Nanometric positioning of a piezo walker

Abstract

This work presents functional description of a walking piezoelectric motor and its control in nanometer precision. For this purpose a dynamical model of the actuator is derived based on simple mass spring damper system. Model parameters are estimated from step response plot and the system is expressed with second order transfer function. Additional identification experiments verified the theoretical kinematics of the bimorph legs. These experiments demonstrate approximately linear relation between the legs displacement in x and y directions to the applied voltages. Based on derived system model and identification results a PI controller followed by Hadamard transformation is proposed as a controller scheme. Experimental results for staircase and sinusoidal references reveal precise positioning capabilities of the system with the proposed control scheme down to few nanometers.