Adaptive charge estimation of piezoelectric actuators with a variable sensing resistor, an artificial intelligence approach

Experiments have shown that, for an extensive area of operating, charge of a piezoelectric actuator is proportional to its displacement from relaxing state. Consequently, accurate estimation of charge can lead to position/displacement estimation for piezoelectric actuators, a prominent progress towards precise sensorless micro/nanopositioning. However, disadvantageously, all known charge estimators of piezoelectric actuators have electrical element(s), e.g. (a) resistor(s) or (a) capacitor(s), in series with the actuator. Such elements, known as sensing elements, take a considerable share of the excitation voltage. Voltage taken by the sensing elements is called voltage drop. Charge estimators with a resistor in series with the actuator (also known as digital charge estimators) have been reported to witness the smallest voltage drop. The aim of this paper is to design such charge estimators so as to achieve maximum precision at minimum possible voltage drop. The aforementioned aim is shown to be obtained when the range of the voltage across the resistor equals the narrowest input range of the analogue to digital convertor of the charge estimator. This, however, is impossible to happen for wide operating areas with a sensing resistor with unchangeable resistance, according to experimental results. The alternative is an adaptive charge estimator with a resistor, in which its resistance varies with operating conditions. This paper presents two methods to estimate such a varying sensing resistor: Approximate analytical formulation and artificial intelligence, in which, the latter shows evident superiority.