Friction with Hysteresis Loop Modeled by Tensor Product

Abstract

Original scientific paperEngineers encounter the problem of friction in any mechanical system. Friction force is strongly nonlinear and varies considerably while the system is working. In the case of high-precision applications friction makes the situation even more complex, as the stick-slip effect occurs near the target position. This paper introduces a pneumatic servo-system for investigation of the behavior of friction near the target position. A new model is proposed which takes the hysteresis loop of the friction also into consideration emphasizing the importance of hysteresis. This paper presents the tensorproduct (TP) based modeling of friction which is suitable for control design. The main advantage of the TP model transformation is that due to its polytopic model form Linear Matrix Inequality (LMI) can be immediately applied to the resulting model to yield controllers with guaranteed performance. The main contribution of this paper is the application of TP model transformation making the identification of friction parameters unnecessary by utilizing directly the measured data itself. Key words: Tensor Product, Friction Compensation, Pneumatic Cylinder, Stribeck EffectIdentifikacija modela trenja s histerezom korištenjem tenzorskog produkta. Inženjeri se susreću s pojavom trenja u svakom mehaničkom sustavu. Sila trenja ima izraženu nelinearnost i promjenjiva je ovisno o radnim uvjetima procesa. U slučaju pozicioniranja s visokom preciznošću trenje dodatno komplicira situaciju, što rezultira pojavom oscilatornog ponašanja u okolini referentne pozicije sustava upravljanja. U ovom radu je predstavljen pneumatski servosustav koji se koristi za analizu ponašanja sile trenja u blizini referentne pozicije. Predložen je novi model sile trenja koji uzima u obzir histereznu karakteristiku trenja. U radu je predstavljeno modeliranje trenja na principu tenzorskog produkta koji je prikladan za sintezu sustava upravljanja. Glavna prednost transformacije modela korištenjem tenzorskog produkta je što politopski oblik modela u obliku linearnih matričnih nejednadžbi omogućava njegovu direktnu primjenu za sintezu regulatora s garantiranim performansama. Glavni znanstveni doprinos ovog rada je primjena transformacije modela trenja korištenjem tenzorskog produkta, pričemu identifikacija parametara trenja postaje suvišna direktnim korištenjem izmjerenih podataka.

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