Basic introduction
- 1. Basic Concepts of Measurement Methods 2141-375 Measurement and Instrumentation
- 2. What Is Measurements? Measurement: an estimation of a physical (chemical or biological) variable by a measurement device. Instrument Environment parameter (P, T, rh etc.) Measurement Method V CV C operator Data Physical parameter
- 3. General Measurement System -amplifier -filter -meter -oscilloscope -recorder Sensor or Transducer State Signal Conditioning State Output State Measured variable (Input signal or measurand) stimulus System output Optional state Sensor or transducer is an input device convert the quantity under measurement into a detectable signal form: electrical, mechanical, optical etc. Signal conditioning modifies the transducer signal into a desired form e.g. amplification, noise reduction. Output State provides an indication of the value of the measurement (readout device or recording)
- 4. Examples of Measurement Systems A bulb thermometer Atom Force Microscope: example of a complicated system
- 5. Transducer a device which converts a signal from one physical form to a corresponding signal having a different physical form. (energy converter) Sensor (input transducer) a device converts the physical or non-physical signal which is to be measured into an electrical signal which can be processed or transmitted electronically. (physical signal/electrical signal) Actuator (output transducer) a device converts the modified electrical signal into a non- electrical signal. (electrical signal/physical signal) Some Useful Definitions
- 6. Composition, concentration, reaction rate, pH, oxidation/reduction potential Chemical Intensify, phase, wavelength, polarization, reflectance, transmittance, refractive index Radiant Field intensity, flux density, magnetic moment, permeabilityMagnetic Voltage, current,charge, resistance, inductance, capacitance, dielectric constant, polarization, electric field, frequency, dipole moment Electrical Temperature, (specific) heat, entropy, heat flow, state of matter Thermal Length, area, volume, all time derivatives such as linear/angular velocity/acceleration, mass flow, force , torque, pressure, acoustic wavelength and intensity Mechanical Signal domains with examples
- 7. Applications of Measurement System Monitoring of processes and operations Control of processes and operations Experimental engineering analysis A simple closed-loop control system Heater Room Temp. sensor Error signal Reference value, Td Ta Td - Ta Room Temperatrue, Ta Dummy driver
- 8. Classification: Active and Passive Passive or Self-generating Instrument: an instrument whose output energy is supplied entirely or almost entirely by its input signal Active or Modulating Instrument: an instrument has an auxiliary of power which supplies a major part of the output power while the input signal supplies only an insignificant portion. input output System Self-generating Measurement System input output System Modulating Measurement System External power
- 9. Classification: Null and Deflection Methods Deflection-type The measured quantity produced some physical effects that engenders a similar but opposing effect in some part of the instrument. The opposing effect increases until a balance is achieved, at which point the “deflection” is measured. Null-type Method: a null-type device attempts to maintain deflection at zero by suitable application of a known effect opposing the generated by the measured quantity. (a null detector and a means of restoring balancing are necessary). An equal arm balance A spring balance
- 10. Analog and Digital Instruments Digital Instruments: The digital instruments has an output that varies in discrete steps and so can only have a finite number of values. Analog Instrument: An analog instrument gives an output that varies continuously as the quantity being measured changes. The output can have an infinite number of values within the input range. Example of an analog and digital instrument
- 11. G Galvano- meter a b Vx Unknown voltage Im Standard voltage source VS c d Measuring unknown voltage using a voltmeter Potentiometer voltage measurement V + -Vx Vx Classification: Null and Deflection Methods
- 12. Experimental Variables Independent variable a variable that can be changed independently of other variables. Dependent variable a variable that is affected by one or more other variables. Controlled variable a variable that can be held at constant value during the measurement process. Extraneous variable a variable that are not or can not be controlled during measurement but can affected the value of the measured variable.
- 13. Example of Experimental Variables Measured variable: Boiling point (Dependent variable) Extraneous variable: Atmospheric pressure
- 14. Extraneous Variables Interference An undesirable deterministic trends on the measured value because of extraneous variables. Noise a random variation of the value of the measured signal as a consequence of the variation of the extraneous variables. Interference and Noise
- 15. Calibration •Calibration: A test in which known values of the input are applied to a measurement system (or sensor) for the purpose of observing the system (or sensor) output. •Dynamic calibration: When the variables of interest are time dependent and time-based information is need. The dynamic calibration determines the relationship between an input of known dynamic behavior and the measurement system output. •Static calibration: A calibration procedure in which the values of the variable involved remain constant (do not change with time).
- 16. Static Characteristics Static Sensitivity: Incremental ratio of the output signal (y) to the desired input signal (x). y S x ∆ = ∆ S = constant, If y is a linear function of x, i.e. y = ax + b Example of Static calibration curve
- 17. Measurand range, operating range, full-scale range, span: the range of input variable (xmax – xmin) that produces a meaningful output. Full scale output (FSO): Difference between the end points of the output. The upper limit of output over the measurand range is called the full scale (FS) Offset: The output of a sensor, under room temperature condition unless otherwise specified, with zero measurand applied. Static Characteristics ri = (xmax – xmin) ro = (ymax – ymin)
- 18. Static Characteristics Accuracy: the difference between the true (expected) and measured values from the measurement system or sensor. Normally, it is quoted in as a fractional of the full scale output. ( ) (%) 100m t a t y y y ε − = × FSO ( ) (%) 100m t f y y y ε − = × Percentage of reading Percentage of full scale Absolute error εεεε = indicated value- true value
- 19. Static Characteristics bias error precision error true or expected output measured average measuredvalue Trail no. Precision: The ability of the system to indicate a particular value upon repeated but independent applications of a specific value of input. The precision error is a measure of the random variation found during repeated measurements. Illustration of precision and bias errors and accuracy
- 20. Static Characteristics Load cell output (mV) Trail no. A B C 1 10.02 11.50 10.00 2 10.96 11.53 10.03 3 11.20 11.52 10.02 4 9.39 11.47 9.93 5 10.50 11.42 9.92 6 10.94 11.51 10.01 7 9.02 11.58 10.08 8 9.47 11.50 10.00 9 10.08 11.43 9.97 10 9.32 11.48 9.98 Maximum 11.20 11.58 10.08 Average 10.09 11.49 9.99 Minimum 9.02 11.42 9.92 Example: Three load cells are tested for repeatability. The same 50-kg weight is placed on each load cell 10 times. The resulting data are given in the following table. Discuss the repeatability and accuracy of each sensor. If the expected output of these load cells is 10 mV.
- 21. Static Characteristics Trial no. 0 1 2 3 4 5 6 7 8 9 10 Output(mV) 9.0 9.2 9.4 9.6 9.8 10.0 10.2 10.4 10.6 10.8 11.0 11.2 11.4 11.6 x x x x x x x x x x Trial no. 0 1 2 3 4 5 6 7 8 9 10 Output(mV) 9.0 9.2 9.4 9.6 9.8 10.0 10.2 10.4 10.6 10.8 11.0 11.2 11.4 11.6 x x x x x x x x x x Trial no. 0 1 2 3 4 5 6 7 8 9 10 Output(mV) 9.0 9.2 9.4 9.6 9.8 10.0 10.2 10.4 10.6 10.8 11.0 11.2 11.4 11.6 x x x x x x x x x x Load cell A Load cell B Load cell C Max. Min Ave. Max. Min. Max. Min. •not repeatable • Not accurate but repeatable •Accurate and repeatable A transducer or sensor that is repeatable but not overly accurate may still be quite usable in a measurement or control application. As long as the transducer or sensor is repeatable, you will get consistent results. We may correct this inaccuracy by the recalibration this transducer or sensor.
- 22. Static Characteristics Resolution: the smallest increment in the value of the measurand that results in a detectable increment in the output. It is expressed in the percentage of the measurand range max min Resolution (%) 100 x x x ∆ = × − A simple optical encoder Each time the shaft rotates ¼ of a revolution, a pulse will be generated. So, this encoder has a 90oC resolution.
- 23. Static Characteristics Hysteresis: Difference in the output of a sensor or instrument for a given input value x, when x is increased and decreased or vice versa. (expressed in % of FSO) (indication of reproducibility) output(%FSO) measurand (% range) 0 100 0 100 maximum hysteresis upscale downscale
- 24. Static Characteristics Linearity: (also called Nonlinearity) A measure of deviation from linear of a sensor or instrument, which is usually described in terms of the percentage of FSO. (1) best-fit straight line (2) terminal-based straight line (3) independent straight line output(%FSO) measurand (% range) 0 100 0 100 maximum nonlinearity terminal-base line output(%FSO) measurand (% range) 0 100 0 100 maximum nonlinearity best-fit line output(%FSO) measurand (% range) 0 100 0 100 maximum nonlinearity independent line yL(x) = a0 + a1xA predicted output based on linear relation: Linearity error: eL(x) = y(x) - yL(x)
- 25. Static Characteristics Operating conditions: Ambient conditions may have profound effects on the sensor or instrument operation. These include temperature, acceleration, vibration, shock, pressure, moisture, corrosive materials, and electromagnetic field. output(%FSO) measurand (% range) 0 100 0 100 Temperature sensitivity errorTemperature change output(%FSO) measurand (% range) 0 100 0 100 Temperature zero error output(%FSO) measurand (% range) 0 100 0 100 Zero drift Sensitivity drift Total error Nominal desired temp. Temperature zero drift: the change in the output level of a sensor or instrument due to temperature variation when the input is set to zero. Temperature sensitivity drift: the change in the output level of a sensor or instrument due to temperature when the input is set to the specific range.
- 26. Overall Performance: An estimate of the overall sensor error is made based on all known errors. An estimate is computed from Static Characteristics The worst case approach: The root of sum square approach: nc eeeee ++++= L321 22 3 2 2 2 1 nrss eeeee L+++=
- 27. 0-1000 cm H2O ±15 V dc 0-5 V 0-50oC nominal at 25oC ±0.5%FSO Less than ±0.15%FSO ±0.25%of reading 0.02%/oC of reading from 25oC 0.02%/oC FSO from 25oC Operation Input range Excitation Output range Temperature range Performance Linearity error eL Hysteresis error eh Sensitivity error eS Thermal sensitivity error eST Thermal zero drift eZT Specifications: Typical Pressure Sensor The sensor is used to measure a pressure of 500 cm H2O the ambient temperature is expected to vary between 18oC and 25oC . Estimate the magnitude of each elemental error affecting the measured pressure Pressure 500 cm H2O Tamb 18-25oC Vout
- 28. ± 9.9 cm H2O ± 5.6 cm H2O ± 49.25 mV = 0.99 %FSO ± 27.95 mV = 0.56 %FSO Worst case error Root square error Absolute error output ± 25 mV ± 7.5 mV ± 6.25 mV - 3.5 mV - 7.0 mV Absolute error transfer to input ± 5 cm H2O ± 1.5 cm H2O ± 1.25 cm H2O -0.7 cm H2O -1.4 cm H2O Performance Linearity error eL Hysteresis error eh Sensitivity error eS Thermal sensitivity error eST Thermal zero drift eZT Error budget calculation of a pressure sensor %reading1.98%FSO0.99 mV25.4975.325.65.725 == ±=±±±±±= ++++= ZTSTShLc eeeeee %reading1.12%FSO0.56 mV95.2775.325.65.725 22222 22222 ±=±= ±=++++= ++++= ZTSTShLrss eeeeee Worst case error Root of sum square error
- 29. Performance specifications • Accuracy • Resolution • Repeatability • Hysteresis • Linearity • environmental parameter • etc. Confidential band Output (Indicated value) Input Basic specifications • Input range • Output range • Offset • Sensitivity SensorInput Output
- 30. Static Characteristics Example: A load cell is a sensor used to measure weight. A calibration record table is given below. Determine (a) accuracy, (b) hysteresis and (c) linearity of the sensor. If we assume that the true or expected output has a linear relationship with the input. In addition, the expected output are 0 mV at 0 kg load and 20 mV at 50 kg load. Output (mV) Load (kg) Increasing Decreasing 0 0.08 0.06 5 0.45 0.88 10 1.02 2.04 15 1.71 3.10 20 2.55 4.18 25 3.43 5.13 30 4.48 6.04 35 5.50 7.02 40 6.53 8.06 45 7.64 9.35 50 8.70 10.52 55 9.85 11.80 60 11.01 12.94 65 12.40 13.86 70 13.32 14.82 75 14.35 15.71 80 15.40 16.84 85 16.48 17.92 90 17.66 18.70 95 18.90 19.51 100 19.93 20.02 Load (kg) 0 20 40 60 80 100 Output(mV) 0 5 10 15 20 Increasing Decreasing
- 31. Load (kg) 0 20 40 60 80 100 Output(mV) 0 5 10 15 20 Increasing Decreasing Static Characteristics (a) Accuracy … … … … … … %FSO %reading Desired output = 0.2mV/kg x load Accuracy: %FSO = -7.85% at 25 kg increasing %reading = -55% at 5 kg increasing Load (kg) True Output (mV) Actual Output (mV) Error (mV) %FSO %reading 0 0 0.08 0.08 0.40 a 5 1 0.45 -0.55 -2.75 -55.00 10 2 1.02 -0.98 -4.90 -49.00 15 3 1.71 -1.29 -6.45 -43.00 20 4 2.55 -1.45 -7.25 -36.25 25 5 3.43 -1.57 -7.85 -31.40 30 6 4.48 -1.52 -7.60 -25.33 35 7 5.5 -1.50 -7.50 -21.43 40 8 8.06 0.06 0.30 0.75 35 7 7.02 0.02 0.10 0.29 30 6 6.04 0.04 0.20 0.67 25 5 5.13 0.13 0.65 2.60 20 4 4.18 0.18 0.90 4.50 15 3 3.1 0.10 0.50 3.33 10 2 2.04 0.04 0.20 2.00 5 1 0.88 -0.12 -0.60 -12.00 0 0 0.06 0.06 0.30 a
- 32. Static Characteristics (b) Hysteresis Load (kg) 0 20 40 60 80 100 Output(mV) 0 5 10 15 20Output (mV) Load (kg) Increasing Decreasing Hysteresis (%FSO) 0 0.08 0.06 0.10 5 0.45 0.88 2.15 10 1.02 2.04 5.10 15 1.71 3.10 6.95 20 2.55 4.18 8.15 25 3.43 5.13 8.50 30 4.48 6.04 7.80 35 5.50 7.02 7.60 40 6.53 8.06 7.65 45 7.64 9.35 8.55 50 8.70 10.52 9.10 55 9.85 11.80 9.75 60 11.01 12.94 9.65 65 12.40 13.86 7.30 70 13.32 14.82 7.50 75 14.35 15.71 6.80 80 15.40 16.84 7.20 85 16.48 17.92 7.20 90 17.66 18.70 5.20 95 18.90 19.51 3.05 100 19.93 20.02 0.45 %FSO75.9%100 mV20 mV9.85mV11.80 =× − Hysteresis = 9.75 %FSO at 55 kg
- 33. Load (kg) 0 20 40 60 80 100 Output(mV) 0 5 10 15 20 endpoint %FSO85.7%100 mV20 mV00.5mV43.3 −=× − Static Characteristics (c) Linearity: Terminal-based straight line (endpoint straight line) endpoint … … … … Linearity = -7.85 %FSO (at 25 kg) Load (kg) Endpoint line (mV) Actual Output (mV) Linearity (%FSO) 0 0 0.08 0.40 5 1 0.45 -2.75 10 2 1.02 -4.90 15 3 1.71 -6.45 20 4 2.55 -7.25 25 5 3.43 -7.85 30 6 4.48 -7.60 35 7 5.50 -7.50 40 8 6.53 -7.35 y ~ 0.20 mV/kg x 40 8 8.06 -0.30 35 7 7.02 -0.10 30 6 6.04 -0.20 25 5 5.13 -0.65 20 4 4.18 -0.90 15 3 3.10 -0.50 10 2 2.04 -0.20 5 1 0.88 0.60 0 0 0.06 -0.30
- 34. Static Characteristics (c) Linearity: Best-fit straight line Least square method: minimizes the sum of the square of the vertical deviations of the data points from the fitted line. Here, we will estimate y by y = mx + b N = Total number of data points ( )22 xxN yxxyN m ∑−∑ ∑∑−∑ = N x m N y b ∑ − ∑ =
- 35. Static Characteristics 45 9.35 2025.00 420.75 40 8.06 1600.00 322.4 35 7.02 1225.00 245.7 30 6.04 900.00 181.2 25 5.13 625.00 128.25 20 4.18 400.00 83.6 15 3.10 225.00 46.5 10 2.04 100.00 20.4 5 0.88 25.00 4.4 0 0.06 0.00 0 2100 409.89 143500 28499.45 x = Load (kg) y = Load cell output (mV) x y x xy 0 0.08 0.00 0 5 0.45 25.00 2.25 10 1.02 100.00 10.2 15 1.71 225.00 25.65 20 2.55 400.00 51 25 3.43 625.00 85.75 30 4.48 900.00 134.4 35 5.50 1225.00 192.5 40 6.53 1600.00 261.2 45 7.64 2025.00 343.8 50 8.70 2500.00 435 2 … … … … ∑∑∑∑ Here No. of Data N = 42 m = 0.2079 mV/kg b = -0.6368 mV y = 0.2079 mV/kg x -0.6368 mV Obtained eq.
- 36. 60 11.84 12.94 -5.30 55 10.80 11.80 -4.82 50 9.76 10.52 -3.66 45 8.72 9.35 -3.04 40 7.68 8.06 -1.83 35 6.64 7.02 -1.83 30 5.60 6.04 -2.12 25 4.56 5.13 -2.74 20 3.52 4.18 -3.17 15 2.48 3.10 -2.97 10 1.44 2.04 -2.88 5 0.40 0.88 -2.30 0 -0.64 0.06 -3.35 %FSO70.5%100 mV20.15 mV68.7mV.536 −=× − Static Characteristics (c) Linearity: Best-fit straight line… … … … Linearity = -5.70 %FSO (at 40 kg) Load (kg) 0 20 40 60 80 100 Output(mV) 0 5 10 15 20 %FSO70.5%100 mV20.79 mV68.7mV.536 −=× − Load (kg) best-fit line (mV) Actual Output (mV) Linearity (%FSO) 0 -0.64 0.08 -3.45 5 0.40 0.45 -0.23 10 1.44 1.02 2.03 15 2.48 1.71 3.71 20 3.52 2.55 4.67 25 4.56 3.43 5.44 30 5.60 4.48 5.39 35 6.64 5.50 5.48 40 7.68 6.53 5.53 45 8.72 7.64 5.19 50 9.76 8.70 5.09 55 10.80 9.85 4.56
- 37. Load (kg) 0 20 40 60 80 100 Output(mV) 0 5 10 15 20 %FSO85.5%100 mV20 mV65.5mV48.4 −=× − Static Characteristics (c) Linearity: Independent straight line Linearity = -5.85 %FSO (at 30 kg)