Control Engineering BDA30703
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1 Control Engineering BDA30703 Lecture 3: Performance characteristics of an instrument Prepared by: Ramhuzaini bin Abd. Rahman
2 Expected Outcomes At the end of this lecture, students should be able to; 1) Explain the differences between the static and dynamic characteristics of an instrument. 2) List the static and dynamic characteristics of an instrument 3) Elaborate the static calibration process Topics Learning: 1) Static characteristics 2) Static calibration 3) Dynamic characteristics 2
3 1.0 Static characteristics Definition The steady state relationship between input and output of an instrument Measurement of quantities that are constant or vary quite slowly with respect to time. It does not involve differential equations. All the static performance characteristics are obtained by one form or another via a process called static calibration. 3
4 Precise vs Accurate 1.0 Static characteristics (cont. d) Measurements that are close to each other are precise. Measurements that are close to the correct value are accurate. Measurements can be: Precise but inaccurate Neither precise nor accurate Precise and accurate 4
5 1.0 Static characteristics (cont. d) Example Three industrial robots were programmed to place components at a particular point on a table. The target point was the center of a circle shown below. The results are: (a) Low precision and low accuracy (b) Precise but not accurate (c) Precise and accurate 5
6 Output of device 1.0 Static characteristics (cont. d) Inaccuracy/measurement uncertainty Is the extent to which a reading might be wrong, and is often quoted as percentage of the full-scale (f.s) reading of an instrument. Tolerance Ideal device accuracy at % of f.s Value of measurand defines as the maximum error that is to be expected in some value. 6
7 1.0 Static characteristics (cont. d) Range or span Defines as the minimum and maximum values of a quantity that the instrument is designed to measure. Threshold A certain minimum level of input that an instrument has to reach before the output reading is of a large enough magnitude to be detectable. Resolution A lower limit on the magnitude of the change in the input measured quantity that produces an observable change in the instrument output. 7
8 1.0 Static characteristics (cont. d) Linearity The input and output relationship of a linear transducer can be represented by the following equation: y = mx + c where y is the output of transducer, x is the input of transducer, m is the slope of curve (transfer function), c is the offset. Often, the straight line approach is used for certain range of operation for a non-linear system. It is highly desirable that the measurement system has a linear relationship between input and output means that the change in output is proportional to the change in the value of the measurand. Deviation from true linearity is called linearity error. 8
9 Sensitivity 1.0 Static characteristics (cont. d) Sensitivity is the ratio of change in magnitude of the output to the change in magnitude of the measurand Sensitivity=Δ(output)/Δ(input) Sensitivity vs nonlinearity 9
10 Hysteresis 1.0 Static characteristics (cont. d) Hysteresis results in predictable error. May be due to internal friction, freeplay or looseness in the mechanism of an instrument. Also in electrical phenomena (relation between the output voltage and the input field current in a d.c. generator) - the effect is due to magnetic hysteresis of the iron in the field coils. The transfer functions differ with the increase and decrease of inputs. 10
11 1.0 Static characteristics (cont. d) Instrument characteristic with hysteresis 11
12 Dead space 1.0 Static characteristics (cont. d) defines as the range of different input values over which there is no change in output value. Instrument characteristic with dead space 12
13 2.0 Static calibration Imagine a situation in which all inputs (desired, interfering or modifying) except one are kept at some constant values. The one input under study is varied over some range of constant values which causes the output(s) to vary over some range of constant values. The input/output relationships developed in this way comprise a static calibration valid under the stated constant conditions of all other inputs. The procedure may be repeated for other inputs for overall instrument static behaviour Ultimate objective is to define measurement accuracy 13
14 3.0 Dynamic characteristics The dynamic characteristics of a measuring instrument describe its behavior between the time a measured quantity changes value and the time when the instrument output attains a steady value in response. Instruments rarely respond instantaneously to changes in the measured variables due to such things as mass, thermal capacitance, fluid capacitance or electrical capacitance There are three most common variations in the measured quantity: step change linear (ramp) change sinusoidal change The static characteristics of measuring instruments are concerned only with the steadystate reading that the instrument settles down to, such as the accuracy, etc 14
15 3.0 Dynamic characteristics (cont. d) Zero order instrument Following a step change in the measured quantity at time t, the instrument output moves immediately to a new value at the same time instant t. A potentiometer, which measure motion, is a good example of such an instrument, where the output voltage changes instantaneously as the slider is displaced along the potentiometer track. q o = Kq i Note: K is instrument sensitivity Zero order instrument characteristic 15
16 3.0 Dynamic characteristics (cont. d) First order instrument First order instrument characteristic A large number of measuring instruments belong to this first class order. (e.g., liquid-in-glass thermometer) It is necessary to take account of the time lag that occurs between a measured quantity changing in value and the measuring instrument indicating the change where: q o = K 1 + τs q i K is instrument sensitivity τ is time constant 16
17 3.0 Dynamic characteristics (cont. d) Second order instrument Second order instrument characteristic The shape of the step response depends on the value of the damping ratio parameter ξ. The output responses of a second order instrument for various value of ξ following a step change in the value of the measured quantity at time t are shown in the figure. q o q i = Kω 2 s 2 + 2ξωs + ω 2 K is instrument sensitivity, ω is undamped natural frequency and ξ is damping ratio 17
18 Exercise What is the meaning of the following words: Measurand Physical quantity Data Parameter Transducer Actuator 18
19 Answers Measurand: Physical quantity being measured Physical quantity: Variable such as pressure, temperature, mass, length, etc Data: Information obtained from the instrumentation/measurement system as a result of the measurements made of the physical quantities Parameter: Physical quantity within defined (numeric) limits. Transducer: A device that converts one form of energy to another Actuator: Electronic transducer that converts electrical energy into mechanical energy 19
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