Sensors

As we outlined in the previous chapters, the measuring device is actually made up of two main components:

The sensor, which transforms the variable to be measured into the type of variable that is required for measurement
The transducer, which accepts information in the form of a physical or chemical variable and converts it into a variable of a different nature (typically electric)

Very often, the sensor and transducer coincide in the same physical component, and this is why the words sensor and transducer are often used interchangeably to indicate a device that measures a quantity and provides a signal, typically electrical, as an output.

A sensor is based on the identification of a physical law that binds two variables of a different nature, such as temperature and resistance or speed and potential voltage. Therefore, there are many different types of sensors. You can distinguish between them according to the type of output supplied:

Analogical sensors: The output of analogical sensors are continuous values within a certain interval
Digital sensors: The output of digital sensors can only be discrete values within a range
Binary sensors: The output of binary sensors can only be one of two values

A sensor has the following characteristics:

Transduction: This describes the relationship between the input variable (the variable to be measured) and the output quantity. This relationship can be of direct proportionality, at least in the range specified for the input quantity. It is therefore either characterized by a proportionality constant, or it is non-linear.
Bandwidth: This information is of fundamental importance in the controller project, as it gives an indication of the maximum frequency at which the transducing characteristics of a linear sensor do not degrade. If this is much higher than the maximum frequency that is needed for a project, which is usually the frequency needed by the closed loop to be able to follow the dynamics of the process, the sensor is simply characterized by its own constant proportionality between the input and the output. Therefore, there is no need to consider a dynamic model.
Dynamic features: These features are usually defined against the step response of the sensor. They include delay, rise time, time to the half value, overshoot, and settling time.
Input range: This refers to the range of variation of the input quantity for which the sensor guarantees certain properties, such as linearity, accuracy, or ace.
Output range: This is the range of values that the output can be.
Sensitivity: This is the ratio between the output and the input variation at a steady state.
Resolution: This is the minimum variation of the input that produces a variation in the output and is therefore captured by the sensor.
Linearity: This is usually defined as a range of input values for which the sensor has linear behavior with proportionality between the input and the output.
Deterministic error (offset): This is the systematic error that is produced at every measure. If known, this can usually be eliminated through sensor calibration.
Probabilistic error: This is a random error, which may depend on multiple factors.
Accuracy: This term defines the maximum error that the sensor can make in a measurement operation. It is not to be confused with the resolution. Accuracy can be thought of as the sum of the deterministic and probabilistic errors.
Precision: This is defined as the variance between several measures. In the following diagram:
- Archer a has a high distance from the target (offset) and poor accuracy. Therefore, they have a poor accuracy overall.
- Archer b has high offset and good accuracy. Therefore, they have a poor accuracy overall.
- Archer c has low offset and poor accuracy. Therefore, they have a poor accuracy overall.
- Archer d has low offset and good accuracy. This means that they are accurate:

Sensor offset, accuracy, and precision

Hysteresis: This means that the output signal for a specific input can take several values, depending on whether the input variation is negative or positive.
Drift: This can be defined as the variation of the output over long time periods when a constant signal is applied to the input.
Electrical output impedance: This is useful to deal with problems related to interfacing. It's better to have a low impedance value since this helps to couple the sensors to the device.
Loading effect: This refers to the fact that the introduction of a sensor to a piece of equipment to measure a variable can alter the operation of the equipment itself.
Noise: A sensor can generate noise in the output, which can corrupt the detected information.