Chapter 2: Instrument Characteristics

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Chapter 2 Instrument Characteristics

• Overview
• Static Characteristics
• Dynamic Characteristics
• Choice of Instruments

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Static Characteristics

• Static characteristics are those that describe an
  instruments parameters in
• Accuracy, inaccuracy and uncertainty
• accuracy the degree of correctness of a
  measurement ( which may exist in a
  measurement)
• inaccuracy measurement uncertainty
• accuracy ? percentage of full-scale reading
• Measurement error measured value true value

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Example

• A weighting scale might have a full-scale reading
  of 5kgs and an accuracy quoted as 5. What does
  this mean?
• This means that the accuracy of a reading of the
  scale between 0- 5kgs is plus or minus 5 of 5kg
  0.25 kgs. Hence if the reading was, say, 2kgs
  then a that can be said is that the actual
  weight lies between (2 0.25)kgs and (2
  0.25)kgs

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Static Characteristics

• Precision/repeatability/reproducibility
• Precision is a term that describes an
  instruments degree of freedom from in its
  output when measuring a constant quantity (Q?
  instruments range?)
• Precision ? accuracy low-accuracy from
  high-precision instrument (bias in the
  measurement)? recalibration
• Repeatability output- same input with
  measurement conditions (precision)
• Reproducibility closeness output- same input
  with the measurement conditions (precision) .

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Static Characteristics

• Example robots place components at a particular
  point on a table
• low precision high precision high precision
  low accuracy low accuracy high accuracy

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Static Characteristics

• Tolerance of a manufactured component for
  some specified value (related to accuracy)
• Range or span of an instrument the of a
  quantity that the instrument is designed to
  measure
• Bias which exist over the full range of
  measurement of an instrument and removable by
  calibration.
• Linearity output is linearly proportional to
  the input

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Static Characteristics

• Sensitivity of measurement a in instrument
  when the quantity being measured ( ) changes by
  a given amount scale deflection/ value of
  measurand causing deflection (slope)
• Sensitivity of disturbancea of the magnitude
  of a certain static instrument characteristics
  when changes. Two ways of change
• zero drift the effect where the of an
  instrument is modified by a change in ambient
  conditions?
• sensitivity drift (scale factor drift) the
  amount by which an instrument s of
  measurement varies as ambient conditions change.

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Examples

• Example 1 The following resistance values of a
  platinum resistance thermometer were measured at
  a range of temperatures. Determine the
  measurement sensitivity of the instrument in
  ohm/oC
• Resistance (ohm) 307 314 321 328
• Temperature (oC) 200 230 260 290
• Example 2 A spring balance is calibrated in an
  environment at a temperature of 20oC and has the
  following deflection/load characteristic
• Load (kg) 0 1 2 3
• Deflection (mm) 0 20 40 60
• It is then used in an environment at a
  temperature of 30oC and the following
  deflection/load characteristic is measured
• Load (kg) 0 1 2 3
• Deflection (mm) 5 27 49 71
• Determine the zero drift and sensitivity drift
  per oC change in ambient temperature

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Solution

• Example 1 for a change in temperature of 30oC,
  the change in resistance is 7 ohm. Hence the
  measurement sensitivity 7/30 0.233ohm/oC
• Example 2
• At 20oC, Sensitivity 20mm/kg
• At 30oC, sensitivity 22mm/kg
• Bias 5mm
• Sensitivity drift 2mm/kg
• Zero drift/oC 5/10 0.5mm/oC
• Sensitivity drift/oC 2/10 0.2 mm/kg/oC

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Static Characteristics

• Hysteresis is the output characteristic of an
  instrument that varies differently when input
  quantity change increasingly (decreasingly).
• Dead space the range of different input values
  over which there is in output value.
• Threshold that before the change in the
  instrument output reading reaches a
  magnitude.
• Resolution of the change in the which
  produces an in the instrument output.

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Example (resolution)

• A force-measuring system has a range of 0-200N
  with a resolution of 0.1 f.s.r. what is the
  smallest change in force that can be measured
• The smallest change is (0.1/100)200 0.2N

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Dynamic Characteristics

• Dynamic characteristics of an 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
• In any linear, time-invariant measuring system,
  we have
• Where qi is the measured quantity, q0 is output
  reading, aj, bkconst

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Choice of Instruments

• Match the instrument to the requirements
• Study the specifications of the instrument
  characteristics required carefully, especially
  parameters accuracy, resolution, sensitivity.
• Environmental conditions
• Cost
• Others durability, maintainability, constancy
  of performance

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Example 3

• A balloon is equipped with temperature and
  altitude measuring instruments and has radio
  equipment which can transmit the output readings
  of these instruments back to ground. The balloon
  is initially anchored to the ground with the
  instrument output readings in steady state. The
  altitude measuring instrument is approximately
  zero order and the temperature transducer first
  order with a time constant of 15sec. The
  temperature on the ground, T0, is 10oC and the
  temperature Tx at an altitude of x metres is
  given by the relation Tx T0
  0.01x if
  the balloon is released at time zero, and
  thereafter rises upwards at a velocity of 5m/sec,
  draw a table showing the temperature and altitude
  measurements reported at intervals of 10sec over
  the first 50sec of travel. Show also in the table
  the error in each temperature reading

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Solution

• We have the following equation
• The solution of this differential equation is
• Tr Ce-t/1510-0.05(t-15)
• At t 0 Tr 10, we have C -0.75. Thus the
  final relationship between temperature reading
  and travel time is
• Tr 10-0.75e-t/15-0.05(t -15)
  

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Review 1st Order Differential Equation

• Standard form
• Solution

17
Review Laplace Transform