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Chapter 2: Performance Characteristics of Instruments By Sintayehu Challa

Introduction to Instrumentation Engineering. Chapter 2: Performance Characteristics of Instruments By Sintayehu Challa. Goals for this Chapter. Differentiate the difference between steady state and transient behaviors of instruments

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Chapter 2: Performance Characteristics of Instruments By Sintayehu Challa

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  1. Introduction to Instrumentation Engineering Chapter 2: Performance Characteristics of Instruments By Sintayehu Challa

  2. Goals for this Chapter • Differentiate the difference between steady state and transient behaviors of instruments • They describe performance characteristics of an instruments • Identify terminologies used to define static and dynamic performance Introduction to Instrumntaion Eng‘g - Ch. 2 Performance Char. of Instruments

  3. Overview • Static characteristics • Dynamic characteristics Introduction to Instrumntaion Eng‘g - Ch. 2 Performance Char. of Instruments

  4. Performance Characteristics • Type of instrument to be used is decided on the characteristics required • E.g., a  0.5oC accuracy instrument is allowable for human body (feeling) while it may be useless for an instrument in a control system • So for selection, the performance characteristics of measuring instruments must be known • Various terminologies are used to define the performance • Instrument performance characteristics is generally broken down into two, namely • Static characteristics • Dynamic characteristics Introduction to Instrumntaion Eng‘g - Ch. 2 Performance Char. of Instruments

  5. Static Characteristics • Static characteristics describes performance of instruments under constant or slowly-varying input • Concerned with steady-state reading, i.e., when the instrument settles down • Since static characteristics affects the dynamic behavior, the overall performance is then judged by a semi-quantitative superposition of the static and dynamic characteristics • Terminologies used to define static characteristics • Range, span, linearity, sensitivity, threshold, resolution, error, etc . . . Introduction to Instrumntaion Eng‘g - Ch. 2 Performance Char. of Instruments

  6. Range and Span • Range: Is the limits between which the input can vary • Range of an instrument defines the minimum and maximum values of a quantity that the instrument is designed to measure, i.e., • Input range – Imin , Imax • Output range – Omin , Omax • E.g., a resistance thermometer sensor might be quoted as having a range of 00C to +8000C • Span: Is the maximum variation • Input span – Imax – Imin • Output span – Omax– Omin Introduction to Instrumntaion Eng‘g - Ch. 2 Performance Char. of Instruments

  7. Linearity • The output reading of an instrument is linearly proportional to the quantity being measured • Input output relation is governed by a straight line • One desirable property of instruments Introduction to Instrumntaion Eng‘g - Ch. 2 Performance Char. of Instruments

  8. Sensitivity • Ratio of the change in output to the corresponding change in input under steady-state conditions • Is the slope of the input-output curve • Indicates by how much the output of an instrument changes when the quantity being measured changes by a given amount • The sensitivity can be linear or non-linear Introduction to Instrumntaion Eng‘g - Ch. 2 Performance Char. of Instruments

  9. Threshold and Resolution • Threshold • If the instrument’s input is increased very gradually from zero, there will be some minimum value below which no output change can be detected • This minimum value defines the threshold of the instrument • Manufacturers specify it as an absolute value or percentage of full scale reading • Resolution • Smallest possible increment discernible between measured values • Or the minimum input change that can be detected by the system • As the term is used, higher resolution means smaller increments • An instrument with a five-digit display (say, 0.0000 to 9.9999) is said to have higher resolution than an identical instrument with a three-digit display (say, 0.00 to 9.99) Introduction to Instrumntaion Eng‘g - Ch. 2 Performance Char. of Instruments

  10. Hysteresis • This is an effect of producing different readings when the measured quantity is approached from above or below • Instrument will not have the same output for the same input in repeated trials • It may be the result of mechanical friction, or thermal effects Introduction to Instrumntaion Eng‘g - Ch. 2 Performance Char. of Instruments

  11. Accuracy • The maximum expected difference in magnitude between measured and true values • Accuracy of an instrument is a measure of how close the output reading of the instrument is to the true/correct value • Equivalently, accuracy is the extent to which the value indicated by a measurement system or element might be wrong • Often expressed as a percentage of full scale reading • E.g., A 1% accuracy over a full scale pressure reading of 100 kPa will be accurate within 1 kPa • Plus or minus inaccuracies are also termed as measurement uncertainties Introduction to Instrumntaion Eng‘g - Ch. 2 Performance Char. of Instruments

  12. Precision • Indicates the ability of an instrument to reproduce a certain reading of a constant input with a given accuracy • If no reproducibility, then the instrument is said to have a drift • E.g., for a true value of 100 V, if measured values are 104, 103, 105, 100, 105, then the accuracy is 5 V • Precision is also defined as the maximum deviation from mean • In the above example, mean = 103.4 so that max. deviation = 1.6 V • Hence precision is 1.6% • High precision measurement instrument gives a small spread of readings and vice versa Introduction to Instrumntaion Eng‘g - Ch. 2 Performance Char. of Instruments

  13. Accuracy vs. Precision Introduction to Instrumntaion Eng‘g - Ch. 2 Performance Char. of Instruments

  14. System Disturbances (or Environmental Effects) • Zero drift or bias or interfering input • Describes the effect where the zero reading (or intercept) of an instrument is modified by a change in the ambient conditions • Causes a constant error that exists over the full range of measurement of the instrument • Sensitivity drift or scale factor drift or modifying input • Defines the amount by which an instrument’s sensitivity varies as ambient conditions change • It is quantified by sensitivity drift coefficient Introduction to Instrumntaion Eng‘g – Ch.2 Performance Char. of Instruments

  15. Sensitivity to Disturbance • Instrument’s specifications are valid only under controlled conditions of temperature, pressure etc… • As variations occur in the ambient temperature etc., certain static instrument characteristics change • E.g., sensitivity can be affected by zero and sensitivity drift as shown in the figure • Sensitivity to disturbance measures the magnitude of this change Introduction to Instrumntaion Eng‘g - Ch. 2 Performance Char. of Instruments

  16. Sensitivity to Disturbance … Introduction to Instrumntaion Eng‘g - Ch. 2 Performance Char. of Instruments

  17. Error • Two types of errors, namely systematic and random errors • Systematic error: Cause repeated readings to be in error by the same amount, i.e., consistent error signs • Due to instrument short coming and environmental effects • Related to calibration errors and can be eliminated by correct calibration • Accuracy is related to such type of errors • Random errors: Caused by random electronic fluctuations in instruments, unpredictable behavior of the instrument, influences of friction, etc… • Such errors are related to precision • Characterized by positive and negative errors • Random fluctuations usually follow certain statistical distribution Introduction to Instrumntaion Eng‘g - Ch. 2 Performance Char. of Instruments

  18. Error • Difference between result of measurement and true value of the quantity being measured • E.g., If the measured value is 10.1 when the true value is 10.0, the error is +0.1. If the measured value is 9.9 when the true value is 10.0, the error is-0.1. Introduction to Instrumntaion Eng‘g - Ch. 2 Performance Char. of Instruments

  19. Tolerance • A term that is closely related to accuracy and defines the maximum error that is to be expected in some value • When used correctly, tolerance describes the maximum deviation of a manufactured component from some specified value • E.g., crankshafts are machined with a diameter tolerance quoted as so many microns (10-6m) • Electric circuit components such as resistors have tolerances of perhaps 5% • One resistor chosen at random from a batch having a nominal value 1000 ohm and tolerance 5% might have an actual value anywhere between 950 ohm and 1050 ohm Introduction to Instrumntaion Eng‘g - Ch. 2 Performance Char. of Instruments

  20. Overview • Static characteristics • Dynamic characteristics Introduction to Instrumntaion Eng‘g - Ch. 2 Performance Char. of Instruments

  21. Dynamic Characteristics of Instruments • Describe behaviors between the time an input quantity changes its value and the time when the instrument output attains a steady value • Are useful when the input signal is rapidly varying • Used to study performance under transient conditions • In general, both static and dynamic characteristics are important to characterize a given instrument • Ordinary linear differential equation with constant coefficients is the most widely used mathematical model to study dynamic response in the form • Usually linear, time-invariant (LTI) system assumed Introduction to Instrumntaion Eng‘g - Ch. 2 Performance Char. of Instruments

  22. Dynamic Characteristics … • In an LTI system, input and output, for time t > 0, are related as: • where qiis the measured (input) quantity, q0 is the output reading and a0 . . . an, b0 . . . bm are constants • Using the method of Laplace-transform, equation (2.1) is • Or (2.1) (2.2) Introduction to Instrumntaion Eng‘g - Ch. 2 Performance Char. of Instruments

  23. Dynamic Characteristics …. • If we limit consideration to step changes in the measured quantity only, then Equation (2.1) reduces to: • So that • Based on the order of Equation (2.3), equipments are classified as zero-, first-, and second-order instruments (2.3) Introduction to Instrumntaion Eng‘g - Ch. 2 Performance Char. of Instruments

  24. Zero-order Instrument • When all the coefficients a1 . . . an other than a0and bo are assumed to be zero, Equation (2.3) then degenerates into • Any instrument that closely obeys Equation (2.4) is defined to be a zero-order instrument • The two constants can be combined to give • where K=bo/ao is static sensitivity • From Equation (2.4), no matter how qi might vary with time, the output follows it perfectly with no distortion or time lag • Zero-order instrument represents ideal or perfect dynamic performance (2.4) (2.5) Introduction to Instrumntaion Eng‘g - Ch. 2 Performance Char. of Instruments

  25. Zero-order Instrument … • Example: Displacement measuring potentiometer • Given linear distribution of resistance along length L, the output voltage eo can be written as • Measurement error em = Kqi - eo = o (ideal) Introduction to Instrumntaion Eng‘g - Ch. 2 Performance Char. of Instruments

  26. First-order Instrument • If all the coefficients a2 . . . an except for a0, a1, and b0 are assumed zero in equation (2.3) then: • Using the Laplace transform and rearranging, we get • Defining K = b0/a0 as the static sensitivity and =a1/a0 as the time constant of the system, equation (2.7) becomes (2.6) (2.7) (2.8) Introduction to Instrumntaion Eng‘g - Ch. 2 Performance Char. of Instruments

  27. First-order Instrument … • Examples of first-order instruments • Temperature measurement system • Amplifiers • Electromechanical and electronic meters • Graphical recorders • CRO (RC and RL network of CRO) • The dynamic behavior can be studied with the response of the system due to standard test inputs • Example: Impulse, step, ramp, sinusoidal inputs Introduction to Instrumntaion Eng‘g - Ch. 2 Performance Char. of Instruments

  28. First-order Instrument … • If equation (2.8) is solved analytically, the output q0 in response to a step change in qi at time t is shown in the figure below • Time constant  is the time taken for the output quantity q0 to reach 63% of its final value Introduction to Instrumntaion Eng‘g - Ch. 2 Performance Char. of Instruments

  29. Performance Parameters • Dynamic characteristics that are useful in characterizing the speed of response of any instrument include • Rise Time: Time required for a response to reach 90% of the step input (final value) • Settling time: Time to reach and stay within a stated  tolerance value around its final value • Knowing fast response requires a small value of  • Need to know which parameters to vary to reduced settling time Introduction to Instrumntaion Eng‘g - Ch. 2 Performance Char. of Instruments

  30. Exercise • From the First order RC and RL SERIES NETWORK A) Find the input and output Equation? B) Find the time constant and static sensitivity factor? C) Find the Transfer and System function? 2. Determine the step response of First order system and sketch the system including all parameter? 3. Repeat Exercise 2 for the Ramp response? 4. Repeat Exercise 2 for the Sinusoidal signal? Instrum. & Control Eng. for Energy Systems - Ch. 3 Performance Char. of Instruments

  31. Second-order Instrument • If all coefficients a3 . . . an other than a0, a1 and a2 in equation (2.2) are assumed zero, then we get: • Applying Laplace transform and rearranging: • Defining K (static sensitivity), ωn (un-damped natural frequency) and  (damping ratio) as • Equation (2.9), in terms of K, ω and , becomes (2.9) (2.10) Introduction to Instrumntaion Eng‘g - Ch. 2 Performance Char. of Instruments

  32. Second-order Instrument … • If equation (2.10) is solved analytically, the shape of the step response depends on the value of  • = 0 is no damping case and constant amplitude oscillations • =0.2, we is still oscillatory response, but the oscillations gradually die down • When  is increased further, oscillations reduces and overshoot (see curves (C) and (D)) • Overdamped response as shown by curve (E) • Output reading creeps up slowly towards the correct reading Introduction to Instrumntaion Eng‘g - Ch. 2 Performance Char. of Instruments

  33. Second-order Instrument … • = 1: critically damped • <1: under damped • >1: Over damped • Exercise: 1. Determine the step and sinusoidal response analytically the second order system. 2. Consider a series RLC circuit and find the Transfer function and all constants? • Example of 2nd order system • The d’Arsonval (permanent magnet moving coil) movement Introduction to Instrumntaion Eng‘g – Ch.2 Performance Char. of Instruments

  34. d’Arsonval Movement • Used in analogue voltmeter • It consists of a rectangular coil wound round a soft iron core that is suspended in the field of a permanent magnet • The signal being measured is applied to the coil and this produces a radial magnetic field • Interaction between this induced field and the field produced by the permanent magnet causes a torque • Torque results in rotation of the coil Introduction to Instrumntaion Eng‘g - Ch. 2 Performance Char. of Instruments

  35. Dynamic characteristics of Measurement System • Measurement Systems especially in industrial, aerospace and Biological applications are subject to inputs which are not static but dynamic in nature i.e. the inputs vary with time and also the output vary with time. • The Dynamic characteristics of any measurement system described by • Speed of Response • Measuring Lag • Fidelity • Dynamic Error Instrum. & Control Eng. for Energy Systems - Ch. 3 Performance Char. of Instruments

  36. Terms used for dynamic characteristics • Response time: Time elapsed between an input is applied and the time in which the system gives an output corresponding to some specified percentage, e.g. 95%, of its final value • Rise time: Time taken for the output to rise to some specified percentage of the steady-state output. Often the rise time refers to the time taken for the output to rise from 10% of the steady-state value to 90 of the steady-state value. • Settling time: This is the time taken for the output to settle to within some percentage, e.g. 2%, of the steady-state value Introduction to Instrumntaion Eng‘g - Ch. 2 Performance Char. of Instruments

  37. Contd. 4. Measuring Lag:-An instrument does not immediately react a change in output Measuring Lag is defined as the delay in the response of an instrument to a change in a Measuring quantity. Two types of Measuring Lag • Retardation type:-In this case the response of the instrument begins immediately after a change in the measured has occurred. • Time Delay type:-In this case the response of the system begins after a “Dead Time” that means after the application of the input. 5. Fidelity of a measurement system is defined as the ability of the system to reproduce the output in the same variation of the input. In Fidelity measurement system , there is no time lag or Phase shift between the input and output Instrum. & Control Eng. for Energy Systems - Ch. 3 Performance Char. of Instruments

  38. Contd. 6. Dynamic Error is the difference between the measured value of the instrument changing with time and the value indicated by the instrument if no static error is assumed. 7. Standard signals of Instrumentation system Dynamic behavior of measurement systems can be studied with the help of certain standard signals. These standard signals are Step Input, Ramp Input and Sinusoidal input Instrum. & Control Eng. for Energy Systems - Ch. 3 Performance Char. of Instruments

  39. Example A Step input of 5A is applied to the Analogue current meter. the Analogue current meter pointer swings to 5.18A and finally comes to rest at 5.02A. • Determine the Overshoot of the reading in Ampere and in percentage of final reading • Determine the percentage error of the instrument. Given ISTEP= 5 A I1A= 5.18 A I2A= 5.02 A Instrum. & Control Eng. for Energy Systems - Ch. 3 Performance Char. of Instruments

  40. Solution • The overshoot of the reading Overshoot Reading= I1A - I2A =5.18 A – 5.02 A =0.16 A B) The percentage of Errors becomes Instrum. & Control Eng. for Energy Systems - Ch. 3 Performance Char. of Instruments

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