Introduction:
The rotating speed of a work piece and the feed rate of a tool are measured in controlling machining operations.
Displacements and speeds (both angular and translator) at joints (revolute and prismatic) of robotic manipulators or kinematic linkages are used in controlling manipulator trajectory In high-speed ground transit vehicles, acceleration and jerk measurements can be used for active suspension control to obtain improved ride quality.
Motion Transducers
By motion, we mean the four kinematic variables:
A. Displacement (including position, distance, proximity, and size or gage)
B. Velocity
C. Acceleration
D. Jerk
Note that each variable is the time derivative of the preceding one. Motion measurements are extremely useful in controlling mechanical responses and interactions in mechatronic systems.
Numerous examples can be cited:
Angular speed is a crucial measurement that is used in the control of rotating machinery, such as turbines, pumps, compressors, motors, and generators in power-generating plants. Proximity sensors (to measure displacement) and accelerometers (to measure acceleration) are the two most common types of measuring devices used in machine protection systems for condition monitoring, fault detection, diagnostic, and on-line (often real-time) control of large and complex machinery The accelerometer is often the only measuring device used in controlling dynamic test rigs. Displacement measurements are used for valve control in process applications. Plate thickness (or gage) is continuously monitored by the automatic gage control (AGC) system in steel rolling mills.
A one-to-one relationship may not always exist between a measuring device and a measured variable. For example, although strain gages are devices that measure strains (and, hence, stresses and forces), they can be adapted to measure displacements by using a suitable front-end auxiliary sensor element, such as a cantilever (or spring). Furthermore, the same measuring device may be used to measure different variables through appropriate data interpretation techniques.
For example, piezoelectric accelerometers with built-in microelectronic integrated circuitry are marketed as piezoelectric velocity transducers. Resolver signals, which provide angular displacements, are differentiated to get angular velocities.
Pulse generating (or digital) transducers, such as optical encoders and digital tachometers, can serve as both displacement transducers and velocity transducers, depending on whether the absolute number of pulses is counted or the pulse rate is measured. Note that pulse rate can be measured either by counting the number of pulses during a unit interval of time or by gating a high-frequency clock signal through the pulse width. Furthermore, in principle, any force sensor can be used as an acceleration sensor, velocity sensor, or displacement sensor, depending on whether:
1. An inertia element (converting acceleration into force)
2. A damping element (converting velocity into force), or
3. A spring element (converting displacement into force)
We might question the need for separate transducers to measure the four kinematic variables—displacement, velocity, acceleration, and jerk—because any one variable is related to any other through simple integration or differentiation. It should be possible, in theory, to measure only one of these four variables and use either analog processing (through analog circuit hardware) or digital processing (through a dedicated processor) to obtain any of the remaining motion variables.
The feasibility of this approach is highly limited, however, and it depends crucially on several factors, including the following:
1. The nature of the measured signal (e.g., steady, highly transient, periodic, narrowband, broad-band)
2. The required frequency content of the processed signal (or the frequency range of interest)
3. The signal-to-noise ratio (SNR) of the measurement
4. Available processing capabilities (e.g., analog or digital processing, limitations of the digital processor, and interface, such as the speed of processing, sampling rate, and buffer size)
5. Controller requirements and the nature of the plant (e.g., time constants, delays, complexity, hardware limitations)
6. Required accuracy in the end objective (on which processing requirements and hardware costs will depend)
