Original scientific paperPiezoelectric actuators, widely used in different micro/nanopositioning applications, generally exhibit nonlinear hysteresis characteristics. The compensation of hysteretic behavior of piezoelectric actuators is mandatory for precise micro/nanopositioning. In this paper, nonlinear hysteresis effect is first characterized using the PrandtlIshlinskii hysteresis model. The inverse of the Prandtl-Ishlinskii hysteresis model is employed as a feed-forward controller to compensate for hysteresis nonlinearities of the piezoelectric actuator. Slight hysteresis nonlinearity is still observed in the experimental results due to small mismatch between the identified hysteresis model and the measured hysteresis loop. To further enhance the performance of the piezoelectric actuator in terms of mitigation of hysteresis nonlinearity and precise reference tracking, advanced robust full-order as well as fixed-order H∞ feedback controllers are designed and applied to this actuator in the presence of feed-forward compensator. The experimental results verify the effectiveness of the proposed control scheme in achieving the improved tracking performance with peak-to-peak tracking error of less than 1% for the desired displacement of 12 µm with tracking frequency of 10 Hz.Key words: Feed-forward compensator, Full-order and fixed-order H∞ feedback controllers, Piezoelectric actuator, Prandtl-Ishlinskii hysteresis model Sinteza H∞ regulatora s unaprijednom granom za kompenzaciju histereze kod piezoelektričnih aktuatora. Piezoelektrični aktuatori, rasprostranjeni u različitim primjenama mikro/nanopozicioniranja, općenito su izloženi nelinearnim histereznim karakteristikama. Kompenzacija histereznog ponašanja piezoelektričnih aktuatora nužna je za precizno mikro/nanopozicioniranje. Inverzni Prandtl-Ishlinskii histerezni model korišten je za unaprijednu kompenzaciju histereznih nelinearnosti piezoelektričnog aktuatora. Neznatna histerezna nelinearnost još uvijek je vidljiva u eksperimentalnim rezultatima zbog malog neslaganja izmeu identificiranog histereznog modela i mjerene histerezne petlje. Za daljnje poboljšanje performansi piezoelektričnog aktuatora u smislu smanjenja histerezne nelinearnosti i preciznog slijeenja reference, napredni robusni H∞ regulatori punog i odreenog reda sintetizirani su i primijenjeni na ovaj aktuator uz prisutnost unaprijednog kompenzatora. Eksperimentalni rezultati potvruju efektivnost predložene upravljačke strukture u postizanju poboljšanih performansi slijeenja, uz vršnu vrijednost pogreške manju od 1% za ciljani pomak od 12 µm s frekvencijom slijeenja od 10 Hz.Ključne riječi: Unaprijedni kompenzator, H∞ regulator punog i odreenog reda, piezoelektrični aktuator, PrandtlIshlinskii histerezni model
INTRODUCTIONMicro/nanopositioning is an important aspect of research in micro/nanotechnology where ultrahigh positioning precision is one of the pivotal requirements. Piezoelectric actuators are widely used in different micro/nanopositioning [1] and atomic-scale surface scanning applicatio...