�����Unit 1�Basics of Instruments�

Measurement - Definition and Methods - Generalized Measurement System - Units and Standards- Calibration- Primary- Secondary and Working Standards - National and International Standards - Types of Inputs - Order of Instruments - Static Characteristics - Accuracy - Error - Precision - Sensitivity - Linearity - Reproducibility - Repeatability - Resolution - Threshold - Drift - Stability - Tolerance - Range and Span - Dynamic Characteristics Study - Speed of Response - Response Time - Lag - Fidelity - Dynamic Error - Overshoot - Response of First Order Instrument for Step and Ramp Inputs.

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GENERALISED MEASUREMENT SYSTEM AND ITS FUNCTIONAL ELEMENTS

• Primary sensing element.
• It is an element that is sensitive to the measured variable.
• The sensing elements sense the condition, state or value of the process variable by extracting a small part of energy from the measurand, and then produce an output which reflects this condition, state or value of the measurand

• Variable conversion of transducer element.
• This element converts the signal from one physical form to another without changing the information content of the signal.
• Manipulation element.
• This element operates on the signal according to some mathematical rule without changing the physical nature of the variable.
• Data transmission element.
• This element transmits the signal from one location to another without changing its information contents.

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• Data presentation element.
• This element provides a display record or indication of the output from the manipulation elements

METHODS OF MEASUREMENT

• Direct comparison methods
• In this method the parameter to be measured is directly compared with either a primary or a secondary standard.
• Direct comparison is quite commonly used for measurements of length..
• Indirect comparison methods
• In this method the comparison is done with a standard through the use of a calibrated system.
• These methods for measurements are used in those cases where the desired parameter to be measured is difficult to be measured directly, but it has got some correlation in the some other parameter which can be easily measured.

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MODES OF MEASUREMENT

• Primary measurements
• In this case the sought value of a parameter is determined by comparing it directly with "reference standards". There is no conversion of measurand in terms of length.
• Examples: Measurement of time by counting the number of strokes of a clock.
• Secondary measurements
• The indirect measurements involving 'one translation' are called secondary measurements.
• The pressure measurement by manometers
• Tertiary measurements.
• The indirect measurements involving two conversions' are called tertiary measurements
• The measurement of temperature of an object by thermocouple

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• Static characteristics refer to the performance of a measuring system for the measurement of quantities that remain constant over a period of time.
• Dynamic characteristics of a measuring system show the relationship between the input and output of the system, when the measured quantity is varying rapidly.
• Dynamic quantities are further classified as
• Steady-state periodic
• Non-repetitive or transient
• Single pulse or aperiodic
• Continuing or periodic

Accuracy, Precision , Repeatability

• Accuracy is the degree of agreement of the measured dimension with its true magnitude. It can also be defined as the maximum amount by which the result differs from the true value or as the nearness
• Precision is the repeatability of the measuring process.
• The ability of the measuring instrument to repeat the same results during the act of measurements for the same quantity is known as repeatability.

• Resolution - It is the smallest increment of quantity being measured which can be detected with certainty by an instrument.
• Sensitivity - Sensitivity is the increment of the output signal (or response) to the increment of the input measured signal.
• Repeatability - Repeatability is the variation in measurements taken on the same item under the same conditions.
• Reproducibility- Reproducibility is the ability of a measurement to be duplicated, either by the same person or by someone else under changed conditions.
• Drift- Drift is the change in instrument output over time - when the true value is constant.

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• Threshold - Threshold is when a minimum input is required to generate change in output.
• Hysteresis - Hysteresis is when unloading applied input don't creates the same output.
• Creep - Creep is caused by the time an instrument need to adapt to change in applied input.
• Resolution - Depending on the instrument - but minimum change in input may required for change in output.
• Range is defined as the difference between the lower and higher values that an instrument is able to measure
• Span- Algebraic difference between upper and lower range values of the instruments

Error

• The difference between the true value and the mean value of the set of readings on the same component is termed as an error. Error can also be defined as the difference between the indicated value and the true value of the quantity measured.
• Types
• Random Errors The errors caused by happening or disturbances about which we are unaware are Random Errors. Its also known as residual Errors.
• Gross Errors - Gross Errors mainly covers the human mistakes in reading instruments and recording and calculating measurement results
• Systematic Errors
• Instrumental Errors
• Environmental Errors
• Observational Errors

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• Instrumental Errors
• Due to inherent shortcoming in the instrument
• Due to misuse of the instruments
• Due to Loading effects of instruments.
• Environmental Errors
• These errors are due to conditions external to the measuring Device including conditions in the are surrounding the instrument.
• These may be effects of Temperature, Pressure, Humidity, Dust, Vibrations, magnetic or electrostatic fields.
• Observational Errors
• There are many sources of observational errors
• Parallax, i.e. Apparent displacement when the line of vision is not normal to the scale.
• Inaccurate estimate of average reading
• Wrong scale reading and wrong recording the data
• Incorrect conversion of units between consecutive reading

Dynamic Characteristics

• The time response shows the behavior of the sensor or the instrument at system to the changes in the magnitude of interest by observing the signal output with time. The step response is used as a basic test and for characterizing the system. The dynamic characteristics of an instrument are:
• Speed of response – speed of response is defined as the speed with which the measuring instrument responds to the changes in the measured quantity.
• Dynamic error: The difference between the true and measured value with no static error.
• Lag – It is the time when an instrument begins to respond to a change in the measured quantity.
• Fidelity - It is defined as the degree to which a measurement system indicates the changes in the measured quantity without any dynamic error.

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Response of First Order Instruments for Step and Ramp Inputs

• A first-order instrument refers to a system or device that responds to changes in input in a manner that can be described by a first-order differential equation.
• Step Input Response: A step input is a sudden change in the input value from one constant value to another.

The response of a first-order system to a step input can be divided into two phases:

• Transitory Response: In this phase, the system's output changes rapidly and approaches the final value.
• Steady-state Response: Once the transitory phase settles, the system reaches a steady-state where the output stabilizes at the final value.
• Ramp Input Response: A ramp input is a linearly increasing (or decreasing) input with time. Let's examine how a first-order mechanical system responds to a ramp input.
• The response of a first-order system to a ramp input will eventually reach a steady-state. However, unlike the step input, the output will continue to change linearly with time due to the ramp input.�