18.1 Measurement Techniques: Sensors and Transducers
18.1.1 Introduction
An automatic control system is said to be error actuated because the forward path components (comparator, controller, actuator, and plant or process) respond to the error signal (Fig. 18.1). The error signal is developed by comparing the measured value of the controlled output to some reference input, and so the accuracy and precision of the controlled output are largely dependent on the accuracy and precision with which the controlled output is measured. It follows then that measurement of the controlled output, accomplished by a system component called the transducer, is arguably the single most important function in an automatic control system.
A transducer senses the magnitude or intensity of the controlled output and produces a proportional signal in an energy form suitable for transmission along the feedback path to the comparator. (The term proportional is used loosely here because the output of the transducer may not always be directly proportional to the controlled output; that is, the transducer may not be a linear component. In linear systems, if the output of the transducer (the measurement) is not linear, it is linearized by the signal conditioner.) The element of the transducer which senses the controlled output is called the sensor; the remaining elements of a transducer serve to convert the sensor output to the energy form required by the feedback path. Possible configurations of the feedback path include
✁ Mechanical linkage
✁ Fluid power (pneumatic or hydraulic)
✁ Electrical, including optical coupling, RF propagation, magnetic coupling, or acoustic propagation
Electrical signals suitable for representing measurement results include
✁ DC voltage or current amplitude
✁ AC voltage or current amplitude, frequency, or phase (CW modulated)
✁ Voltage or current pulses (digital)
In some cases, representation may change (e.g., from a DC amplitude to digital pulses) along the feedback path.
The remainder of this discussion pertains to a large number of automatic control systems in which the feedback signal is electrical and the feedback path consists of wire or cable connections between the feedback path components. The transducers considered hereafter sense the controlled output and produce an electrical signal representative of the magnitude, intensity, or direction of the controlled output.
The signal conditioner accepts the electrical output of the transducer and transmits the signal to the comparator in a form compatible with the reference input. The functions of the signal conditioner include
• Amplification/attenuation (scaling)
• Buffering
• Isolation
• Digitizing
• Sampling
• Filtering
• Noise elimination
• Impedance matching
• Linearization
• Wave shaping
• Span and reference shifting
• Phase shifting
• Mathematical manipulation (e.g., differentiation, division, integration, multiplication, root finding, squaring, subtraction, or summation)
• Signal conversion (e.g., DC–AC, AC–DC, frequency–voltage, voltage–frequency, digital–analog, analog–digital, etc.)
In cases in which part or all of the required signal conditioning is accomplished within the transducer, the transducer output may be connected directly to the comparator. (Connection of the transducer output directly to the comparator should not be confused with unity feedback. Unity feedback occurs when the cascaded components of the feedback path (transducer and signal conditioner) have a combined transfer function equal to 1 (unity).) In a digital control system, many of the signal conditioning functions listed here can also be accomplished by software.
Transducers are usually considered in two groups:
✁ Motion and force transducers, which are mainly associated with servomechanisms
✁ Process transducers, which are mainly associated with process control systems
As will be seen, most process transducers incorporate some sort of motion transducer.
18.1.2 Motion and Force Transducers
This section discusses those transducers used in systems that control motion (i.e., displacement, velocity, and acceleration). Force is closely associated with motion, because motion is the result of unbalanced forces, and so force transducers are discussed concurrently. The discussion is limited to those transducers that measure rectilinear motion (straight-line motion within a stationary frame of reference) or angular motion (circular motion about a fixed axis). Rectilinear motion is sometimes called linear motion, but this leads to confusion in situations where the motion, though along a straight line, really represents a mathematically nonlinear response to input forces. Angular motion is also called rotation or rotary motion without ambiguity.
The primary theoretical basis for motion transducers is found in rigid-body mechanics. From the equations of motion for rigid-bodies (Table 18.1), it is clear that if any one of displacement, velocity, or
acceleration is measured, the other two can be derived by mathematical manipulation of the signal within an analog signal conditioner or within the controller software of a digital control system.
Position is simply a location within a frame of reference; thus, any measurement of displacement relative to the frame is a measurement of position, and any displacement transducer whose input is referenced to the frame can be used as a position transducer.
Displacement (Position) Transducers
Displacement transducers may be considered according to application as gross (large) displacement transducers or sensitive (small) displacement transducers. The demarcation between gross and sensitive dis- placement is somewhat arbitrary, but may be conveniently taken as approximately 1 mm for rectilinear
displacement and approximately 10 arc (1/6◦) for angular displacement. The predominant types of gross displacement transducers (Fig. 18.2) are
✁ Potentiometers (Fig. 18.2(a))
✁ Variable differential transformers (VDT) (Fig. 18.2(b))
✁ Synchros (Fig. 18.2(c))
✁ Resolvers (Fig. 18.2(d))
✁ Position encoders (Fig. 18.2(e))
Potentiometer-based transducers are simple to implement and require the least signal conditioning, but potentiometers are subject to wear due to sliding contact between the wiper and the resistance element and may produce noise due to wiper bounce (Fig. 18.2(a)). Potentiometers are available with strokes ranging from less than 1 cm to more than 50 cm (rectilinear) and from a few degrees to more 50 turns (rotary).
VDTs are not as subject to wear as potentiometers, but the maximum length of the stroke is small, approximately 25 cm or less for a linear VDT (LVDT) and approximately 60◦ or less for a rotary VDT (RVDT). VDTs require extensive signal conditioning in the form of phase-sensitive demodulation of the AC signal; however, the availability of dedicated VDT demodulators in integrated circuit (IC) packages mitigates this disadvantage of the VDT.
Synchros are rather complex and expensive three-phase AC machines, which are constructed to be precise and rugged. Synchros are capable of measuring angular differences in the positions (up to ±180◦) of two continuously rotating shafts. In addition, synchros may function simultaneously as reference input, output measurement device, feedback path, and comparator (Fig. 18.2(c)).
Resolvers are simpler and less expensive than synchros, and they have an advantage over RVDTs in their ability to measure angular displacement throughout 360◦ of rotation. In Fig. 18.2(d), which represents one of several possibilities for utilizing a resolver, the signal amplitude is proportional to the cosine of the measured angle at one output coil and the sine of the measured angle at the other. Dedicated ICs are available for signal conditioning and for conversion of resolver output to digital format. The same IC, when used with a Scott-T transformer can be used to convert synchro output to digital format.
Position encoders are highly adaptable to digital control schemes because they eliminate the requirement for digital-to-analog conversion (DAC) of the feedback signal. The code tracks are read by track sensors, usually wipers or electro-optical devices (typically infrared or laser). Position encoders are available for both rectilinear and rotary applications, but are probably more commonly found as shaft encoders in rotary applications. Signal conditioning is straightforward for absolute encoders (Fig. 18.2(e)), requiring only a decoder, but position resolution depends on the number of tracks, and increasing the number of tracks increases the complexity of the decoder. Incremental encoders require more complex signal conditioning, in the form of counters and a processor for computing position. The number of tracks, however, is fixed at three (Fig. 18.2(f)). Position resolution is limited only by the ability to render finer divisions of the code track on the moving surface.
Although gross displacement transducers are designed specifically for either rectilinear or rotary motion, a rack and pinion, or a similar motion converter, is often used to adapt transducers designed for rectilinear motion to the measurement of rotary motion, and vice versa.
The predominant types of sensitive (small) displacement transducers (Fig. 18.3) are
✁ Differential capacitors
✁ Strain gauge resistors
✁ Piezoelectric crystals
Figure 18.3(a) provides a simplified depiction of a differential capacitor used for sensitive displacement measurements. The motion of the input rod flexes the common plate, which increases the capacitance of one capacitor and decreases the capacitance of the other. In one measurement technique, the two capacitors are made part of an impedance bridge (such as a Schering bridge), and the change in the bridge output is an indication of displacement of the common plate. In another technique, each capacitor is allowed to serve as tuning capacitor for an oscillator, and the difference in frequency between the two oscillators is an indication of displacement.
A strain gauge resistor is used to measure elastic deformation (strain) of materials by bonding the resistor to the material (Fig. 18.3(b)) so that it undergoes the same strain as the material. The resistor is usually incorporated into one of several bridge circuits, and the output of the bridge is taken as an indication of strain.
The piezoelectric effect is used in several techniques for sensitive displacement measurements (Fig. 18.3(c)). In one technique, the input motion deforms the crystal by acting directly on one electrode. In another technique, the crystal is fabricated as part of a larger structure, which is oriented so that input motion bends the structure and deforms the crystal. Deformation of the crystal produces a small output voltage and also alters the resonant frequency of the crystal. In a few situations, the output voltage is taken directly as an indication of motion, but more frequently the crystal is used to control an oscillator, and the oscillator frequency is taken as the indication of strain.
Velocity Transducers
As stated previously, signal conditioning techniques make it possible to derive all motion measurements— displacement, velocity, or acceleration—from a measurement of any one of the three. Nevertheless, it is sometimes advantageous to measure velocity directly, particularly in the cases of short-stroke recti- linear motion or high-speed shaft rotation. The analog transducers frequently used to meet these two requirements are
✁ Magnet-and-coil velocity transducers (Fig. 18.4(a))
✁ Tachometer generators
A third category of velocity transducers, Counter-type velocity transducers (Fig. 18.4(b)), is simple to implement and is directly compatible with digital controllers.
The operation of magnet-and-coil velocity transducers is based on Faraday’s law of induction. For a solenoidal coil with a high length-to-diameter ratio made of closely spaced turns of fine wire, the voltage induced into the coil is proportional to the velocity of the magnet. Magnet-and-coil velocity transducers are available with strokes ranging from less than 10 mm to approximately 0.5 m.
A tachometer generator is, as the name implies, a small AC or DC generator whose output voltage is directly proportional to the angular velocity of its rotor, which is driven by the controlled output shaft. Tachometer generators are available for shaft speeds of 5000 r/min, or greater, but the output may be nonlinear and there may be an unacceptable output voltage ripple at low speeds.
AC tachometer generators are less expensive and easier to maintain than DC tachometer generators, but DC tachometer generators are directly compatible with analog controllers and the polarity of the output is a direct indication of the direction of rotation. The output of an AC tachometer generator must be demodulated (i.e., rectified and filtered), and the demodulator must be phase sensitive in order to indicate direction of rotation.
Counter-type velocity transducers operate on the principle of counting electrical pulses for a fixed amount of time, then converting the count per unit time to velocity. Counter-type velocity transducers rely on the use of a proximity sensor (pickup) or an incremental encoder (Fig. 18.2(f)). Proximity sensors may be one of the following types:
✁ Electro-optic
✁ Variable reluctance
✁ Hall effect
✁ Inductance
✁ Capacitance
Two typical applications of counter-type velocity transducers are shown in Fig. 18.4(b).
Since a digital controller necessarily includes a very accurate electronic clock, both pulse counting and conversion to velocity can be implemented in software (i.e., made a part of the controller program).
Hardware implementation of pulse counting may be necessary if time-intensive counting would divert the controller from other necessary control functions. A special-purpose IC, known as a quadrature decoder/counter interface, can perform the decoding and counting functions and transmit the count to the controller as a data word.
Acceleration Transducers
As with velocity measurements, it is sometimes preferable to measure acceleration directly, rather than derive acceleration from a displacement or velocity measurement. The majority of acceleration transducers may be categorized as seismic accelerometers because the measurement of acceleration is based on measuring the displacement of a mass called the seismic element (Fig. 18.5). The configurations shown in Fig. 18.5(a) and Fig. 18.5(b) require a rather precise arrangement of springs for suspension and centering of the seismic mass. One of the disadvantages of a seismic accelerometer is that the seismic mass is dis- placed during acceleration, and this displacement introduces nonlinearity and bias into the measurement. The force-balance configuration shown in Fig. 18.5(c) uses the core of an electromagnet as the seismic element. A sensitive displacement sensor detects displacement of the core and uses the displacement signal in a negative feedback arrangement to drive the coil, which returns the core to its center position. The output of the force-balance accelerometer is the feedback required to prevent displacement rather than displacement per se.
A simpler seismic accelerometer utilizes one electrode of a piezoelectric crystal as the seismic element (Fig. 18.5(d)). Similarly, another simple accelerometer utilizes the common plate of a differential capacitor (Fig. 18.3(a)) as the seismic element.
Force Transducers
Force measurements are usually based on a measurement of the motion which results from the applied force. If the applied force results in gross motion of the controlled output, and the mass of the output element is known, then any appropriate accelerometer attached to the controlled output produces an output proportional to the applied force (F = Ma). A simple spring-balance scale (Fig. 18.6(a)) relies on measurement of displacement, which results from the applied force (weight) extending the spring.
Highly precise force measurements in high-value servomechanisms, such as those used in pointing and tracking devices, frequently rely on gyroscope precession as an indication of the applied force. The scheme is shown in Fig. 18.6(b) for a gyroscope with gimbals and a spin element. A motion transducer (either displacement or velocity) on the precession axis provides an output proportional to the applied force.
Other types of gyroscopes and precession sensors are also used to implement this force measurement technique.
Static force measurements (in which there is no apparent motion) usually rely on measurement of strain due to the applied force. Figure 18.6(c) illustrates the typical construction of a common force transducer called a load cell. The applied force produces a proportional strain in the S-shaped structural member, which is measured with a sensitive displacement transducer, usually a strain gauge resistor or a piezoelectric crystal.
