Evaluation Algorithms for Linear Position Sensors ... - Science Direct

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ScienceDirect Procedia Engineering 168 (2016) 908 – 911

30th Eurosensors Conference, EUROSENSORS 2016

Evaluation algorithms for linear position sensors assisted by artificial neural network Zoltán Kántor*, Attila Szabó Balluff Elektronika Kft., Pápai út 55., 8200 Veszprém, Hungary

Abstract An artificial neural network assisted compact linear inductive position sensor is presented. The sensor operates with a long primary printed circuit coil excited with periodically alternating current, and with multiple secondary printed circuit coils possessing different induced voltages as a position of a metallic or resonant target moving along the coil system. The secondary coil signals are phase sensitively demodulated, digitized and passed to the input layer of an artificial neural network trained to estimate the position of the target, its distance from the sensor and the signal quality. © Published by Elsevier Ltd. This © 2016 2016The TheAuthors. Authors. Published by Elsevier Ltd. is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility ofthe organizing committee of the 30th Eurosensors Conference. Peer-review under responsibility of the organizing committee of the 30th Eurosensors Conference Keywords:Inductive distance sensor; artificial neural network; linear distance sensing; compact industrial sensor

1. Introduction Linear inductive position sensors unify superior properties over other common types of industrial sensors, like short response time, wear resistance, and operation in contaminated environments. An important class of sensors is based on a printed circuit board containing a plurality of planar coils, which excel by their reproducibility and reduced price [1, 2]. There are coil systems acting as variable transformers with one primary and multiple secondary coils, wherein the induced signals on the secondary coils depend primarily on the longitudinal position of a metallic or resonant target along the measurement path as the sine and cosine functions of the position by design [3], comprising long-period and short-period quadrature pairs used for the coarse and accurate determination of the target position, respectively, by means of arcus tangent based calculation [4, 5]. However, the perfect sine and cosine characteristics are valid only in a limited range of the distance between the target and the active surface of the sensor, and several factors may also influence the reliability and the accuracy of the evaluation:

* Corresponding author e-mail address: [email protected]

1877-7058 © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license

(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of the 30th Eurosensors Conference

doi:10.1016/j.proeng.2016.11.303

Zoltán Kántor and Attila Szabó / Procedia Engineering 168 (2016) 908 – 911

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• Imperfect realization of the design due to the discretization of the PCB patterns, vias, soldering pads, etc. This results in the distance dependent variation of the shape of the position dependent signal characteristics. • Influence of other constructional parts, like housing, shielding components, electronics boards • Non-ideal amplifier chain, nonlinearities • Mounting of the sensor into conductive environment (i.e. a machine wall) • Application of non-optimized targets (material and shape) The intrinsic factors induce some post-treatment after the arcus tangent evaluation, e.g. post-linearization by the calibration data stored look-up table (LUT) addressed by the estimated positions, while the application specific factors, like embedding and target variations, or when the kind and measure of non-linearity depend strongly on the distance of the target from the sensor, a real robust evaluation is needed. In this manuscript we make the first step in this direction by demonstrating that even a non-ideal design results in linear sensors characteristics when the sensing signals are evaluated with artificial neural networks (ANN) [6]. 2. Measurements and results 2-sided PCB coil system was used consisting of an excitation coil, two four-period and two single-period quadrature coil pairs. The measurement range was approx. 100 mm at a distance of 2 mm by design, and the width of the non-magnetic target (V2A) in the direction of the measurement axis was 8 mm. The excitation coil was resonantly excited at 2-MHz by a microcontroller and a buffer gate, and the pre-amplified sensing coil signals were phase sensitively demodulated by means of an array of analog switches and low-pass filters, and the demodulated voltages were converted into digital values with a resolution of 12 bits. The background signals (i.e. the digital coil signal values without target) were previously recorded and removed constantly from the signals upon measurements with target. Although for the larger distances the short-period signals possessed nearly sinusoid form, the traditional arc tan method resulted in a typically linear evaluation characteristics with residual irregularities (Fig. 1, left side). The amplifier gain was set so that the demodulated signals were well measurable even at larger target distances (beyond 6mm), with no respect to the amplifier saturation when the target is close to the sensor's active surface, which caused a systematic added deviation from the sinusoid character of the individual sensing signals (for 0.5 mm target distance, see Fig. 1, right side). While the main linear character of the evaluated characteristics was maintained, the distorted sensing signals resulted in larger deviations from the linear characteristics. We hypothesized that, whenever the target is in the sensing range, there is a unique combination of the sensing signals for each possible values of the longitudinal position and distance of the target from the sensor surface. In this case, the relationship between the coil signals and the target position dependent linear output is a piecewise varying multivariate non-linear function, which is well handled by artificial neural networks (ANN) [6], without the expectation of the primary sensing signals to be of any regular shape like sine or cosine. The training databases were compiled of various real position and distance data, a signal strength data indicating the magnitude of the sensing signals, and the four corresponding coil signals themselves. Four artificial neural networks of the same structure were generated and applied for the evaluation of the sensing signals. Each consisted of one input layer with 4 inputs, two hidden layers with 8 and 5 neurons, respectively, operating with the hyperbolic tangent evaluation function, and one output neuron. One neural network was trained to evaluate the signal strength and two others were trained to estimate the target position, using two different subsets of the training database. The fourth network was trained to evaluate the target distance. During operation, the evaluation of the longitudinal position and distance of the target was enabled only at sufficiently high signal strength and the two position estimating networks were used alternately to evaluate signal quartets acquired upon subsequent signal acquisition cycles for efficient output filtering. Fig. 2 shows the proper linear output characteristics of the position measurement for various target distances, while the comparison of the output error characteristics for the traditional and ANN based evaluations is shown in Fig. 3, both without post treatment of the data. Depending on the application, the signal strength and target distance evaluations are treated as diagnostic functions added to the main function, so the smart sensor can be integrated into environments, where assistance to installation and maintenance are critical functions.

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In the present embodiment, the sensor operated with a Cortex-M4 based microcontroller, using FPU, but without DSP calls. The acquisition of the primary sensing signal groups (four signals) was performed at 100 kSps, and the signal strength, position and distance estimation networks iterated at approx. 2000 per second.

Figure 1: High- and low-resolution sin/cos quadrature signal pairs of a transformer-type inductive position sensor (top) and the calculated phase of the high-resolution (short-period) quadrature (bottom). The low-resolution quadrature is used to avoid the phase period (arc tan) unambiguity. The height of the target above the sensor was 2.5 mm and 0.5 mm for the left and right panels, respectively. Post-linearization of the characteristics is possible between 45 and 150 mm, though not with different linearization functions only.

Figure 2: The target position (top) and distance (bottom) as estimated by an appropriately trained artificial neural network as a function of the real target position. The correlation between the estimated and real target distance at three different target positions (bottom). The target distances were Z = 6.50, 6.10, 6.00, 5.85, 5.30, 4.80, 4.25, 3.60, 2.80, 2.15, 1.40 and 0.75 mm (top to bottom in the middle graph). The position was estimated by two independently trained networks to improve the system stability, and another network was used to estimate the signal strength (not shown), which was used to enable the position and distance estimation (the high values at the left and right parts in the top and middle graph indicate the "out of range" condition).


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Figure 3: The comparison of the absolute errors of arc tan based evaluation for 1 mm target distance (dotted line) with those of the ANN assisted evaluations for 0.75 and 1.4 mm target distances (thick and thin lines, respectively). For the latter two distances original training data were not available.

3. Conclusion and outlook In this paper we demonstrated that the signals of a planar coil based inductive position transducer can be successfully evaluated by appropriately trained artificial neural networks. Further work is necessary to improve the robustness to tolerate flush mounting into metal environment, which results in a typical shift of the target-free background signal values and further signal distortions at both ends of the sensing range, and the unexpected variations of the target metals, which change the signal strength and phase relations, and in particular, for ferromagnetic targets even in a distance dependent manner. Preliminary experiments show that the incorporation of further independent coil elements and the application of a grey-box model for the evaluation (treating the distortions of the sin and cos signals as perturbations and the application of the ANN for the correction of the coil signal characteristics only, rather than to represent the complete evaluation chain) are promising. References [1] T. Burkhardt, A. Feinäugle, S. Fericean, A. Forkl (2004): Lineare Weg- ung Abstandssensoren. Verlag Moderne Industrie. ISBN 3-93788907-8 [2] L. Killik, E. Gass (2002): Inductive displacement sensor with linear characteristic has voltage induced in variable geometry measuring loop compared with voltage in constant geometry reference loop. Patent Script No. DE10120822 (C2) [3] J. Golby. Induktive Weg–Sensoren –– Neues Messprinzipermöglicht maßgeschneiderte Entwicklungen, Elektronik, 6(2009),pp.22-26, [4]V. E. Zhitomirsky (2006): Position Sensor. Patent Script No. WO2008032008 (A1) [5] B. Aschenbrenner, B. G. Zagar (2014): Contactless high frequency inductive position sensor withDSP read out electronics utilizing band-pass sampling. ACTA IMEKO, September 2014, Volume 3, Number 3, 50 – 56 [6] S. Haykin (2009): Neural Networks and Learning Machines. 3rd ed. Prentice Hall. ISBN-13:978-0-13-147139-9