## Abstract

The project aimed at design of a precise sensorless nanopositioning systems with use of piezoelectric actuators. Nanopositioning has a wide variety of high tech applications. The major task in nanopositioning is to control displacement/position of the actuator. Piezoelectric actuators are the most precise actuators for nanopositioning. Feedback position control systems need displacement/position sensors, and these sensors are the major source of cost and operation limit in nanopositioning systems. For example, a capacitive displacement sensor (to be used for nanopositioning) is almost 20 times more expensive than a regular piezoelectric actuator. In addition, a lot of space, time and effort is needed to use these sensors.

It is known, since 1982, that for a wide operating area, charge of a piezoelectric actuator is proportional to its position. That is, a precise charge estimator can play the role of a displacement/position sensor. This research made a major progress in this area. The first practical charge estimator of piezoelectric actuators, for nanopositioning purposes, was introduced in 2006, with a capacitor in series with the actuator. However, in such a systems, a large portion of the applied voltage is taken by the aforementioned capacitor, namely voltage drop. Voltage drop is not used in excitation of the actuator. In 2010, a resistor (known as the sensing resistor) was suggested to replace the capacitor. This new method needed a digital processor for calculations (along with other components listed in Methodology). These charge estimators of piezoelectric actuators with sensing resistor (CEPASRs) showed smaller voltage drops and are being further developed. However, all reported CEPASR, before this project, used a fixed resistor for the entire operating area.

During research sponsored by this internal grant, the investigators first identified a rigorous design guideline/criterion for CEPASRs: the range of VS should be equal to the smallest input range of the analogue to the employed digital (A/D) converter. This guideline guarantees the maximum precision at the smallest possible voltage drop, as discussed in detail in Methodology section. Then, the investigators found that with a fixed resistor this guideline cannot be met for a wide operating area, as clearly shown in Figs. 2 and 3 in Methodology section. Thus, the idea of adaptive CEPASR was proposed: change of the sensing resistor with change of operating conditions.

Design of an adaptive CEPASR requires an algorithm to approximate the sensing resistor so that the aforementioned design guideline is met. This approximation problem was tackled with two approaches: analytical modelling and data driven modelling. Analytical modelling is based on the assumption that the piezoelectric can be approximated as a capacitor. The developed analytical model overestimates the sensing resistor in all operating area. As detailed in Methodology section, overestimation leads to loss of access to charge data for period of time, due to saturation of A/D converter, a serious consequence. Eight different data-driven methods were tried in this research including five Artificial Intelligence (AI) methods and three statistical methods. AI methods include Mutli Layer Perceptrion (MLP), Neurofuzzy network, Fully Connected Cascade (FCC) network and exact and efficient Radial Basis Function Network (RBFN). Statistical methods include linear modelling, cubic interpolation and averaging. MLP presented the best approximation of the sensing resistance. However, in order to reduce the chance of overestimation to 1%, it is suggested to deduct MLP output from (3 estimation standard deviation+ estimation bias). With use of accurately approximated sensing resistors, a sensorless control systems was designed and implemented.

It is known, since 1982, that for a wide operating area, charge of a piezoelectric actuator is proportional to its position. That is, a precise charge estimator can play the role of a displacement/position sensor. This research made a major progress in this area. The first practical charge estimator of piezoelectric actuators, for nanopositioning purposes, was introduced in 2006, with a capacitor in series with the actuator. However, in such a systems, a large portion of the applied voltage is taken by the aforementioned capacitor, namely voltage drop. Voltage drop is not used in excitation of the actuator. In 2010, a resistor (known as the sensing resistor) was suggested to replace the capacitor. This new method needed a digital processor for calculations (along with other components listed in Methodology). These charge estimators of piezoelectric actuators with sensing resistor (CEPASRs) showed smaller voltage drops and are being further developed. However, all reported CEPASR, before this project, used a fixed resistor for the entire operating area.

During research sponsored by this internal grant, the investigators first identified a rigorous design guideline/criterion for CEPASRs: the range of VS should be equal to the smallest input range of the analogue to the employed digital (A/D) converter. This guideline guarantees the maximum precision at the smallest possible voltage drop, as discussed in detail in Methodology section. Then, the investigators found that with a fixed resistor this guideline cannot be met for a wide operating area, as clearly shown in Figs. 2 and 3 in Methodology section. Thus, the idea of adaptive CEPASR was proposed: change of the sensing resistor with change of operating conditions.

Design of an adaptive CEPASR requires an algorithm to approximate the sensing resistor so that the aforementioned design guideline is met. This approximation problem was tackled with two approaches: analytical modelling and data driven modelling. Analytical modelling is based on the assumption that the piezoelectric can be approximated as a capacitor. The developed analytical model overestimates the sensing resistor in all operating area. As detailed in Methodology section, overestimation leads to loss of access to charge data for period of time, due to saturation of A/D converter, a serious consequence. Eight different data-driven methods were tried in this research including five Artificial Intelligence (AI) methods and three statistical methods. AI methods include Mutli Layer Perceptrion (MLP), Neurofuzzy network, Fully Connected Cascade (FCC) network and exact and efficient Radial Basis Function Network (RBFN). Statistical methods include linear modelling, cubic interpolation and averaging. MLP presented the best approximation of the sensing resistance. However, in order to reduce the chance of overestimation to 1%, it is suggested to deduct MLP output from (3 estimation standard deviation+ estimation bias). With use of accurately approximated sensing resistors, a sensorless control systems was designed and implemented.

Original language | English |
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Type | Grant Report |

Number of pages | 27 |

Publication status | Unpublished - 2020 |