Paul Kim The Yaw Rate Sensor How It works To understand how the quartz Yaw rate sensor works requires familiarity with the Coriolis principle. Simply stated, this means that a linear motion within a rotating framework will have some component of velocity that is perpendicular to that linear motion. The handiest example of the Coriolis effect is that exhibited by wind patterns on Earth. Convection cells in the atmosphere set up a wind flow from the poles toward the equator (with a north-south orientation). The Earth’s rotation, however, causes these linear flows to develop a sideways (orthogonal) component of motion. This “bends” the wind from a north-south direction to an east-west direction. It is the Coriolis effect that creates the east-west “trade winds”, and which is responsible for the spirals of clouds observed in satellite photos. In Figure 1 you can see that the quartz Yaw rate sensor is essentially divided into two sections: drive and pickup.The drive portion looks and acts exactly like a simple tuning fork. Because the drive tines are constructed of crystalline quartz, it is possible to electronically “ring” this tuning fork. Each fork tine has a mass and an instantaneous radial velocity which changes sinusoidally as the tine moves back and forth. As long as the fork’s base is stationary the momenta of the two tines exactly cancel one another and there is no energy transfer from the tines to the base. In fact, it takes only ~6μW of power to keep the fork ringing. As soon as the tuning fork is rotated around its axis of symmetry, however, the Coriolis principle exerts a profound influence on the behavior of this mechanism. By convention, (the “right-hand rule”), the rotational vector, ωi, is described by an arrow that is aligned with the axis of rotation. The instantaneous radial velocity of each of the tines will, through the Coriolis effect, generate a vector crossproduct with this rotation vector. The net effect is that each tine will generate a force perpendicular to the instantaneous radial velocity of each of the tines: F = 2mωi ∗ V r (1) where: m = tine mass ω i = rotation rate V r = radial velocity Note that this force is directly proportional to the rotation rate, and since the radial velocity of the tines is sinusoidal, the force on each tine is also sinusoidal. Because the radial velocities of the two tines are equal and opposite, the Coriolis forces are equal and opposite, producing an oscillating torque at the base of the drive tine fork which is proportional to the input angular rate. The pickup portion of the QRS now comes into play. The sinusoidal torque variation causes the pickup tines to begin moving tangentially to the rotation and at the samefrequency as the drive vibration. Since the forces causing the pickup tines to move are directly proportional to the rotation rate, if there is no rotation the pickup tines will not move. The QRS can therefore truly detect a zero rotation input. Once the pickup tines are in motion, it is a simple matter to amplify the pickup signal and then demodulate it using the drive frequency as a reference. One additional stage of amplification allows for some signal shaping and produces a DC signal output which is directly proportional to the input angular rate. Application Examples Stabilization. There is a special in-stance of closed-loop control–stabilization–in which the item being controlled is intended to remain stationary even during movement of the platform to which it is attached. It is important that the QRS be tightly coupled mechanically to the object to be controlled, usually a camera or antenna on a multi-axis gimbal. This gimbal mechanism must have no mechanical resonances in the bandwidth of the servo-control loop. The system designer must take into account the transfer function of the system servo loop and ensure enough phase margin to prevent oscillation. Because it is often necessary to independently move the camera or antenna, a commandable DC offset must be included in the control loop to allow an operator to rotate and point the camera in the gimbal. This method has been used successfully to stabilize antennas aboard ships and land vehicles, as well as cameras aboard helicopters and survey airplanes. Damping. The ability to accurately measure rotational velocity opens up new possibilities for control of structures. One of the most useful types of control applications is to damp out the resonant behavior of mechanical systems. Very few mechanical systems produce pure linear motion?most machines have parts that rotate or pivot. Aircraft, land vehicles and ships are governed by means of roll, pitch, and/or yaw controls. By monitoring and controlling these motions it is possible to provide active roll damping on ships, remove “Dutch roll” from aircraft flight, reduce body roll on a car as it takes a turn, or damp out end-defector shake in an industrial robot. Integrator. This is where the angular velocity information is turned into angular position. Since the initial conditions are indeterminate at startup, it is recommended that a reset capability be included. This allows you to initialize the integrator to zero or some known position at startup. The portion of the platform that is to be measured must usually be held very steady during startup so that the initial conditions represent as closely as possible a true “zero input” state. Any residual error at startup will cause the apparent output from the integrator to drift. One method to reduce the startup error is to average the input to the integrator for a few seconds during the initialization sequence, and then subtract this average value to establish the zero point. As a practical matter, it is virtually impossible to measure the “pure” rotational velocity without introducing or reading some error at the same time. This accumulation of errorsmeans that over time, the true angular position and the calculated angular position will diverge. The sensor output my not be drifting, but the apparent calculated angle is. The rate of this divergence is determined by a variety of factors including: how well the initial conditions are established; the accuracy of the alignment of the sensor to the true axis of rotation; the quantization errors of the signal (if it has been digitized); and the stability of the environment in which the measurement is being done. For most practical applications, there-fore, the