For many piezoelectric actuators and their areas of operating, charge is proportional to the position of the actuator. Thus, for such actuators, estimation of charge is largely considered as an equivalent to position estimation. That is, a charge estimator may replace a position sensor. Nevertheless, a significant portion of the excitation voltage is wasted for charge estimation. This voltage, not used to deform the actuator, is called voltage drop. A class of charge estimators of piezoelectric actuators have a resistor in series with the actuator and can only work together with a digital processor. These are called digital charge estimators and have been shown to witness the smallest voltage drop compared to other charge estimators. This chapter first proposes a design guide for digital charge estimators of piezoelectric actuators to maximise the accuracy with the smallest possible voltage drop. The chapter then details the use of five different artificial intelligence (AI) techniques to tackle this design problem and assesses their effectiveness through even-handed comparison.
TopIntroduction
Piezoelectricity, the inter-convertibility of mechanical and electrical quantities in so-called piezoelectric materials was discovered in 19th century by Curie brothers (Jayesh Minase et al., 2010). Currently, quartz and other crystals, ferroelectric polycrystalline ceramics, piezoceramics (e.g. barium titanate) and most commonly lead zirconate titanate (PZT) are used to produce piezoelectric materials (Aggrey et al., 2020; Izyumskaya et al., 2007; Jayesh Minase et al., 2010; Yang et al., 2020).
In piezoelectric materials, electrons are distributed asymmetrically in ions (Sabek et al., 2015). Therefore, mechanical force, which moves ions, provides energy to electrons, and this results in electrical voltage. In addition, electrical voltage, through pushing electrons, moves ions and generates deformation. The latter case is known as inverse piezoelectricity (Chopra, 2002). Devices, made of piezoelectric materials and deliberately produced to employ inverse piezoelectricity, are called piezoelectric actuators(Rios & Fleming, 2014). Piezoelectric actuators have applications in energy harvesting (Hou et al., 2021), vibration control (Singh et al., 2021) and precise positioning (Flores & Rakotondrabe, 2021) including micro/nanopositioning.
Piezoelectric actuators are both the most compact and the most precise actuators in micro/nanopositioning (Mohammadzaheri & AlQallaf, 2017). Micro/nanopositioning aims at precise position control of matter at micro/nanometre scale (Morteza Mohammadzaheri et al., 2021), which is not necessarily equivalent to the development of micrometric scale actuators or sensors, e.g. in (Versaci et al., 2021; Xu et al., 2019). Fine machining (Hu et al., 2021), manipulation of biological cells (Deng et al., 2021), scanning probe microscopy (Szeremeta et al., 2021) and precise robotic surgery (Meinhold et al., 2020) are among applications of micro/nanopositioning with piezoelectric actuators or piezo-actuated micro/ nanopositioning .
The key task in piezo-actuated micro/nanopositioning is precise position control of (an unfixed point/surface of) the actuator (Miri et al., 2015). The origin of the position of (a point/surface on) a piezoelectric actuator is its position at relaxed state, when the actuator has not been subject to any electrical or mechanical excitation for a considerably long period of time (e.g. some minutes). That is, position of a piezoelectric actuator is its displacement from the relaxed state. Experiments have indicated that charge of a piezoelectric actuator is proportional to its position for a wide area of operating (Bazghaleh et al., 2010; M Bazghaleh et al., 2013; J. Minase et al., 2010; Yi & Veillette, 2005). Consequently, a charge estimator can replace a costly and demanding position/displacement sensor. This has been a prominent motivation for design and built of charge estimators for piezoelectric actuators (Liu et al., 2018; Mohammadzaheri & AlQallaf, 2017; Yang et al., 2017).