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Computation of the largest positive Lyapunov exponent using rounding mode and recursive least square algorithm

CHAOS SOLITONS & FRACTALS 2018年 112卷 36-43页

作者： Peixoto, Marcia L. C. Nepomuceno, Erivelton G. Martins, Samir A. M. Lacerda, Marcio J. Univ Fed Sao Joao del Rei Dept Elect Engn Control & Modelling Grp GCOM Praca Frei Orlando 170 BR-36307352 Joao Del Rei MG Brazil

It has been shown that natural interval extensions (NIE) can be used to calculate the largest positive Lyapunov exponent (LLE). However, the elaboration of NIE are not always possible for some dynamical systems, such as those modelled by simple equations or by Simulink-type blocks. In this paper, we use rounding mode of floating-point numbers to compute the LLE. We have exhibited how to produce two pseudo-orbits by means of different rounding modes;these pseudo-orbits are used to calculate the Lower Bound Error (LBE). The LLE is the slope of the line gotten from the logarithm of the LBE, which is estimated by means of a recursive least square algorithm (RLS). The main contribution of this paper is to develop a procedure to compute the LLE based on the LBE without using the NIE. Additionally, with the aid of RLS the number of required points has been decreased. Eight numerical examples are given to show the effectiveness of the proposed technique. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： Dynamical systems Lyapunov exponent Rounding mode Lower bound error Chaos recursive least square algorithm

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Adaptive thermal error prediction for CNC machine tool spindle using online measurement and an improved recursive least square algorithm

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CASE STUDIES IN THERMAL ENGINEERING 2024年 56卷

作者： Wei, Xinyuan Ye, Honghan Wang, Gao Hu, Weidong Anhui Univ Technol Sch Elect & Informat Engn Maanshan 230009 Peoples R China Univ Wisconsin Coll Letters & Sci Sch Comp Data & Informat Dept Stat Madison WI 53705 USA Anhui Prov Key Lab Special Heavy Load Robot Maanshan 243032 Peoples R China

Establishing models for predicting and compensating for spindle thermal errors is cost-effective and necessary to improve the accuracy of machine tools for smart manufacturing. However, the prediction performance of existing methods deteriorates significantly with dynamic working conditions of machine tools because training from static conditions leads to the inability to adapt to dynamic conditions. Therefore, an adaptive thermal error modeling method using online measurement and an improved recursive least square algorithm is proposed to fill this research gap, which updates the thermal error model adaptively to ensure that dynamic working conditions are learned in real time. Particularly, Spearman's rank correlation coefficient method is first adopted for temperature -sensitive point selection to capture the nonlinear relationship between temperature and thermal error variables. Furthermore, a variable -forgetting factor -based recursive least square (VFF-RLS) algorithm is proposed to improve the prediction performance, in which the proposed variable forgetting factor is adaptively updated according to real-time thermal error data collected by online measurement. The experimental results showed that the proposed VFFRLS method can maintain a high prediction accuracy of 1.75 mu m and robustness of 0.16 mu m on both constant and dynamic working conditions. The effectiveness of the VFF-RLS method is validated by verification experiments.

关键词： CNC machine tools Thermal error modeling Adaptability recursive least square algorithm Variable forgetting factor

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Model-Based recursive least square algorithm for Estimation of Brake Pressure and Road Friction

Model-Based Recursive Least Square Algorithm for Estimation ...

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FISITA 2012 World Automotive Congress--Volume 10：Chassis Systems and Integration Technology

作者： Nenggen Ding Xiaofei Zhan

A recursive least square algorithm for estimation of brake cylinder pressure and road surface coefficients of adhesion using wheel speeds and control inputs for the hydraulic unit is *** is intended for providing useful information for anti-lock brake systems(ABS) to improve the perfomiance of control logic and diagnostic *** on the brake pressure model and wheel/vehicle dynamics,the errors between estimated wheel angular acceleration and its actual value according to the measured wheel speeds are *** load transfer is considered for calculation of tire normal forces based on the estimated deceleration according to the vehicle reference speeds from the ABS control *** proposed algorithm is evaluated using ABS simulation data under various braking conditions on a hardware-in-the-loop(HIL) test rig.

关键词： Brake pressure estimation Road friction estimation recursive least square algorithm ABS

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Nonlinear Modeling and Identification of the Electro-hydraulic Control System of an Excavator Arm Using BONL Model

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Chinese Journal of Mechanical Engineering 2013年第6期26卷 1212-1221页

作者： YAN Jun LI Bo GUO Gang ZENG Yonghua ZHANG Meijun College of Field Engineering PLA University of Science and Technology

Electro-hydraulic control systems are nonlinear in nature and their mathematic models have unknown parameters. Existing research of modeling and identification of the electro-hydraulic control system is mainly based on theoretical state space model, and the parameters identification is hard due to its demand on internal states measurement. Moreover, there are also some hard-to-model nonlinearities in theoretical model, which needs to be overcome. Modeling and identification of the electro-hydraulic control system of an excavator arm based on block-oriented nonlinear（BONL） models is investigated. The nonlinear state space model of the system is built first, and field tests are carried out to reveal the nonlinear characteristics of the system. Based on the physic insight into the system, three BONL models are adopted to describe the highly nonlinear system. The Hammerstein model is composed of a two-segment polynomial nonlinearity followed by a linear dynamic subsystem. The Hammerstein-Wiener（H-W） model is represented by the Hammerstein model in cascade with another single polynomial nonlinearity. A novel Pseudo-Hammerstein-Wiener（P-H-W） model is developed by replacing the single polynomial of the H-W model by a non-smooth backlash function. The key term separation principle is applied to simplify the BONL models into linear-in-parameters struc^tres. Then, a modified recursive least square algorithm（MRLSA） with iterative estimation of internal variables is developed to identify the all the parameters simultaneously. The identification results demonstrate that the BONL models with two-segment polynomial nonlinearities are able to capture the system behavior, and the P-H-W model has the best prediction accuracy. Comparison experiments show that the velocity prediction error of the P-H-W model is reduced by 14%, 30% and 75% to the H-W model, Hammerstein model, and extended auto-regressive （ARX） model, respectively. This research is helpful in controller design, system mo

关键词： electro-hydraulic control system backlash Pseudo-Hammerstein-Wiener model nonlinear identification recursive least square algorithm

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Iterative learning based model identification and state of charge estimation of lithium-ion battery

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IET POWER ELECTRONICS 2019年第4期12卷 852-860页

作者： Zhu, Qiao Chen, Jun-Xiong Xu, Meng-En Zou, Chen Southwest Jiaotong Univ Sch Mech Engn Chengdu Sichuan Peoples R China

This work focuses on the accurate identification of lithium-ion battery's non-linear parameters by using an iterative learning method. First, the second-order resistance-capacitance model and its regression form of the battery are introduced. Then, when the battery repeatedly implements a discharge trial from the state of charge (SOC) 100 to 0%, an iterative learning based recursive least square (IL-RLS) algorithm is presented to accurately identify the non-linear parameters of the regression model. The essential idea of the IL-RLS algorithm is to improve the current parameter estimates by learning the predictive errors of the previous trials. After that, the parameters are identified as the functions of SOC by using the IL-RLS, which are verified by comparing with the results of the classic identification method for current pulses. As a result, an application-oriented SOC estimation scheme is proposed, where the IL-RLS calibrates the battery parameters offline and the classic extended Kalman filter (EKF) estimates the SOC in real-time. Finally, based on the EKF as well as the parameters identified by the IL-RLS, one static and three dynamic operating conditions are given to show the efficiency of the IL-RLS, where all the SOC estimation errors are <2%.

关键词： secondary cells regression analysis least squares approximations Kalman filters iterative methods nonlinear filters recursive estimation iterative learning method second-order resistance-capacitance model recursive least square algorithm regression model IL-RLS algorithm application-oriented SOC estimation scheme iterative learning based model identification charge estimation lithium-ion battery SOC estimation state of charge extended Kalman filter

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Eigenspace-based blind pattern optimisations of steerable antenna array for interference cancellation

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IET MICROWAVES ANTENNAS & PROPAGATION 2008年第4期2卷 358-366页

作者： Sugiura, S. Kikuma, N. Iizuka, H. Toyota Cent Res & Dev Labs Inc Aichi 4801192 Japan Nagoya Inst Technol Nagoya Aichi 4668555 Japan

A novel adaptive algorithm for an array using directional elements called a hybrid smart antenna system is proposed. The algorithm controls the element patterns on the basis of an objective function composed of eigenvalues of a covariance matrix. A high and stable array output signal-to-interference-plus-noise ratio is achieved by improving both the received powers and the spatial correlation coefficient between incident waves, without prior knowledge such as directions-of-arrival, channel state information or training signals. The characteristics of the proposed algorithm are theoretically and numerically clarified for a simple case involving two incident waves. Convergence with least mean squares algorithm is found to be as fast as that with recursive least squares algorithm in this system. Also, simulation for statistical performance evaluation is carried out in comparison with a conventional system. Furthermore, a method to implement the proposed eigenspace control algorithm without having to solve the eigenvalue problem is shown.

关键词： eigenspace-based blind pattern optimisation smart antenna system recursive estimation Optimisation techniques spatial correlation coefficient Signal processing and detection correlation methods optimisation recursive least square algorithm Algebra adaptive antenna arrays covariance matrix covariance matrices least squares approximations interference cancellation Antenna arrays array signal processing convergence Interpolation and function approximation (numerical analysis) eigenvalues and eigenfunctions steerable antenna array least mean square algorithm adaptive array algorithm array output signal-to-interference-plus-noise ratio interference suppression

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Modelling Length/Pressure Hysteresis of a Pneumatic Artificial Muscle using a Modified Prandtl-Ishlinskii Model

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STROJNISKI VESTNIK-JOURNAL OF MECHANICAL ENGINEERING 2017年第1期63卷 56-64页

作者： Liu, Yixiang Zang, Xizhe Lin, Zhenkun Liu, Xinyu Zhao, Jie Harbin Inst Technol State Key Lab Robot & Syst 2 Yikuang St Harbin 150080 Peoples R China

Pneumatic artificial muscles have been widely used in various fields owing to their inherent compliance and high power-to-weight ratio. However, the natural hysteresis nonlinearity including length/pressure hysteresis and force/pressure hysteresis degrades their performance in precise tracking control, making it necessary to build a mathematical hysteresis model for hysteresis compensation. This paper deals with the modelling of length/pressure hysteresis of pneumatic artificial muscles. The length/pressure hysteresis loops measured by the isotonic test are found to be asymmetric and independent of the external load when the load is small. Considering that the classical Prandtl-Ishlinskii model is only effective for symmetric hysteresis, a modified Prandtl-Ishlinskii model is proposed to describe the length/pressure hysteresis behaviour. The developed model utilizes two asymmetric operators with simple mathematical forms to independently model the ascending branch and descending branch of hysteresis loops. The model parameters are identified using the recursive least square algorithm. Comparisons between simulation results and experimental measurements demonstrate that the proposed model can characterize the asymmetric major hysteresis loop and minor hysteresis loops with high accuracy.

关键词： asymmetric hysteresis length/pressure hysteresis modified Prandtl-Ishlinskii model pneumatic artificial muscles recursive least square algorithm

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Identification of linear time-varying fractional order systems using block pulse functions based on repetitive principle

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ISA TRANSACTIONS 2022年 123卷 218-229页

作者： Zhang, Bo Tang, Yinggan Lu, Yao Yanshan Univ Inst Elect Engn Qinhuangdao 066004 Hebei Peoples R China Yanshan Univ LiRen Coll Qinhuangdao 066004 Hebei Peoples R China

A novel method for identifying linear time-varying fractional order systems based on a repetitive principle is proposed in this study. According to the repetitive principle, the system operates repetitively for several times, so the time-varying parameters are invariant on the fixed time for different operations. In the identification process, the time-varying parameters, independent from the input/output signals, are expanded onto some block pulse functions. The system is then converted to an algebraic system via the fractional differential operational matrix of the block pulse functions. Finally, recursive least square and instrumental variable recursive least square algorithms along the iteration axis are designed to identify the time-varying parameters without and with noise. Simulation results demonstrate that our proposed method is powerful in tracking time-varying parameters. (C) 2021 ISA. Published by Elsevier Ltd. All rights reserved.

关键词： Identification Fractional order system Repetitive principle Time-varying parameter recursive least square algorithm

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Integration of optimized feedrate into an online adaptive force controller for robot milling

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INTERNATIONAL JOURNAL OF ADVANCED MANUFACTURING TECHNOLOGY 2020年第3-4期106卷 1533-1542页

作者： Xiong, Gang Li, Zhou-Long Ding, Ye Zhu, LiMin Shanghai Jiao Tong Univ Sch Mech Engn State Key Lab Mech Syst & Vibrat Shanghai 200240 Peoples R China

Maximum resultant cutting force control provides a great benefit of improving productivity in machining tasks. This paper presents a new force control method for robot milling that can prevent force overshoots during abrupt part geometry changes. Firstly, the feedrates of the robot at critical cutter locations are optimized offline according to the cutting force model and the part geometry. Secondly, an online parameter self-adaptive proportional-integral (PI) controller is designed in consideration of the robot feed-direction dynamics and the time-varying first-order model of the cutting process. Finally, the offline scheduled feedrates are integrated into the online adaptive controller via a feedforward-like strategy. Experiments demonstrate the effectiveness and advantages of the proposed force control method.

关键词： Robot machining Force control Feedrate scheduling Parameter self-adaptive PI controller recursive least square algorithm

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Adaptive online state-of-charge determination based on neuro-controller and neural network

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ENERGY CONVERSION AND MANAGEMENT 2010年第5期51卷 1093-1098页

作者： Shen Yanqing Chongqing Ind Polytech Coll Dept Automat Chongqing 400050 Peoples R China

This paper presents a novel approach using adaptive artificial neural network based model and neuro-controller for online cell State of Charge (SOC) determination. Taking cell SOC as model's predictive control input unit, radial basis function neural network, which can adjust its structure to prediction error with recursive least square algorithm, is used to simulate battery system. Besides that, neuro-controller based on Back-Propagation Neural Network (BPNN) and modified PID controller is used to decide the control input of battery system, i.e., cell SOC. Finally this algorithm is applied for the SOC determination of lead-acid batteries, and results of lab tests on physical cells, compared with model prediction, are presented. Results show that the ANN based battery system model adaptively simulates battery system with great accuracy, and the predicted SOC simultaneously converges to the real value quickly within the error of +/- 1 as time goes on. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： State of Charge (SOC) Neuro-controller Radial Basis Function Neural Network (RBFNN) Lead-acid batteries recursive least square algorithm

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