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     

Adaptive control based on fast online algebraic identification and GPI control for magnetic levitation systems with time-varying input gain

This paper considers the position tracking problem of a voltage-controlled magnetic levitation system (MLS) in the presence of modelling errors caused by uncertainties in the system’s physical parameters. An adaptive control based on fast online algebraic parameter estimation and generalised proportional integral (GPI) output feedback control is considered as a control scheme candidate. The GPI controller guarantees an asymptotically exponentially stable behaviour of the controlled ball position and the possibilities of carrying out rest-to-rest trajectory tracking tasks. The nature of the control input gain in an MLS is that of a state-dependent time-varying gain, reflecting the nonlinear character of the magnetic force with regard to the distance and the properties of the metallic ball. The system gain has therefore been locally approximated using a periodically updated time polynomial function (of second degree), where the coefficients of the polynomial are estimated during a very short period of time. This estimation is achieved using the recently introduced algebraic online parameter estimation approach. The stability of the closed-loop system is demonstrated under the assumption that no external factors cause changes in the parameter during the time interval in which the stability is analysed. Finally, experimental results are presented for the controlled MLS demonstrating the excellent stabilisation and position tracking performance of the control system designed in the presence of significant nonlinearities and uncertainties of the underlying system.     

A modeling and control approach to magnetic levitation system based on state-dependent ARX model

Magnetic levitation (Maglev) systems are usually strongly nonlinear, open-loop unstable and fast responding. In order to control the position of the steel ball in a Maglev system, a data-driven modeling approach and control strategy is presented in this paper. A state-dependent AutoRegressive with eXogenous input (SD-ARX) model is built to represent the dynamic behavior between the current of electromagnetic coil and the position of the ball. State-dependent functional coefficients of the SD-ARX model are approximated by Gaussian radial basis function (RBF) neural networks. The model parameters are identified offline by applying the structured nonlinear parameter optimization method (SNPOM). Based on the model, a predictive controller is designed to stabilize the magnetic levitation ball to a given position or to make it track a desired trajectory. The real-time control results of the proposed approach and the comparisons with other two approaches are given, which demonstrate that the modeling and control method presented in this paper are very effective and superior in controlling the fast-responding, strongly nonlinear and open-loop unstable system. This paper gives the real experimental evidence that the RBF-ARX model is capable of not only globally, but also locally capturing and quantifying a nonlinear and fast-response system's behavior, and the model-based predictive control strategy is able to work quite well in a wide working-range of the nonlinear system.     

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 novel levitation control strategy for a class of redundant actuation maglev system

In most maglev (magnetic levitation) systems, redundant electromagnetic actuators are usually used to increase the stability and robustness of the levitation motion. However, the obvious interactions generate between the redundant actuators and other general electromagnetic actuators. In this paper, a new and efficient redundant levitation control strategy is developed to overcome the interactions in this maglev system. In the strategy, some separate general controllers are designed for all general actuators, and then some special controllers are used to real-time track the electromagnetic forces of all general actuators, and accordingly they create control signal for the redundant actuators to counteract the interactions among general actuators and redundant actuators. To further illustrate the strategy, a novel redundant actuation maglev system is then demonstrated, and a simplified expression of the redundant control strategy is investigated for the maglev system. The experimental results show that the redundant levitation controller successfully removes the interactions between redundant actuator and general actuators, and the redundant levitation controller maintains good robustness under disturbance.     

基于MATLAR的磁悬浮球系统PID控制器设计与实现

介绍了磁悬浮球系统的结构和工作原理,建立了磁悬浮系统的数学模型并进行线性化处理;设计PID控制器,在Simulink环境下搭建控制系统的模型进行仿真研究,并在固高GML1001系列磁悬浮装置上进行实时控制实验。实验结果表明,采用PID控制,能使钢球快速地悬浮在期望位置,并且有一定的抗干扰能力。     

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.     

Robust nonlinear disturbance suppression of a magnetic levitation system

In this paper the problem of noise suppression for a magnetic levitation system is addressed. The problem is cast as a nonlinear regulation problem and an internal model-based regulator able to offset the noise in spite of the presence of unknown parameters affecting the model of the system is designed. The controller is designed using nested saturation functions and is able to provide a global region of attraction. Simulation results confirm the effectiveness of the design.     

Nonlinear model predictive control of a magnetic levitation system

The paper presents a fast nonlinear model predictive control (MPC) scheme for a magnetic levitation system. A nonlinear dynamical model of the levitation system is derived that additionally captures the inductor current dynamics of the electromagnet in order to achieve a high MPC performance both for stabilization and fast setpoint changes of the levitating mass. The optimization algorithm underlying the MPC scheme accounts for control constraints and allows for a time and memory efficient computation of the single iteration. The overall control performance of the levitation system as well as the low computational costs of the MPC scheme is shown both in simulations and experiments with a sampling frequency of 700 Hz on a standard dSPACE hardware.     

Decomposition-based recursive least squares identification methods for multivariate pseudo-linear systems using the multi-innovation

This paper studies the parameter estimation algorithms of multivariate pseudo-linear autoregressive systems. A decomposition-based recursive generalised least squares algorithm is deduced for estimating the system parameters by decomposing the multivariate pseudo-linear autoregressive system into two subsystems. In order to further improve the parameter accuracy, a decomposition based multi-innovation recursive generalised least squares algorithm is developed by means of the multi-innovation theory. The simulation results confirm that these two algorithms are effective.     

Data filtering based least squares iterative algorithm for parameter identification of output error autoregressive systems

This letter derives a data filtering based least squares iterative identification algorithm for output error autoregressive systems. The basic idea is to use the data filtering technique to transform the original identification model to an equation error model and to estimate the parameters of this model. The proposed algorithm is more efficient and can produce more accurate parameter estimation than the existing least squares iterative algorithm.     

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．     

On parameter convergence in least squares identification and adaptive control

Least squares estimation is appealing in performance and robustness improvements of adaptive control. A strict condition termed persistent excitation (PE) needs to be satisfied to achieve parameter convergence in least squares estimation. This paper proposes a least squares identification and adaptive control strategy to achieve parameter convergence without the PE condition. A modified modeling error that utilizes online historical data together with instant data is constructed as additional feedback to update parameter estimates, and an integral transformation is introduced to avoid the time derivation of plant states in the modified modeling error. On the basis of these results, a regressor filtering–free least squares estimation law is proposed to guarantee exponential parameter convergence by an interval excitation condition, which is much weaker than the PE condition. And then, an identification‐based indirect adaptive control law is proposed to establish exponential stability of the closed‐loop system under the interval excitation condition. Illustrative results considering both identification and control problems have verified the effectiveness and superiority of the proposed approach.     

基于CAN总线磁悬浮球系统分布式控制设计与实现

选用国际上应用最广泛的现场总线之一—CAN总线,对磁悬浮球控制系统进行分布式控制,设计并实现了CAN总线磁悬浮球控制系统。首先,对磁悬浮球控制系统进行了详细分析,确定了系统的总线型网络拓扑结构。在该网络结构下,进行软硬件设计。硬件设计工作主要是设计一个通用CAN节点的设计,使其能够完成模拟量的精确快速采样、高精度输出以及开关量的控制三大功能。软件设计包括两部分:CAN节点中基于ARM的软件设计和PC端监控软件的设计。     

一种新的ARX模型在磁悬浮系统建模中的应用

采用一种新的ARX模型（RBF-ARX模型）对磁悬浮系统进行离线建模,讨论了RBF-ARX模型的原理、结构的选取、模型参数辨识和RBF参数优化等问题。文章分别采用不同的序列作为状态变量,分别建立RBF-ARX模型,并分析了各模型的性能及可靠性。模型的预测输出和仿真结果,证实了RBF-ARX模型在非线性系统建模和辨识中的有效性。通过与ARX模型的比较,证明了RBF-ARX模型在非线性系统建模中效果更好。     

基于辅助模型的递推增广最小二乘辨识方法

针对有色噪声干扰的输出误差滑动平均系统, 将辅助模型与递推增广最小二乘算法相结合: 用辅助模型的输出代替辨识模型信息向量中的未知真实输出项, 用估计残差代替信息向量中的不可测噪声项, 从而提出了基于辅助模型的递推增广最小二乘辨识方法. 为了展示所提方法的特点, 文中还给出了经过模型变换的递推增广最小二乘算法. 理论分析和仿真研究表明, 提出的方法原理简单、计算量小, 可以给出高精度参数估计, 且能够用于在线辨识.     

Control of a magnetic levitation system with communication imperfections: A model-based coupling approach

This work presents a control strategy to control a magnetic levitation system under the influence of coupling imperfections (disturbances). To overcome problems arising whenever the interconnections between plant and controller have a non-negligible influence on the control-loop behavior a so-called model-based coupling approach is used. The main idea of this coupling approach is to use prediction schemes based on recursively identified plant and controller models which compensate for performance degradation due to coupling imperfections. Coupling failures such as time-delays, data-losses and noise drastically influence the control-loop performance. Especially when systems in form of real hardware (real-time systems) are present such disturbances have to be handled adequately. To demonstrate the effectiveness of the model-based coupling approach, a control-loop of a magnetic levitation system is analyzed in simulation as well as in real world laboratory setup (HiL simulation). Furthermore a first insight into the stability analysis of closed-loop systems including the model-based coupling technique is performed for a simplified configuration.     

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...     

A robust least squares based approach to min‐max model predictive control

This article deals with the model predictive control (MPC) of linear, time‐invariant discrete‐time polytopic (LTIDP) systems. The 2‐fold aim is to simplify the treatment of complex issues like stability and feasibility analysis of MPC in the presence of parametric uncertainty as well as to reduce the complexity of the relative optimization procedure. The new approach is based on a two degrees of freedom (2DOF) control scheme, where the output r(k) of the feedforward input estimator (IE) is used as input forcing the closed‐loop system ∑_f. ∑_f is the feedback connection of an LTIDP plant ∑_p with an LTI feedback controller ∑_g. Both cases of plants with measurable and unmeasurable state are considered. The task of ∑_g is to guarantee the quadratic stability of ∑_f, as well as the fulfillment of hard constraints on some physical variables for any input r(k) satisfying an “a priori” determined admissibility condition. The input r(k) is computed by the feedforward IE through the on‐line minimization of a worst‐case finite‐horizon quadratic cost functional and is applied to ∑_f according to the usual receding horizon strategy. The on‐line constrained optimization problem is here simplified, reducing the number of the involved constraints and decision variables. This is obtained modeling r(k) as a B‐spline function, which is known to admit a parsimonious parametric representation. This allows us to reformulate the minimization of the worst‐case cost functional as a box‐constrained robust least squares estimation problem, which can be efficiently solved using second‐order cone programming.     

无轴承异步电机悬浮系统的非线性滤波器自适应逆控制

讨论了基于非线性自适应滤波器的无轴承异步电机(bearlngless induction motor,BIM)悬浮系统自适应逆解耦控制问题.利用非线性自适应滤波器,建立系统模型和逆模型.复制逆模型,将其串联在悬浮系统之前作为逆控制器,并采用改进的最小均方(least mean square,LMS)算法在线调整权值,从而实现转子的悬浮控制.相比于传统的控制方法,此方法不必依靠转矩系统来传递磁链信息,从而避免了各自的控制策略之间的相互制约问题.仿真结果验证了该方法的有效性,完成了系统模型和逆模型的建立,并且能够实现两自由度径向悬浮力之间解耦.