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Session A1: High Performance Inertial Sensor Technologies

Rate Table Improvements in Rate Stability using Look-up Tables: Faster Commissioning through Automated Processes
André S.P. Niederberger, Remo Kälin, Sascha Revel, Acutronic Switzerland Ltd., Switzerland; Dino Smajlovic, Acutronic USA Inc.
Location: Big Sur
Alternate Number 2

Abstract
ACUTRONIC’s customers keep pushing the performance boundaries of their devices such as gyroscopes, and they demand more performance out of their test equipment, the rate tables. This paper shows how ACUTRONIC continually increases the performance of its products, and in particular how imperfections of motors and angular sensors are compensated for to yield superior rate stability. This is accomplished by introducing look-up tables into the signal path. An innovative method to quickly tune the parameters of theses tables is put forth, which automates tedious and time consuming work, and yields improved results compared to the previously established method of manual tuning.
Keywords—rate table, gyroscope, rate stability, look-up table, commissioning
I. INTRODUCTION
The recent times have seen a tremendous increase in the performance of all classes of gyroscopes. ACUTRONIC makes the commitment to serve its customers with suitable motion simulators, and therefore responds to these trends. In particular, the rate stability of ACUTRONIC rate tables is an important buying criterion for knowledgeable customers. Besides ensuring high quality hardware is delivered to the customers, ACUTRONIC also employs software measures to enhance the rate stability performance of its rate tables. This paper explains how ACUTRONIC is able to tune look-up tables to the extent that the rate stability experienced by the user’s unit-under-test UUT is significantly improved.

II. ACUTROL®3000E REAL-TIME COMPUTER
The ACUTROL®3000e is the industry-leading real-time computer for rate table applications. Its superiority has been confirmed in over 700 installations worldwide. ACUTRONIC rate tables are equipped with angular position encoders such as Inductosyn®/Resolver, as well as more recent optical encoders from different manufacturers.

III. RATE STABILITY
The rate stability achieved by a rate table is an important performance criterion [1]. ACUTRONIC specifies the rate stability at a certain rate, and over a certain angular increment. Classical combinations are a rate of 50°/s over an interval of 10°, or a rate of 100°/s and increments of 360°. This means that the table rotates at a rate of 100°/s, and the precise time increment is determined when successive angular increments of 360° are covered. To that end, the built-in observer estimates the time stamp when the current increment ends and the next angle increment starts, based on the current position and rate. It then triggers an internal high-precision counter, which releases an electric pulse through a BNC connector at the right time. These pulses are registered by an external, independent high-precision counter device, which determines the time elapsed between two successive pulses. A software application on a host computer communicates with the counter device, and runs statistics on the recorded data to determine the rate stability.

IV. SENSOR IMPERFECTIONS AND MOTOR COGGING
A. Angular position sensor imperfections
The Inductosyn® is a field-proven, robust angular encoder. With adequate signal processing, sub arc-second precision is achievable. Its analog interface signals are easily transferrable over contacting slip rings, which makes it an encoder of choice for an inner axis, whose position signals have to travel over slip rings. The Inductosyn angular position encoders have a grating of either 180 or 360 lines. When rotating an axis equipped with such an encoder, disturbance signals with a frequency of 180 and 360 repetitions per whole revolution are registered, as well as multiples and submultiples thereof. In addition, spurious frequency components appear, possibly related to non-linear effects. On top of that, sensor mounting imperfections can be observed as low-frequency disturbances, typically on the order of only a few Hertz. ACUTRONIC subsumes all these sensor effects under the term “snaky effect”. It has been observed that high precision optical encoders have both a much lower noise floor, and nearly non-existent frequency peaks. These sensors with built-in bearings also facilitate mechanical mounting on the rate table.
B. Electric motor cogging
The interaction between the permanent magnets present in electric motors and the stator slots create periodic torque ripples, which can easily be felt when turning a motor by hand. These disturbances are also called “detent” or “no-current torque”. These perturbations are also experienced by a servo controller tasked with keeping the rotational rate of a spinning axis constant, which will attempt to counteract these external disturbances to ensure smooth operation. This works well if the rotational rate is such that the perturbations are within the controller’s bandwidth. If the rate is higher than the bandwidth, these cogging effects manifest themselves as jerkiness, resulting in uneven rate signals. If the rotational rate is very high, the inertia of the axis “low-pass filters” the effects of cogging torque on rate. As a complicating factor, the cogging effect depends on many factors, such as direction of rotation, speed and acceleration of rotation, among others. Mechanical measures to reduce cogging - such as slot and magnet housing redesign - also reduce the torque available for rotating the axis, which makes these motors less suitable for rate table applications.

V. SENSORS, ACUTROL®3000E SIGNAL ROUTING AND LUT POPULATION
A. Signal routing in the ACUTROL®3000e
Referring to Figure 1, the Inductosyn’s sine and cosine signal are used to calculate an angular position signal, which has a range of [-0.5 0.5[ deg. Together with the angular position signal from the resolver, which is in the range of [-180 180[ deg, a high precision angular position signal is obtained. This signal can be corrected in a first look-up table, called the “Snaky LUT”. The purpose of this look-up table is to remove deterministic imperfections of the sensor and mounting errors with respect to the axis. The corrected angular position signal is processed in the feedback controller, which generates a torque output signal. Before this signal is applied to the electric drive, another look-up table is employed to account for deterministic motor imperfections, called cogging. The drive thus receives a corrected torque signal, and generates an electric current corresponding to the torque required. The electric motors are connected to the drive, and generate a torque which rotates the axis of the rate table. The angular position is picked up by angular encoders such as Inductosyn or optical encoders, and delivered back to the ACUTROL real-time computer to close the loop.
B. The traditional way of populating two look-up tables during commissioning
An ACUTRONIC field engineer is required to carry an external oscilloscope to the customer’s site, and connect it to the analog output of the ACUTROL®3000e. The position signal after the snaky LUT is routed to the analog output, and the FFT of that signal is calculated on the oscilloscope. Several spikes in the spectrum can be observed when rotating the axis, for instance at 36°/s. The project engineer now adjusts the magnitude and phase of the LUT values such as to decrease the spike visible on the oscilloscope. This process is repeated for each spike that is deemed too high. The process to populate the cogging LUT is similar, but this time the torque command signal is assessed.
This is a very time-consuming and tedious task. Finding a more time-efficient manner would significantly reduce time on site and therefore cost to the customer, all the while improving the performance of the system.

VI. AN INNOVATIVE WAY OF POPULATING THE LOOK-UP TABLES
A. General idea
The proposed way depends on the capability of the ACUTROL®3000e to log data, and does not require additional hardware. An external program running on a Windows PC interfaces with the ACUTROL®3000e over TCP/IP, commands the rates, and retrieves the data. After the calculations are done, it writes configuration data back into the ACUTROL®3000e memory.
The suggested method is a five-step procedure, which is amenable to automation. It is mixture of online measurements and offline calculations, and requires no external hardware other than a standard computer with a TCP/IP connection to the ACUTROL®3000e.
B. Diagnosing the problem
The first step is finding out what disturbances are associated with the particular system. To that end, several rotations of the axis under investigation are carried out. The rate and rotational direction are selected by the user. At the end of this step, the user is presented with a spectrum plot of the estimated rate. This allows selecting frequency components which should be reduced in the subsequent steps. They can be assigned to be corrected either in the “cogging” or “snaky” LUT, depending on whether the engineer determines they are related to motor or sensor issues. The blue line in Figure 3 is the spectrum of such a measurement. Distinct peaks are discernible.
C. System identification
In order to find a good starting point for look-up table values, the influence of the look-up table signals on the system signals needs to be known. To that end, an identification step is carried out as follows: Each of the two look-up tables is populated with a set of discrete frequencies and prescribed amplitudes. For the cogging LUT, the frequencies are lower, and they are higher for the “snaky” LUT. After rotating the axis, the resulting signal (after it travels through the controller, plant and back) is related to the excitation signal of the LUT. This allows calculating a transfer function from the LUT to a signal of interest. For the cogging LUT, this resembles a complementary sensitivity, and for the “snaky” LUT it looks like a sensitivity function. Figure 2 shows a typical example of the transfer function as seen from the cogging LUT, which looks like a complementary sensitivity function. It features a low-frequency zero dB gain, followed by peaking of about 6 dB and a high-frequency roll-off.
D. Calculating preliminary look-up table entries
Knowing the disturbance frequencies from the diagnosis step (“where are the spikes?”), and knowing the effective influence from the LUTs based on the system identification (“how can I act on the system?”), one can calculate the ideal look-up table coefficients to reduce the peaks in the frequency spectrum.
E. Optimizing the values of the look-up table
The calculated coefficients serve as the starting point of the optimization step. In experiments, it has been found that the phase of the coefficients often needs individual tuning to achieve optimal results. This is why an optimization step has been introduced which works in the following way: The magnitude of the coefficients is fixed, while the phase is changed in 45° increments. The resulting heights of the peaks in the frequency spectrum are recorded for these eight measurements. In subsequent measurements, the phase of the two best measurements is averaged to yield a new phase setting to be measured. After an additional three to six measurements, a phase value is identified which results in a low peak in the frequency spectrum.
F. Confirmatory measurement
Having identified optimal coefficients, a confirmatory measurement is carried out and compared to the initial measurement from the diagnosis step. This allows assessing the success level of the procedure. If required, another iteration can be started to target other frequencies.

VII. EXPERIMENTAL RESULTS
Figure 3 compares the spectrum of the rate estimate for the case without LUTs (in blue) to the one with tuned LUTs (in red). The frequencies for which a LUT entry was calculated are shown as filled dots in red and blue. The main peaks at 360 Hz and 720 Hz could be reduced by up to 30 dB. These peaks are due to the Inductosyn’s 360 pole grating. The intermediate peaks with 32 Hz spacing could also be reduced to the level of background noise.
Figure 4 shows a histogram of the estimated rate over a period of 24 seconds, sampled at 2000 Hz. The red histogram corresponds to the measurement with tuned LUTs and exhibits a lower standard deviation than the blue, uncorrected measurement. Finally, Figure 5 shows the estimates of rate stability in the standard ACUTRONIC way of determining rate stability with an external counter. The rate is 50°/s, and the increment is 10°. The mean of the uncorrected, blue histogram is higher than the specification of 0.002%. The mean of the red histogram can be reduced lower than the requirement with the help of the correctly tuned LUTs. This demonstrates the benefit of LUTs, and the proposed method is able to achieve this in less than ten minutes, with minimal interaction required from the integration engineer.
To push this to extremes, Figure 6 shows the rate stability measured on the outer axis of a two-axis simulator. This axis is equipped with a low-noise optical encoder. When rotating at 100°/s and measuring with an angle increment of 360°, a rate stability of less than 5*10-6 % is achieved.
VIII. BENEFITS TO THE ACUTRONIC CUSTOMER
With this new method, ACUTRONIC system engineers can improve rate stability in less time than previously possible. This allows them to concentrate on other system tuning task. This assures the ACUTRONIC customer to receive a rate table that meets the given challenging requirements.
ACUTRONIC is convinced that this innovation will continue its tradition of delivering high-performance machines to its demanding customers.



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