Neuronowa korekcja błędów dynamicznych przetwornika II-go rzędu

W artykule przedstawiono wyniki wstępnych badań dotyczących możliwości wykorzystania jednokierunkowych sieci neuronowych do korekcji błędów dynamicznych wprowadzanych przez przetworniki opisane liniowym równaniem różniczkowym II-go rzędu. Oceniono zasadność stosowania tego rodzaju podejścia do zagadnienia korekcji błędów dynamicznych. Wnioski sformułowano w oparciu o wyniki badań symulacyjnych.

Dynamic properties of second order transducers are usually modelled by the linear differential equation (1) which can be converted to the discrete equation of state (6). Recursive solving of this equation for the input quantity (Eqs. 8 and 9) is a dynamic error correction algorithm. This algorithm can be written in the form of equations (10 and 11) which can be solved by simple, feed-forward neural networks of structures shown in Fig.1. Fig. 2 illustrates the use of neural networks for realisation of the dynamic correction recursive algorithm. The possibility of applying neural networks to dynamic error correction was investigated by simulations in the Matlab Neural Toolbox environment. There were taken the following assumptions concerning the transducer model: , , and the discretization period . The network was learned using a 200 - element learning set generated on a basis of relation (14). The network was tested with a 200 000 - element testing set. The test results of both networks showed error - free implementation of (10) and (11) (errors of 10-15 order). At the next stage the learning sets were quantizied with 12 - bit resolution. The influence of the discretization period on the accuracy of correction realisation was also investigated. Fig. 7 presents the results as a dependency of the output results on the discretization period .