A regularized on-line sequential extreme learning machine with forgetting property for fast dynamic hysteresis modeling

Piezoelectric ceramics(PZT)actuator has been widely used in flexure-guided nanopositioning stage because of their high resolution. However, it is quite hard to achieve high-rate precision positioning control because of the complex hysteresis nonlinearity effect of PZT actuator. Thus, an online RELM algorithm with forgetting property(FReOS-ELM) is proposed to handle this issue. Firstly, we adopt regularized extreme learning machine(RELM)to build an intelligent hysteresis model. The training of the algorithm is completed only in one step, which avoids the shortcomings of the traditional hysteresis model based on artificial neural network(ANN) that slow training speed and easy to fall into the local minimum. Then, based on the regularized on-line sequential extreme learning machine(ReOS-ELM), an on-line RELM algorithm with forgetting property(FReOS-ELM) is designed, which can avoid the computational load of ReOS-ELM in the process of adding new data for learning on-line. In the experiment, a real-time voltage signal with varying frequencies and amplitudes is adopted, and the output displacement data of the nanopositioning stage is also acquired and analyzed. The results powerfully verify that the performance of the established hysteresis model based on the proposed FReOS-ELM is satisfactory, which can be used to improve the practical positioning performance for flexure nanopositioning stage.