room temperature Ta Ta Temperature measuring device Fig. 1.1 Elements of a simple closed-loop control system.