MultiRate Predictive Control of Piezoelectric actuators Hossein Habibollahi Najafabadi, Seyed Mehdi Rezaei, Saeed Shiry Ghidary, Mozafar Saadat*, Mohammad Zareinejad and Reza Seifabadi Amirkabir University of Technology, Tehran, Iran *University of Birmingham Abstract: Piezoelectric materials show nonlinear hysteresis behaviour when they are under high electrical field and mechanical load. Fundamental study of PEA depicts that the Hysteresis effect deteriorate the tracking performance of The PEA. This paper proposes a nonlinear model which quantifies the Hysteresis nonlinearity generated in Piezo- actuators in response to applied driving voltages. A novel perfect tracking control method based on multirate feedforward control is proposed which uses the nonlinear model to compensate mentioned limiting factors in PEA. In this study a multirate control method based on modified Prandtle-Ishlinskii operator as nonlinear model is implemented. It compensates rate dependant hysteresis nonlinearity in PEA. The controller structure has a simple design and can be quickly identified. The control system is capable to achieve suitable tracking control and it is convenient to use and can be quickly applied to the practical PEA applications. Experimental results are provided to verify the efficiency of the proposed method. Keywords: Piezoelectric actuators, Hysteresis, Prandtle-Ishlinskii 1. INTRODUCTION Properties of PEA make them efficient in positioning systems (Habibollahi et al. 2007). PEAs convert electrical energy directly to mechanical energy and consume low power. Motion in sub nano-meter is made possible and has fast response time. Consequently it takes to react only several micro seconds. PEAs have no moving parts in contact to each other to limit the resolution. Due to this effect PEAs show no wear and tear which causes a decrease in life time and precision. The advantages of PEAs make them suitable for electromechanical applications. Nowadays, there are increasing interests to piezoelectric and ferroelectric materials which are especially used in scientific and engineering applications such as Active vibration control (Carusoet al. 2003), needle-valve actuation and precision machining in precision mechanic applications. Atomic Force Microscopy (Croft et al. 2003) and cell manipulation in medical technology applications are other examples. To achieve a precise tracking control in a PEA system, a model based controller design is necessary. The model should represent the PEA precisely. Many investigations have been performed to model the dynamics of PEAs (Carusoet al. 2003, Adriaens et al. 2002), One of the critical fields in the study of PEA modeling is the hysteresis effect. Hysteresis occurs via applied voltage and induced displacement. The hysteresis is not a differentiable and nor a one-to-one nonlinear mapping. But it is a nonlinear operator with local memory. It means the output of the system depends not only on the instantaneous input value but also on the history of its operation (Maygergoyz 1991). The Nonlinear hysteresis effect can be corrected using charge control (Georgiou et al. 2005). However, charge control is inherently bulky, costly, uncommon, and offers limited sensitivity. It may lead to drift and saturation problems and reduces the operating range and life of PEA. Consequently, voltage control strategies for PEA proves to be more promising, economical and commercially acceptable control method. Different models of the hysteresis have been utilized in various researches. The models of hysteresis can be divided to mathematical and nonlinear differential models. The Preisach model (Hu at al. 2003, Croft et al. 2001 and Ge et al. 1995) the Maxwell slip model (Georgiou at al. 2006, Goldfarb et al. 1997) are examples of the hysteresis mathematical models. The Preisach model uses first order recursive curve to approximate the hysteresis nonlinearity. It Proceedings of the 17th World Congress The International Federation of Automatic Control Seoul, Korea, July 6-11, 2008 978-1-1234-7890-2/08/$20.00 © 2008 IFAC 15774 10.3182/20080706-5-KR-1001.3594