A novel technique for indirect angular acceleration measurement

This paper presents a novel technique for indirect angular acceleration measurement, based on joint use of four Artificial Neu- ral Networks, which elaborate this processing kind, after opportune transformations of velocity-signal. The result so obtained, is enable to predict the angular acceleration with low delay: making this method- ology suitable in application with high real-time constrains. The de- veloped approach uses Recurrent Neural Networks, which are based on State-Space of Dynamic-Systems, so establishing a direct connec- tion with other approaches based on: Artificial Neural Networks, and Kalman Filters. The indirect measurement of angular acceleration is de- veloped starting from the velocity measure or position sig- nal, generally provided by incremental pulse encoder or dc- tachogenerators (with some postprocessing electronics). The differentiation process amplifies the noise that is unavoid- ably present in measure of velocity or position, thus limiting the application of this indirect measurement. During the last decade some techniques are proposed: they generally predict the acceleration signal by means of Prediction Filters or cas- code compositions of Artificial Neural Networks (1). The ap- proaches, previously described, guarantee an estimation of in- stantaneous acceleration value, which is semi delay-less: this aspect is fundamental in servo motor drive system, where these techniques represent an useful aid to improve the performances of motion control under real-time conditions. Our idea is based on the assumption that there exists a direct connection between the indirect measurement, and the state- space of the system. Along this direction, we think that the velocity-signal represents a specific system. In other words, we assume this signal as a piece-wise linear approximation plus noise: the angular coefficient of every piece-wise linear functions characterizes the system state. Then the problem of indirect angular acceleration measurement can be reformulated as system-state identification with high real-time constrains. This paper presents a novel approach based on joint use of four Artificial Neural Networks (ANNs), which have, as in- puts, four opportune transformations of velocity-signal. Our approach exploits the approximation properties of nonlinear function provided by Artificial Neural Networks, as it is ef- fectively used in (2), where Ovaska et al. use a cascode com- position of Artificial Neural Network, nevertheless with some differences (in our approach): (i) the signals that are ana- lyzed, and processed by the ANNs, are not only the velocity- signal, but signals that are opportunely transformed by contrac- tion operators. (ii) the use of Recurrent Neural Networks (3) that establish direct connections with state-space of Dynamic- System, which determines, and regulates the velocity-signal generation. The obtained result reduces the noise that is unavoidably present on velocity measure, thus it regulates the prediction mechanism based on state characterization of dynamic sys- tem, and finally the representation set (provided by the con- traction operators) permits a better regulation of nondetermin- istic behaviour. The final results have excellent real-time per- formances, and an accuracy that is similar to the actual best practices in this field. The low computational cost of: these operators, and the proposed Artificial Neural Network kind, makes this technique easily implementable On-Chip, and on Embedded System (4).