Fast dynamic hysteresis modeling using a regularized online sequential extreme learning machine with forgetting property

Piezoelectric ceramics (PZT) actuator has been widely used in flexure-guided micro/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 online sequential extreme learning machine (ReOS-ELM), an online 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 online. In the experiment, a real-time voltage signal with varying frequencies and amplitudes is adopted, and the output displacement data of the micro/nanopositioning stage is also acquired and analyzed. The experimental results show that the RELM-based hysteresis modeling algorithm has higher efficiency and more stable learning ability and generalization ability than the traditional neural network. In the aspect of online modeling, FReOS-ELM hysteresis modeling can achieve a better result than ReOS-ELM.