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