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OVERVIEW INSTRUMENTATION Measurement Navigation

SYSTEM COMPONENTS Anti-Aliasing Filter A/D Converter Bandpass Filter Integrator

CONTROL Damping Stabilization

OVERVIEW Systron Donner Inertial Division’s solid-state GyroChip technology features a high MTFB (>1,000,000 hours in fielded applications), and its low cost of ownership is very attractive to automotive, commercial/industrial, and aerospace users alike. GyroChip applications fall into two broad categories: open-loop, or instrumentation applications, and closed-loop, or control applications (see Figure 1). Figure 1 A variety of instrumentation and control applications can benefit from rotational velocity as a means of improving designs, adding navigation capability to autonomous vehicles, and to damp out unwanted motions of control surfaces or gimballed platforms. INSTRUMENTATION These applications involve either instrumenting a structure for purposes of determining its rate of rotational motion (measurement), or processing that information in real time to generate information about orientation (navigation). Typical examples of rotational velocity measurement include instrumenting vehicles for crash studies, determining dynamics of specific platforms (e.g., boats, trains, robots, or even human beings), and environmental measurements such as earthquakes and wave motions. Measurement. One key element in a measurement system design is to determine the peak rotational velocities involved to ensure that an instrument with the proper range is used. If the selected range of the GyroChip is too low, the output will be clipped and valuable information will be lost. A straightforward way to determine the correct range requirement is to establish two parameters: the frequency of movement of the structure to be instrumented; and the peak angular displacement of that movement. Let's assume that we want to determine the dynamics of a vehicle's body roll while it takes a turn, The body roll motion can be described as: = A · sin (2 · Fn · t) in degrees Where: A = amplitude of movement Fn = frequency of movement The parameter of interest for measuring angular velocity is the change in angular position with time, or (dq/dt). Taking the derivative of the above equation: (d/dt) = A · 2 · Fn · cos(2 · Fn · t) Let's assume that the natural frequency of the vehicle suspension system is 6 Hz, and the peak body roll is 10°. Substituting these values into the following equation: (d/dt) = 10 · 2 · 6 · cos( 2 · 6 · t) = 377 · cos(37.7 · t)°/sec Since the cosine term has a maximum value of 1, the peak rotational velocity is 377°/s. Even in a seemingly benign environment, a 10° roll at 6 Hz can generate a fairly high peak rotational velocity. Navigation. Navigation applications are becoming increasingly interesting for the GyroChip, especially with the availability of GPS receivers at a reasonable cost. In principle, by reading the output from the rotation sensor (rotational velocity) and integrating this output over time, it is possible to determine the sensor's angular displacement. A GyroChip can be used for sensing vehicle yaw as part of a navigation package (see Figure 2). Figure 2 By combining the quartz rotation sensor (GyroChip) with a fixed reference such as a GPS receiver, a complete navigation system can be created for an automobile. Attention to signal processing design as well as to blending the GPS reference signal produces a system that can cope with extended GPS blackouts.

SYSTEM COMPONENTS Anti-Aliasing Filter. Because a computer interface requires the use of an analog-to-digital (A/D) converter, the output from the GyroChip becomes part of a sampled data stream. In order to prevent aliasing of the output, a filter must be used with the corner frequency usually set at 1/4 to 1/2 of the sampling frequency. A/D Converter. The A/D conversion should be carried out immediately after antialiasing since this puts the converter close to the GyroChip and reduces the overall noise of the system, yielding the most stable results. A 12-bit converter is generally adequate. The sample frequency should be appropriate for the system, but typical values range from 100 Hz to 1000 Hz. Bandpass Filter. This filter is tailored to the specific application. When the sensor is used as part of a head-mounted display for a virtual reality application, for example, it is not necessary to track very small, high-frequency head movements because they may simply be part of the normal jostling associated with interactive game playing. Only larger, definite head swings need attention. Similarly, low-frequency variations in the GyroChip output, which are usually associated with changes in environmental temperatures or warm-up, are not meaningful tracking information and should be rejected. These two scenarios determine the lower and upper ranges of the bandpass filter. A reasonable starting point would be to choose upper and lower corner frequencies of 0.1 Hz and 10 Hz. Integrator. This is where the angular velocity information is turned into angular position. Since the initial conditions are indeterminate at start-up, 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 errors means that over time, the true angular position and the calculated angular position will diverge. The sensor output may 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, therefore, the GyroChip is used only for short-term navigation. In order to prevent these incremental errors from growing too large, the common practice is to periodically update, or correct, the calculated angle through the use of a fixed, external reference as shown in Figure 2. The reference selected will depend on the situation; examples include a GPS signal, a corner-cube with optical line-of-sight, or an encoded magnetic signal. In fact, the combination of dead reckoning between fixed reference updates is a nearly ideal means of navigation through a variety of dynamic environments. This method has been used for autonomous delivery robots in hospitals, automated forklifts in warehouses, and emergency vehicles deployed in urban environments. CONTROL To employ the GyroChip in control applications requires an understanding of how it works as part of a system. The typical system model takes into account the magnitude and phase relationships of the sensor response. 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-effector shake in an industrial robot. Stabilization. This is a special instance 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 GyroChip be tightly coupled mechanically to the object to be controlled, usually a camera or an 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. An example of such an application is shown in Figure 3. Here, the GyroChip is used as part of a servo-control loop to provide an absolute pointing angle in attitude as well as image stability for a mobile telescope. For simplicity it is assumed that the telescope is mounted on a platform that can rotate only in attitude, and that the control mechanism is therefore an attitude control system only. The principle described can be applied to the other axes of rotation. Refer first to the high-frequency control loop portion of Figure 3. Assume that this circuit is designed to operate at 10 Hz, which is a typical value for a servo control. Let's further assume that the telescope has a rotational inertia J = 12 slug-ft2. Since: n2 = Ks / J Then: Ks = (10 · 2 · )2 · 12 = 47,300 ft-lb/rad where: n = corner frequency of servo-loop Ks represents the servo stiffness The proceeding implies that an external torque of 10 ft-lb. will allow a movement of only 10/47,300 = 0.0002 rad, or 0.7 arc-min. Now let's look at the low-frequency control loop portion of Figure 3. This will act as a vertical reference unit and ensure that the absolute pointing angle of the telescope matches the commanded (or target) angle. To accomplish this, a stable, long-term attitude reference must be provided. For most systems, gravity does the job quite nicely. A simple tilt sensor is always referenced to local gravity, and over a fairly narrow range it will behave linearly. To avoid coupling-in any high-frequency movements that are, by definition, not gravity related, this reference is part of a control loop with a time constant of typically 100 s. This allows the attitude reference to closely follow the typical platform motions you might find on most common mobile platforms; i.e., ships, trains, or planes. In general, the loop will incorporate a proportional and differential control element that does not appear in the figure. Figure 3 As part of an attitude control system for a mobile telescope, the GyroChip can be combined with a simple tilt sensor to provide both absolute pointing accuracy as well as stability. Rapid motions are compensated for in the high-frequency control loop, while the low-frequency control loop provides a vertical reference to gravity.

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