Generalization Enhancement of Operator-LSSVM-Based Hysteresis Model Using Improved Particle Swarm Optimization for Piezoelectric Actuators

Nanopositioning is one of the key requirements for ultrahigh-precision motion applications. Piezoelectric actuators are very popular and widely used in nanopositioning systems due to their superior properties. These actuators are composed of smart materials that are distinguished by the nonlinear hysteresis phenomenon, which limits their positioning accuracy. For this reason, the need for a more accurate hysteresis model is very important to design any controller that can compensate for the hysteresis effect. This paper proposes a hysteresis identification approach based on stop operators and a kernel-based machine learning algorithm optimized by the Improved Particle Swarm Optimization (IPSO) technique. A discrete hysteresis memory is first used by a set of stop operators to solve the multivalued mapping problem, and then the Least Squares Support Vector Machine (LSSVM) algorithm is used to estimate the density function. The generalization ability of the LSSVM model is enhanced by improving the local as well as the global search ability of the PSO algorithm as the learning factors are changed in each iteration. The achieved results are compared with the output displacement obtained from the experiments. The average Root Mean Square Error (RMSE) of the proposed IPSO-LSSVM model through all the datasets is
$\mathbf{0}.\mathbf{013}\ \boldsymbol{\mu}\mathbf{m}$
, as compared to RMSE of
$\mathbf{0}.\mathbf{026}\ \boldsymbol{\mu}\mathbf{m}$
with PSO-LSSVM model. The achieved results indicate that the IPSO-LSSVM model exhibits superior modeling accuracy over the PSO-LSSVM model.