Creep modeling for piezoelectric actuators using fractional order system of commensurate order

This paper focuses on the creep modelling for the piezoelectric actuators (PEAs) using fractional system of commensurate order. The proposed fractional system of commensurate order is derived from another fractional system of non commensurate order through an identification method based on the recursive least squares algorithm. The choice of the fractional system of commensurate order representation is due mainly to the ability to use this representation to implement the PEA using analogue circuits through rational function approximation of its irrational transfer function, to represent the PEA using a fractional order state space representation, to easily study the PEA's stability and to derive its closed form responses. The proposed PEA model has been validated in simulation and on an experimental set-up from Gipsa-lab.