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

Abstract

Piezoelectric ceramics(PZT)actuator has been widely used in flexure-guided micro/nano positioning 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 micro/nano positioning 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. Keywords: Piezoelectric ceramics • micro/nano positioning stage • flexure • hysteresis nonlinearity• extreme learning machine.

Cholesky Factorization Based Online Sequential Extreme Learning Machines with Persistent Regularization and Forgetting Factor

“…It should be noted that some online sequential RELM with forgetting factor, such as SF-ELM [34], RFOS-ELM [35], WOS-ELM [36], DU-OS-ELM [37], and FReOS-ELM [38], take Equation (10) as cost function, but take Equations (8) and (9) or their equivalent form as recursive solutions.…”

“…After stating the real optimization cost function in FR-OSELM and theoretically analyzing FR-OSELM, Guo and Xu pointed out that the regularization term in the cost function of FR-OSELM will be forgotten and tends to zero as time passes; thus, FR-OSELM will probably run into ill-conditioning problems and become unstable after a long period. Incidentally, a similar or the same optimization cost function, or recursive solution in which the regularization term wanes gradually with time, is still utilized in [36][37][38].…”

Combined Control for a Piezoelectric Actuator Using a Feed-Forward Neural Network and Feedback Integral Fast Terminal Sliding Mode Control

“…Machine learning techniques have become increasingly prevalent for modeling the hysteresis behavior of PEAs from experimental data. Among the principal machine learning approaches for this purpose are artificial neural networks (ANNs) [ 27 , 28 , 29 ], support vector machines (SVMs) [ 30 ], random forests [ 31 ], and Gaussian processes (GPs) [ 32 ]. These machine learning techniques provide flexible and data-driven approaches to hysteresis modeling, enabling accurate predictions and enhanced understanding of the dynamic characteristics of PEAs [ 27 ].…”

“…Among the principal machine learning approaches for this purpose are artificial neural networks (ANNs) [ 27 , 28 , 29 ], support vector machines (SVMs) [ 30 ], random forests [ 31 ], and Gaussian processes (GPs) [ 32 ]. These machine learning techniques provide flexible and data-driven approaches to hysteresis modeling, enabling accurate predictions and enhanced understanding of the dynamic characteristics of PEAs [ 27 ]. Recurrent artificial neural networks (RNNs) have become a powerful tool for modeling non-linear dynamics [ 33 ] such as PEA hysteresis behavior.…”

An electromechanical dynamic stiffness matrix of piezoelectric stacks for systematic design of micro/nano motion actuators

“…To this end, plenty of researches were devoted to the modeling and control of such a hysteresis nonlinearity in piezoelectric actuators. These include physical models [44], phenomenological models [45] and intelligent models [46], in which Prandtl-Ishlinskii model, Maxwell-slip model and Bouc-Wen model were widely investigated [47][48][49]. Some hysteresis models were combined with linear transfer functions to configure a Hammerstein model to capture the rate-dependent hysteresis and dynamic characteristics [50].…”