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Nonsmooth identification of mechanical systems with backlash-like hysteresis

控制理论与应用（英文版） 2013年第3期11卷 477-482页

作者： Ruili DONG Yonghong TAN David HE College of Mechanical and Electronic Technology Shanghai Normal University Department of Mechanical and Industrial Engineering University of Illinois

backlash-like hysteresis is one of the nonsmooth and multi-valued nonlinearities usually existing in mechanical systems. The traditional identification method is quite difficult to be used to model the systems involved with such complex nonlinearities. In this paper, a nonsmooth recursive identification algorithm for the systems with backlash-like hysteresis is proposed. In this method, the concept of Clarke subgradient is introduced to approximate the gradients at nonsmooth points and the so-called bundle method is used to obtain the optimization search direction in nonsmooth cases. Then, a recursive algorithm based on the idea of bundle method is developed for parameter estimation. After that, the convergence analysis of the algorithm is investigated. Finally, simulation results to validate the proposed method on a simulated mechanical transmission system are presented.

关键词： Identification Mechanical system Pseudo-Hammerstein model backlash Bundle method Subgradient

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A nonsmooth IMC method for mechanical systems with backlash

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控制理论与应用（英文版） 2013年第4期11卷 600-607页

作者： Ruili DONG Yonghong TAN David HE College of Mechanical and Electronic Technology Shanghai Normal University Department of Mechanical and Industrial Engineering University of Illinois at Chicago

This paper proposes a discrete-time nonsmooth internal model control （NSIMC） approach for mechanical transmission systems described by so-called sandwich system with backlash. In this method, a dynamic compensator is introduced to compensate for the effect of the input linear subsystem. Thus, the sandwich systems with backlash can be simplified as a pseudo-Hammerstein system with backlash. The corresponding NSIMC strategy is designed to control this system. The design procedure of the controller is presented based on the analysis on the robust stability by considering the model errors involved with the effect of backlash as well as the compensated error of the input linear subsystem. Moreover, as the model is switched among the different operating zones, the robust filters are proposed to guarantee the robust stability and satisfactory control performance of the system.

关键词： backlash Internal model control Sandwich system Nonsmooth nonlinear systems

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backlash Error Measurement and Compensation on the Vertical Machining Center

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Engineering（科研） 2010年第6期2卷 403-407页

作者： Huanlao Liu Xiaoning Xue Guangyu Tan 不详

The position errors in the axis direction of a vertical machine center have been measured by means of the VM101 linear encored measurement system. The character of the backlash error is discussed;results show that the backlash error has great influence on the position error. The position accuracy is enhanced after the backlash errors are compensated.

关键词： Position Error backlash Error Error Model Artificial Neural Network

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基于backlash描述函数的迟滞非线性建模

基于Backlash描述函数的迟滞非线性建模

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作者：翟亚伟青岛科技大学

学位级别：硕士

随着高新科技的发展，智能设备及高精度微定位装置得到了大量应用。而这些设备和装置中，“智能材料”构件是重要的组成部分。但是这些材料的一个主要的限制就是由于迟滞现象的存在，尤其是在缺乏精确模型的控制系统中，可能会引起震荡... 详细信息

随着高新科技的发展，智能设备及高精度微定位装置得到了大量应用。而这些设备和装置中，“智能材料”构件是重要的组成部分。但是这些材料的一个主要的限制就是由于迟滞现象的存在，尤其是在缺乏精确模型的控制系统中，可能会引起震荡，甚至会导致不稳定。因此，在控制器设计中，对迟滞非线性建模和预测是十分必要。但是由于迟滞非线性的特殊性，传统的方法难以建立精确的动态模型。论文的任务是提出一种简单而新颖的方法，建立能够预测多类输入信号作用下的迟滞非线性特性的动态模型。由于Preisach模型有着良好的精度和易用性，所以本文是基于Preisach方法建立的迟滞非线性模型。backlash在建立Preisach迟滞模型方面被认为是最简单最有效的工具。运用改进backlash描述函数，建立迟滞非线性动态模型是论文的主要创新点，也是论文的核心内容。首先，我们理论上证明了所给函数的重要性质及其参数在建模中所起的作用，并给出应用该函数建立迟滞模型过程。因所建模型与实际迟滞非线性特性有所不同，但已具备了迟滞非线性的多数特性，同时也建立了二者之间的对应关系。因此，利用神经网络的逼近能力，以所建模型的输出作为神经网络的一个输入，从而建立了一个神经网络迟滞非线性模型。通过试验验证了所提神经网络模型能够以较高的精度逼近给定的实际数据。论文在迟滞建模方面有着清晰的数学表达形式，原理简单易懂。但是该方法只是针对Preisach迟滞非线性特性进行建模，对其它类型的迟滞非线性特性适用性缺乏研究。同时，将所建模型用于控制方案设计，可作为今后的研究课题。

关键词：迟滞非线性 Preisach backlash 描述函数叠加神经网络

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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 monitoring and diagnosis.

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

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Mesh stiffness calculation and vibration analysis of the spur gear pair with tooth crack,considering the misalignment between the base and root circles

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International Journal of Mechanical System Dynamics 2021年第1期1卷 143-156页

作者： Jingyu Hou Shaopu Yang Qiang Li Yongqiang Liu Jiujian Wang School of Mechanical Electronic and Control EngineeringBeijing Jiaotong UniversityBeijingChina State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures Shijiazhuang Tiedao UniversityShijiazhuangChina School of Mechanical Engineering Shijiazhuang Tiedao UniversityShijiazhuangChina State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body Hunan UniversityChangshaChina

An improved variable cross‐section cantilever beam model for evaluating the time‐varying mesh stiffness(TVMS)of the perfect gear tooth is developed in which the tooth number of driving gear is less than 42 and that of driven is more than 42.The TVMS obtained by the proposed method is compared with the result without considering the misalignment between the base circle and gear root.Four types of root crack models and changes inTVMS of 13‐crack levels are presented.The fault vibration characteristic of a single‐stage spur gear reducer with root crack is ana-lyzed and the correctness is qualitatively verified by the vibration signals of an experimental gearbox with crack or missing failure.The results presented in this paper are of great significance for a deep understanding of the possible causes of vibration and noise of gears and provide a theoretical foundation for the fault diagnosis of the gearbox.

关键词： backlash gear potential energy method time‐varying mesh stiffness(TVMS) tooth crack

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A Simplified Formulation to Estimate Influence of Gearbox Parameters on the Rattle Noise

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Sound & Vibration 2019年第2期53卷 38-49页

作者： Jidong Zhang Wentao Sui Jaspreet Dhupia School of Mechanical and Aerospace Engineering Nanyang Technological UniversitySingapore639798Singapore School of Mechanical Engineering Shandong University of TechnologyZibo255000China Department of Mechanical Engineering University of AucklandAuckland1010New Zealand

Occurrence of gear rattle in transmission systems can result in severe vibration and noise,which in applications such as automobiles is an important source of user discomfort.As a result,the reduction of the rattling noise has attracted lot of concerns.The rattling noise level is affected by several gearbox parameters,an understanding of which is essential to prevent the expensive design modifications at later stages of product development.To develop such understanding at the gearbox design stage,this paper analytically evaluates the gear parameters’effect on the root mean square of the wheel gear acceleration under idling condition,which is known to be linearly correlated to the rattling noise level.Therefore,this evaluation allows for an investigation of the gear parameters’influence on the rattling noise as well.This method is then verified by comparing the analytical results with the simulation results from a dynamic model built in SIMPACK as well as previously published experimental results.Thus,the proposed analytical evaluation method can optimize the gearbox specifications at the design stage to reduce the gear rattle noise level.

关键词： Rattle noise gear parameter analytical evaluation backlash dynamic model

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Nonsingular Terminal Sliding Mode Control for PMSM Servo System Based on backlash Compensation and High-order Sliding Mode Observer

Nonsingular Terminal Sliding Mode Control for PMSM Servo Sys...

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第32届中国控制与决策会议

作者： Jianwei Gui Lu Zhang Shihua Li Xiangyu Wang School of Automation Southeast University Key Laboratory of Measurement and Control of Complex Systems of Engineering Ministry of Education

In this paper,the permanent magnet synchronous motor（PMSM） servo system with backlash is studied.Since the mechanical transmission of the servo system uses gears,screw rods,on the one hand,the proper backlash can ensure the normal operation of the transmission mechanism;on the other hand,the existence of backlash nonlinearity will reduce the rigidity of the transmission mechanism,affect the tracking performance of the system,and even lead to mechanical resonance.In order to eliminate the influence of the backlash nonlinearity,the modeling and identification of the backlash nonlinearity are introduced,and the influence of the backlash is compensated in the regulator.In addition,in order to reject the possible model deviation and uncertain interference,reduce steady states fluctuations,a high-order sliding mode observer（HOSMO） based nonsingular terminal sliding mode control（NTSMC） is designed.After simulation verification,the compound controller proposed in this paper can effectively reduce the influence of the backlash nonlinearity and improve the position tracking performance of the system.

关键词： Permanent Magnet Synchronous Motor（PMSM） Servo System backlash Nonsingular Terminal Sliding Mode Control（NTSMC） High-order Sliding Mode Observer（HOSMO）

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Predictive Control of Non-minimum Phase Motor with backlash in an Earth Station Antenna

Predictive Control of Non-minimum Phase Motor with Backlash ...

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第25届中国控制会议

作者： Mohammadzaman Iman Khaki Sedigh Ali Nasirian Mehrzad Faculty of Electrical Engineering Malek Ashtar University of Technology TehranIran Faculty of Electrical Engineering K．N．Toosi University of Technology TehranIran Faculty of Electrical Engineering K．N．Toosi University of Technology TehranIran

＜正＞In this paper, Generalized Predictive Control （GPC） algorithm is implemented to control an earth station antenna with a non-minimum phase motor. Nonlinear term in motors caused by gearbox or other parts is modeled by a backlash block. Simulation results show the effectiveness of GPC method for robust control in the presence of backlash nonlinearity without a priori knowledge about upper and lower bounds of backlash. Also, adaptation mechanism as a self tuning predictive control is used to conquer environment changing.

关键词： Generalized Predictive Control Non-minimum Phase Motor backlash Earth Station Antenna

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Method for backlash and Load Distribution among Pins Determination of Trochoid Transmission with Account Machining Tolerances

Method for Backlash and Load Distribution among Pins Determi...

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第十一届IFTOMM世界大会

作者： Dmitry O. Teterukov Institute of Machine Reliability National Academy of Sciences of Belarus Minsk 220072Belarus

＜正＞In the paper the clear mathematical models of cycloidal speed reducer with account machining tolerances, methods for gap and contact force distribution determination and computer-aided modeling results on these approach basis are presented. The simple practical design equation for backlash calculation, expressing relationship between drive parameters （eccentricity, gear ratio, transmission angle）, machining tolerance and backlash has been developed.

关键词： Cycloid drive Machining tolerance backlash

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