Measurement characteristics



A system is a group of physical components combined to perform a specific function. A system has an input and produces output with the system being a black box that can perform some specific function. For example, an electric generator generates output power when a mechanical rotation is applied at the input. 

Systems are classified into two main categories:

Measurement systems: Systems that measure required quantity are termed as "measurement systems". The key elements of a measurement system are:
  1. Sensor: A sensor is a device that converts the physical quantity (quantity being measured) into a suitable electrical signal (signal related to measured quantity). 
  2. Signal conditioner: The signal conditioner converts the output of the sensor into a suitable form for display.
  3. Display: The display displays the value of a quantity that was being measured.

Control system: The basic objective of a control system is to regulate the value of some quantity. Regulate means maintain that quantity at some desired value regardless of external influences. Examples: making the temperature in a room stay at 21oC  or as complex as manufacturing an integrated circuit or guiding a spacecraft to Jupiter. The key elements of a control system are:
  1. Process: In general, a process can consist of a complex assembly of phenomena that relate to some manufacturing sequence. The process is often also called the plant. There can be single variable processes or multiple variable processes. 
  2. Measurement: To control of a variable in a process, we must have information(found by measuring the variable) about the variable itself. In general, measurement refers to the conversion of the variable into some corresponding analog of the variable, such as a pneumatic pressure, an electrical voltage or current, or a digitally encoded signal. A sensor is a device that performs the initial measurement and energy conversion of a variable into analogous digital, electrical, or pneumatic information. Further transformation or signal conditioning may be required to complete the measurement function.
  3. Error detector: For the automatic control system, error determination must be made before any control action can be taken by the controller. Although the error detector is often a physical part of the controller device, it is important to keep a clear distinction between the two.
  4. Controller: This part of the control system has many names, such as compensator or filter, but the controller is the most common. The evaluation may be performed by an operator, by electronic signal processing, by pneumatic signal processing, or by a computer. 
    In modern control systems, the operations of the controller are typically performed by microprocessor-based computers. The controller requires an input of both a measured indication of the controlled variable and a representation of the reference value of the variable, expressed in the same terms as the measured value. The evaluation consists of determining the action required to drive the controlled variable to the setpoint value. 
  5. Control element: The final element in the process-control operation is the device that exerts a direct influence on the process; that is, it provides those required changes in the controlled variable to bring it to the set point. This element accepts an input from the controller, which is then transformed into some proportional operation performed on the process.  Often an intermediate operation is required between the controller output and the final control element. This operation is referred to as an actuator because it uses the control signal to actuate the final control element. The actuator translates the small energy signal of the controller into a larger energy action on the process.

Two types of characteristics associated with measuring instruments:
  1. Static characteristics
  2. Dynamic characteristics:
Static characteristics
  • Instruments used to measure unvarying process condition
  • Calibration process
Dynamic characteristics
  • Parameters to be measured are time-varying i.e., dynamic in nature
  • The behavior of instruments under varying input-output conditions is called the dynamic response of an instrument
Static characteristics
Range: The range is the minimum and maximum value for which an instrument is designed to measure the parameters. 
Example: A load cell may have a range varying from 10kN to 100kN 
Span: The span is the difference between maximum and minimum values of the quantity to be measured 
i.e., Span = (Max value of the I/P) – (Min value of the I/P)
Example: For a load cell with 10kN to 100kN force range, the span is 90kN
Error: Deviation of the true (actual) value from the desired value i.e., 
Error = Measured value – True Value
Example: A temperature system has its measured value as 34oC & true value as 33oC which results in an error of 1oC.
Accuracy: Accuracy is the ability of an instrument to respond to a true value of a measured variable under the reference condition. Accuracy represents how closely the measured value agrees with the true value. Accuracy is represented in different ways:
  • Accuracy as % of Full-scale reading: is applicable for instruments having a uniform scale. 
Example: If the accuracy of an instrument having a full scale of 50 units is ± 0.1% then there will be an error of 0.05 units
  • Accuracy as % of True value:  is the best way of specifying the accuracy.

Example: If a pressure gauge of range 0 to 100 kN/m2 has an error of ± 1% of true value, the pressure of 100kN/m2 could be read from 99 kN/m2 to 101 kN/m2.
  • Accuracy as % of Span: Accuracy can be specified as % of span
Example: If an instrument has a range of 10 to 150 units and its accuracy is specified as ± 0.1% of the span then the instrument will have ± 0.1% (150-10) = ± 0.14 unit error.
Precision: Precision is the degree of exactness for which an instrument is designed or intended to perform. It refers to repeatability or consistency of measurements when the measurements are carried out under identical conditions at a short interval of time. Precision represents the ability of an instrument to reproduce a group of measurements of the same quantity under the same/identical conditions. 
A measuring instrument can be:
  1. Accurate but not precise
  2. Precise but not accurate
  3. Accurate and precise both
The following figure shows different scenarios of precision and accuracy

The top left image shows the target hit at high precision and accuracy. The top right image shows the target hit at a high accuracy but low precision. The bottom left image shows the target hit at a high precision but low accuracy. The bottom right image shows the target hit at low accuracy and low precision.

Sensitivity:  Sensitivity denotes the smallest change in the measured value to which the instrument responds. Static sensitivity is defined as the slope of the calibration curve. 

When an instrument consists of different elements connected in series and having static sensitivities K1, K2, K3, … then the overall sensitivity is expressed as:
Overall sensitivity, K = K1×K2×K3
Hysteresis: Hysteresis defines the difference in the output for a given input when the value is approached from the opposite direction and usually occurs in mechanical, electrical, physical, and chemical processes.
Repeatability/Reproducibility: Repeatability/reproducibility represents the ability of a transducer(or sensor) to give the same output for repeated applications of the same input
Stability: Stability represents the ability of a transducer(or sensor) to give the same output when used to measure a constant input over a period of time
Zero drift: Zero drift indicates the changes that occur in the output when there is zero input i.e. when no input is applied
Dead band/time/space:  Dead band/time/space is the range of input for which there is no output
Resolution: It is the smallest change in a measured variable to which an instrument will respond. It is also defined as the minimum value of the input signal required to cause an appreciable change or an increment in the output


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