A novel robust position estimator for self-sensing magnetic levitation systems based on least squares identification

In this work a novel method is introduced for the estimation of the position of a self-sensing magnetic levitation system, based on a least squares identification strategy. In the first step, a detailed mathematical model of the magnetic levitation system is derived and the properties of this system are analyzed for the case of a pulse-width modulated control. Based on this model, an estimation algorithm for the inductance of the magnetic levitation system is introduced. In classical position estimation schemes known form the literature large estimation errors are typically induced by a deviation of the electric resistance from its nominal value or by a fast motion of the levitated object. In this work it is shown that these errors can be exactly compensated by means of a suitable estimation strategy. Furthermore, it is outlined that the chosen structure of the estimation scheme allows for a very efficient implementation in real-time hardware. Afterwards, the design of a cascaded position controller for the magnetic levitation system is briefly summarized. Finally, the excellent quality and the high robustness of the proposed position estimator is demonstrated by means of simulation studies and measurement results on a test bench.     

Self-sensing for electromagnetic actuators. Part I: A coupled reluctance network model approach

A self-sensing arrangement in active magnetic bearings (AMBs) comprises a single electromagnetic transducer to realize the actuation and sensing functions concurrently. Minimizing the number of sensing devices and associated interfacing directly reduces possible failure points, system costs, and system complexity. Currently, self-sensing performance is degraded due to problems such as magnetic cross-coupling, eddy currents, saturation, and high losses. This first paper in a two part series presents an integrated model for self-sensing of an 8-pole heteropolar magnetic bearing. The proposed self-sensing approach addresses mechanisms that contribute to modelling error and uncertainty by using several techniques in an integrated structure. A coupled reluctance network model (RNM) is developed which models the coil impedance at the switching frequency. The accuracy of the model is improved by incorporating terms for air gap fringing, complex permeability, and magnetic material nonlinearity. The RNM is verified and refined through a process of iteration using finite element method (FEM) results and experimental AMB measurements. The results demonstrate that a RNM with only 40 nodes can achieve high levels of accuracy when compared to an 80 000 node FEM analysis.In Part II of the series, the refined RNM is incorporated into a multiple input multiple output (MIMO) parameter estimation self-sensing scheme.     

磁悬浮控制系统工程设计方法研究

磁悬浮装置是典型的非线性系统,其模型随悬浮对象的变化而显著变化。控制器设计的复杂性和非通用性制约了磁悬浮的广泛应用。本文致力于探讨一种简单的工程设计方法,其目的是在没有受控对象的精确数学模型和负载不明确的情况下,根据简单实验的数据即可设计控制器参数。文中提出根据电流变化率设计控制器参数的方法,并以一个一自由度磁悬浮装置作为实验对象,对所提出的设计方法进行了验证,得到满意的实验结果。     

On disturbance rejection in magnetic levitation

Magnetic levitation systems belong to an important and challenging class of control engineering problems with nonlinear uncertain dynamics, multiple disturbances and large sensor noise. To obtain a simple and practical solution that does not depends on the exact model information, a time-varying active disturbance rejection solution is proposed and validated in both numerical and experimental results. The proposed method is confirmed with rigorous analysis of transient performance and noise attenuation. Moreover, the proposed solution is tested in a magnetic levitation ball system with disturbances and measurement noise. The results show that the proposed solution is effective and practical.     

基于变量梯度法的磁悬浮控制系统的状态稳定性

磁悬浮系统是个典型的非线性系统,将非线性系统进行线性化后设计磁悬浮控制器,可以保证系统在平衡点附近稳定,但是当存在较大的干扰时,系统有可能失去稳定.本文分析单支点悬浮系统的稳定性,运用变量梯度法构造李雅普诺夫函数,推导出系统相对于平衡点的状态稳定保守区间,给出了系统的一个抗干扰程度,当磁悬浮系统受到较大干扰而偏离这一区间时,就应采取必要的自适应控制措施.最后用试验验证了这种控制方案的可行性.     

无轴承扰动补偿悬浮系统的稳定性分析与验证

目前, 无轴承磁悬浮系统多采用PID等经典控制策略, 然而由于外界扰动、参数摄动等诸多原因, 难以实现高性能的悬浮控制. 本文针对上述问题, 通过在传统PID悬浮控制系统中增加扩张状态观测器, 对悬浮力扰动进行实时补偿, 从而建立基于扩张状态观测器的无轴承悬浮控制系统. 其中, 根据扩张状态观测器对综合扰动进行观测的基本原理, 构建了系统数学模型, 并对其稳定性进行了分析. 在此基础上, 对观测器参数调节的选取原则和稳定域的参考范围进行了理论分析, 从而提出了一套无轴承悬浮控制系统参数整定方案. 此外, 本文还结合模型中主要参数的物理意义, 进一步完善了非线性扩张状态观测器参数的设定原则. 最后, 通过仿真验证了扩张状态观测器对无轴承悬浮系统扰动抑制的作用, 以及所述参数整定方案的正确性.     

Reduced-order Generalized Proportional Integral Observer Based Continuous Dynamic Sliding Mode Control for Magnetic Levitation System with Time-varying Disturbances

In order to reduce the influence of time-varying disturbances for magnetic levitation system, we propose a reduced-order generalized proportional integral observer (RGPIO) based continuous dynamic sliding mode control scheme for magnetic levitation system in this paper. Unlike the popular extended state observer (ESO), it could deal with constant or slowing varying disturbances from theoretical point of view, the reduced-order generalized proportional integral observer (RGPIO) is designed to estimate the time-varying disturbances and system states, then the dynamic sliding mode surface is developed and deduce a continuous sliding mode controller (CSMC) for magnetic levitation system. Compared with ESO based continuous sliding mode controller, the proposed method not only ensures the position tracking accuracy, but also obtain better time-varying disturbance reject ability. Simulation and experimental results are also given to verify the effectiveness.

     

Improved adaptive fuzzy backstepping control of a magnetic levitation system based on Symbiotic Organism Search

Magnetic levitation systems have become very important in many applications. Due to their instability and high nonlinearity, such systems pose a challenge to many researchers attempting to design high-performance and robust tracking control. This paper proposes an improved adaptive fuzzy backstepping control for systems with uncertain input nonlinear function (uncertain parameters and structure), and applies it to a magnetic levitation system, which is a typical representative of such systems. An adaptive fuzzy system is used to approximate unknown, partially known or uncertain input nonlinear functions of a magnetic levitation system. An adaptation law is obtained based on Ljapunov analysis in order to guarantee closed-loop stability and good tracking performance. Initial adaptive and control parameters have been initialized with Symbiotic Organism Search optimization algorithm, due to strong non-linearity and instability of the magnetic levitation system. The theoretical background of the proposed control method is verified with a simulation study and implementation on a laboratory experimental application.     

Direct decentralized neural control for nonlinear MIMO magnetic levitation system

A direct modified Elman neural networks (MENNs)-based decentralized controller is proposed to control the magnets of a nonlinear and unstable multi-input multi-output (MIMO) levitation system for the tracking of reference trajectories. First, the operating principles of a magnetic levitation system with two moving magnets are introduced. Then, due to the exact dynamic model of the MIMO magnetic levitation system is not clear, two MENNs are combined to be a direct MENN-based decentralized controller to deal with the highly nonlinear and unstable MIMO magnetic levitation system. Moreover, the connective weights of the MENNs are trained online by back-propagation (BP) methodology and the convergence analysis of the tracking error using discrete-type Lyapunov function is provided. Based on the direct and decentralized concepts, the computational burden is reduced and the controller design is simplified. Furthermore, the experimental results show that the proposed control scheme can control the magnets to track various periodic reference trajectories simultaneously in different operating conditions effectively.     

A robust optimal sliding‐mode control approach for magnetic levitation systems

This paper presents a robust optimal sliding‐mode control approach for position tracking of a magnetic levitation system. First, a linear model that represents the nonlinear dynamics of the magnetic levitation system is derived by the feedback linearization technique. Then, the robust optimal sliding‐mode control developed from the linear model is proposed. In the proposed control scheme, the integral sliding‐mode control with robust optimal approach is developed to achieve the features of high performance in position tracking response and robustness to the matched and unmatched uncertainties. Simulation and experimental results from the computer‐controlled magnetic levitation system are illustrated to show the validity of the proposed control approach for practical applications. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

磁悬浮球系统的自适应控制器设计

本文以磁悬浮球系统为研究对象,基于该系统的线性化模型,通过Backstepping设计方法设计了一类自适应控制器,所设计的控制器具有结构简单易于实现,控制输入易于得到等优点,仿真实验验证了该控制器的有效性.     

Design of a Novel Fuzzy Sliding-Mode Control for Magnetic Ball Levitation System

This paper presents the design of a novel fuzzy sliding-mode control (NFSMC) for the magnetic ball levitation system. At first, we examine the nonlinear dynamic models of the magnetic ball system, where the singular perturbation method is used. Next, we address the design schemes of sliding mode control (SMC) and traditional fuzzy sliding-mode control (FSMC), where two kinds of FSMCs are introduced. Then we provide the design steps of the NFSMC, where the Lyapunov stability analysis is also given. Finally, a magnetic ball levitation system is used to illustrate the effectiveness of the proposed controller.     

Robust Dynamic Sliding-Mode Control Using Adaptive RENN for Magnetic Levitation System

In this paper, a robust dynamic sliding mode control system (RDSMC) using a recurrent Elman neural network (RENN) is proposed to control the position of a levitated object of a magnetic levitation system considering the uncertainties. First, a dynamic model of the magnetic levitation system is derived. Then, a proportional–integral–derivative (PID)-type sliding-mode control system (SMC) is adopted for tracking of the reference trajectories. Moreover, a new PID-type dynamic sliding-mode control system (DSMC) is proposed to reduce the chattering phenomenon. However, due to the hardware being limited and the uncertainty bound being unknown of the switching function for the DSMC, an RDSMC is proposed to improve the control performance and further increase the robustness of the magnetic levitation system. In the RDSMC, an RENN estimator is used to estimate an unknown nonlinear function of lumped uncertainty online and replace the switching function in the hitting control of the DSMC directly. The adaptive learning algorithms that trained the parameters of the RENN online are derived using Lyapunov stability theorem. Furthermore, a robust compensator is proposed to confront the uncertainties including approximation error, optimal parameter vectors, and higher order terms in Taylor series. Finally, some experimental results of tracking the various periodic trajectories demonstrate the validity of the proposed RDSMC for practical applications.      

磁悬浮球系统的神经网络辨识及变结构控制

磁悬浮球系统是一个典型的非线性的不稳定的系统,基于对其建模的复杂性和不准确性,文章利用神经网络能逼近任意非线性函数这一特性,对磁悬浮球系统进行辨识;再根据滑模变结构控制原理设计了磁悬浮球系统的变结构控制器,利用MATLAB对系统进行建模仿真,仿真结果表明,RBF网络能很好地逼近本磁悬浮球系统;滑模变结构控制对于此非线性系统有较好的控制效果,小球能很快地悬浮在平衡位置,该控制系统具有较好的稳态特性和抗干扰性.     

磁悬浮球旋转控制系统

磁悬浮球是磁悬浮列车，磁悬浮轴承，磁悬浮飞轮储能系统，磁悬浮发射等一切磁悬浮研究的基础。同时也是闭环和非线性控制研究很好的平台。本文在分析磁悬浮球控制原理的基础上得出其悬浮、旋转数学模型，给出了使其悬浮、旋转的控制方案和仿真、实验结果。     

磁悬浮球系统的变结构控制

磁悬浮球系统是一种典型的非线性、不稳定性系统。本文根据变结构控制理论,设计了一个动态变结构控制器,该控制器能够保证磁悬浮球系统的各个状态逐渐趋近于设计值。同时利用Modelica对磁悬浮球系统进行建模仿真,仿真结果表明磁悬浮球的变结构控制系统具有很好的动态性能和很强的鲁棒性。     

面向磁悬浮视触觉交互的多速率系统框架

非接触式磁悬浮视触觉交互克服了机械式交互的固有摩擦,具有广阔应用前景,但存在交互过程中虚拟工具穿透物体、图形渲染与触觉渲染速率不一致等问题.针对上述问题,提出面向磁悬浮视触觉交互的多速率系统框架,通过扩展三自由度(3-DOF)单射线触觉渲染方法,利用多射线对虚拟工具进行建模,避免工具穿透,实现六自由度(6-DOF)触觉...     

多模型切换控制方法在磁悬浮系统中的应用

针对磁悬浮装置的非线性及对实时性要求高的特点,对磁悬浮装置构造线性二次型调节器(Linear Quadratic regulator-LQR)并采用多模型切换的控制方法对磁悬浮装置进行实时控制,取得了较好的控制效果.讨论了ARX模型的结构、原理、模型阶次的选择和辫识方法等问题,介绍了状态空间的创建方法和LQR控制器的构...     

基于等价输入干扰滑模观测器的磁悬浮球系统模型预测控制

本文针对系统不确定性和外部干扰引起的磁悬浮球系统控制性能下降的问题,提出了一种基于等价输入干扰滑模观测器的模型预测控制(MPC+EIDSMO)方法.首先将原系统转化为EID系统,采用等价输入干扰滑模观测器对EID系统状态变量及等价输入干扰进行估计;然后基于状态估计值设计模型预测控制器,并将等价输入干扰估计值以前馈的方式...     

受控磁悬浮系统非线性随机响应分析

讨论了非线性磁悬浮控制系统随机振动响应预测问题．基于等效非线性微分方程方法,从理论上对非线性磁悬浮控制系统的随机响应进行了深入分析,建立了此高维系统非线性模型;根据中心流形理论对系统进行约化、降维,给出了此系统响应的近似解析解．这对此系统实现进一步稳定控制提供了有效的理论依据．