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Velocity is the first differentiation of position, and acceleration is the second. Position sensors can be used, therefore, in speed and position control systems.

If the controller is a digital computer, the change in position per time interval (first differential of position) can be calculated and used in a speed control program. A change in velocity per time interval calculation (second differential) can be used in an acceleration control program. The differentiation can be done in hardware in an analog controller. Figure 1.24 demonstrates how op amp differentiators can be used to generate velocity and acceleration signals when a simple potentiometer rotary position sensor is attached to a shaft.

Certain sensors, such as incremental encoders and magnetic sensors, emit pulses as they detect positional changes. Magnetic sensors, shown in Figure 1.25, consist of magnets embedded in the moving object, and stationary coils. The magnets might be in the vanes of a turbine flowmeter or in the teeth of a gear. As the magnets move past the coils, they induce a voltage in the coil. A controller can count these pulses during a time interval to determine speed.

AC generators can be used as speed sensors in high precision control systems. The AC generator rotor is rotated by the rotating shaft. Output AC frequency is proportional to shaft speed. Zero crossings per time interval can be counted to determine speed for a simple speed control system.

Fig. 1.24 Position sensor and op-amps for velocity and acceleration outputFig. 1.24 Position sensor and op-amps for velocity and acceleration output

If high precision speed and position control are required, the controller can generate a reference AC with frequency proportional to the desired speed. The control system can monitor the phase shift between the reference AC and the sensor's output AC. If the phase shift comparator detects that the actual system is lagging the reference, even if the speed is the same, the actuator is driven harder until it catches up with the reference AC. Such a control system is called a phase locked loop speed control system. An AC generator and a phase locked loop control system is demonstrated in Figure 1.26.

A DC generator sensor (with a commutator) is popularly called a tachometer. It generates DC proportional to speed, and can be used as a speed sensor.

Doppler effect speed sensors are used in police radar speed detectors and similar electromagnetic wave speed sensors. Figure 1.27 demonstrates that when a wave of a given frequency reflects from a moving object, the frequency shifts. If the object is moving toward the transmitter/receiver, the frequency increases, and the amount of frequency shift is directly proportional to the approach speed. A receding reflective surface shifts the frequency downward.

Devices to measure acceleration are known as accelerometers. Accelerometers measure the force required to cause a mass to accelerate. The housing of the accelerometer shown in Figure 1.28 is rigidly attached to the object that is being accelerated. Inside the housing, a known mass is centered by an arrangement of springs. Because of its inertia, the mass does not accelerate as fast as the housing, so there is a displacement of the mass from the accelerometer center. The amount of displacement, which is proportional to the acceleration moving the housing, can be measured with a position sensor.

Fig. 1.25 Magnetic sensorFig. 1.25 Magnetic sensor

Fig. 1.26 AC generator speed sensor and phase locked loop speed controlFig. 1.26 AC generator speed sensor and phase locked loop speed control

Accelerometers may be used as vibration sensors. Where high frequency vibrations (such as sound) are measured, spring mass accelerometers may not be fast enough. The springs are replaced by piezoelectric materials that output a voltage proportional to forces that cause only tiny deformations.


1.4.1 Sensors Measuring Alternating Signals

Choosing an accelerometer, or indeed any sensor, to operate in a vibrating system requires that the user be aware of the frequency response of the sensor.

Fig. 1.27 The Doppler effectFig. 1.27 The Doppler effect

Fig. 1.28 AccelerometersFig. 1.28 Accelerometers

The Bode diagram for an accelerometer in Figure 1.29 shows that, up to a certain frequency (f1), the output amplitude of the sensor is proportional to the amplitude of the vibration being sensed, and in phase with the vibration.

Its output cannot be trusted. Even a temperature sensor requires a short time to respond to a temperature, and if temperature changes too quickly, the sensor will not report the temperature correctly. As a general rule, sensors and sensor systems should not be required to measure variables that change faster than one half of the natural frequency (fn) of the sensor or system.

Fig. 1.29 Frequency response of an accelerometer (Bode diagram)Fig. 1.29 Frequency response of an accelerometer (Bode diagram)




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