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。     

分片线性逼近及其在预测控制中的应用

介绍了分片线性逼近的相关理论并将其应用于预测控制。自适应链接超平面模型(AHH)是一种具有应用潜力的分片线性模型。采用AHH模型对被控制系统进行建模,由于AHH模型的辨识算法是自适应的,整个过程简单易实现。随后,在线解一个开环优化问题得到最优控制序列并应用滚动优化控制策略对系统进行控制。并且证明此开环优化问题实质上可以看成一系列子问题,每个子问题都是二次规划问题,因此,全局最优解的存在性得以保证。对于实际问题,提出了一个下降算法用以搜索局部最优解,仿真结果表明,基于AHH模型的预测控制具有一定的应用前景。     

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...     

Predictive Functional Control Based on Fuzzy Model: Comparison with Linear Predictive Functional Control and PID Control

The implementation of the fuzzy predictive functional control (FPFC) on the magnetic suspension system is presented in the paper. The magnetic suspension system was in our case the pilot plant for magnetic bearing and is an open-loop unstable process, therefore a lead compensator was used to stabilize it. The high quality control requirements were a-periodical step response and zero steady-state error. Adding the integrator to a feedback causes overshoot. The solution to the problem was cascade control with fuzzy predictive functional controller in the outer loop. To cope with the unknown model parameters and the nonlinear nature of the magnetic system, a fuzzy identification based on FNARX model was used. After successful validation the obtained fuzzy model was used for controller design. The FPFC is compared with a cascade linear predictive functional control (PFC) and PID control. The results we obtained with the FPFC are very promising and hardly comparable with conventional control techniques.     

Valve Position‐based Control at Engine Key‐on of an Electro‐mechanical Valve Actuator for Camless Engines: A Robust Controller Tuning Via Bifurcation Analysis

Electro‐mechanical valve actuators (EMVA) formed by two opposed electromagnets and two balanced springs are appealing solutions to implement advanced combustion concepts for camless engines. A crucial control problem for this valve actuator regards the first valve lift manoeuvre (termed 'first catching') to be rapidly performed after each insertion of the engine ignition key, when the EMVA rests at middle position where electromagnets offer low control authority. The control problem is challenging due to system nonlinear behavior. Mathematically, the EMVA system can be assumed to be a spring‐mass impacting system affected by a non‐smooth friction force and a dynamic saturated magnetic force. In this work an effective valve position‐based first catching control strategy is proposed to control the strongly nonlinear system. Bifurcation analysis and parameter space simulations are used to study the closed‐loop system behavior and to tune the controller gains as well. The effectiveness of the control approach is validated through numerical simulations of a highly predictive dynamic model of the valve actuator developed by authors in a previous work.     

基于模糊PID的磁悬浮球控制系统研究

针对磁悬浮球系统的本质不稳定性,设计模糊PID算法实现系统的稳定控制,并使之动态性能及稳态性能满足要求;文中首先分析了磁悬浮球系统的基本原理,并进行力学分析,建立系统的数学模型,并对其中的非线性部分进行了平衡点处的线性化,而后采用用PID控制设计,PID可以实现系统的稳定控制,且控制精度较高,但对于动态性能的改善不足,且当模型中的参数改变时,PID参数的适应性较差;因此在PID参数的基础上,采用模糊PID控制,使得系统既可以满足三性要求,又可以使其具有参数变化的适应能力。     

无轴承同步磁阻电机逆系统解耦控制仿真研究

研究无轴承同步磁阻电机稳定性控制问题,由于无轴承同步磁阻电机是一个强耦合的非线性系统,为实现负载条件下的稳定悬浮运行,需解除电机转矩和径向悬浮力等多变量之间的耦合关系。针对前馈补偿解耦的缺陷,给出了无轴承同步磁阻电机包含转矩控制和悬浮力控制的统一数学模型,证明电机逆系统存在,设计了一种通过非线性状态反馈的逆系统解耦控制方案,将复杂的无轴承同步磁阻电机系统解耦成两个转子径向位置二阶积分子系统和一个转速一阶积分子系统,并用PI和PID调节器分别对转子位置与转速进行综合设计。运用MATLAB软件对电机控制系统进行仿真。仿真结果证明,解耦控制方案的有效性,为电机系统优化设计提供了保证。     

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.     

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.     

Trajectory tracking for the magnetic ball levitation system via exact feedforward linearisation and GPI control

The output feedback control of the popular magnetic ball levitation system is addressed from a suitable combination of several complementary viewpoints. We use: first, recent developments on exact feedforward linearisation controllers for nonlinear flat systems to substantially reduce the linear feedback controller efforts through pre-compensation. Second, an on-line ball velocity estimation strategy is proposed by using a model-based integral reconstructor, which is a linear combination of iterated integrals of the input and the output of the system, thus avoiding the use of traditional observers or noisy derivative estimations. Finally, we use a generalised proportional integral (GPI) controller which compensates the errors in the integral reconstructor and further bestows the enhanced robustness on the closed-loop system via output tracking error iterated integration feedback. This methodology only requires the measurements of the position of the levitated ball and of the control input voltage. The proposed feedback regulation scheme is shown to locally guarantee an asymptotically exponentially stable behaviour of the controlled ball position and, definitely, allows for the possibilities of safely carrying out the rest-to-rest trajectory tracking tasks on the ball position. The proposed output feedback controller is actually implemented on a laboratory prototype with excellent experimental results for, both, stabilisation and trajectory tracking tasks.     

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     

基于双霍尔传感器的磁性小球悬浮控制系统研究

本文设计并实现了一种基于双线性霍尔传感器结构的磁性小球悬浮控制系统,在电磁驱动器底端及顶端中心位置各同向布置一个线性霍尔传感器,通过传感器信号调理电路,将两路传感器的输出信号作减法处理,消除了电磁驱动器磁场对传感器输出信号的影响。试验表明,磁性小球到电磁驱动器底端距离为16.46~42.46 mm时,调理电路输出电压值与磁性小球到电磁驱动器底端距离的负三次方成正比。基于PID控制策略,设计了一个磁性小球悬浮控制系统,选取合适的PID控制器参数,试验表明,系统的超调量和响应速度能够符合设计要求,磁性小球实现了在25 mm位置处的稳定磁悬浮,系统的位置控制精度达到±0.125 mm。     

磁悬浮系统的极点配置控制器设计研究

单自由度磁悬浮1球系统是多自由度磁悬浮控制研究基础,本文在分析磁悬浮系统构成及工作原理的基础上,建立了单自由度磁悬浮系统的数学模型,并将非线性模型进行了线性化。采用极点配置法设计了PI线圈电流控制器和PIV-前馈小球位置控制器,利用MATLAB／SIMULINK和RTX实时系统进行了实验,实验结果表明,小球可以稳定地悬浮在期望位置,并且具有一定的抗干扰能力。     

A multiple model approach for predictive control of nonlinear hybrid systems

This paper presents modeling and control of nonlinear hybrid systems using multiple linearized models. Each linearized model is a local representation of all locations of the hybrid system. These models are then combined using Bayes theorem to describe the nonlinear hybrid system. The multiple models, which consist of continuous as well as discrete variables, are used for synthesis of a model predictive control (MPC) law. The discrete-time equivalent of the model predicts the hybrid system behavior over the prediction horizon. The MPC formulation takes on a similar form as that used for control of a continuous variable system. Although implementation of the control law requires solution of an online mixed integer nonlinear program, the optimization problem has a fixed structure with certain computational advantages. We demonstrate performance and computational efficiency of the modeling and control scheme using simulations on a benchmark three-spherical tank system and a hydraulic process plant.     

A Novel Method Of Controller Design For Simultaneous Stabilization And Performance Improvement Of An Electromagnetic Levitation System

This paper describes design and implementation of a control philosophy for simultaneous stabilization and performance improvement of an electromagnetic levitation system. An electromagnetic levitation system is an inherently unstable and strongly nonlinear system. To determine the overall closed loop stability for such a system, cascade lead‐lag compensation has mostly been reported [1,2]. However, a single lead controller can not satisfy both stability and performance for such unstable systems [3]. Performance enhancement to satisfy the conflicting requirements of fast response with almost zero overshoot and zero steady state error has been successfully achieved by using a two loop controller configuration. The lead controller in the inner loop is designed to ensure stability while the outer loop PI controller is designed for performance enhancement. This approach decouples the twin requirements of stabilization (by the inner loop) and performance achievement (by the outer PI loop). The outermost PI controller has been designed using the ‘Approximate Model Matching’ technique [4]. The proposed control strategy has been implemented and the experimentation has been demonstrated successfully. Different experimental results have been included for verification.     

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。     

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.     

Limit cycle generation for a class of non-linear systems with jumps using a low dimensional predictive control

In this paper, it is shown that using a low dimensional non-linear predictive control scheme, provably stable limit cycles can be obtained for open-loop non-linear systems with unstable equilibrium point. A particular case, where the limit cycle may be reduced to a single point in the state space, can be obtained, which corresponds to asymptotic stabilization. The system may present hybrid nature in the sense that discontinuities (jump phenomena) on the state evolution may be handled. The proposed feedback scheme holds for classical jump-free systems as a particular case. The proposed strategy is illustrated through two examples: a jump-free system (the ball and beam) and a non-linear hybrid dynamical system including state jumps (the modified impulsive Lorenz chaotic system).     

基于LabVIEW的磁悬浮球系统PID控制算法研究

磁悬浮球系统是一个实时控制系统,利用参数易于修改和代码便于工程应用特点的NI LabVIEW平台,对磁悬浮球系统的比例-积分-微分(PID)控制算法进行仿真。本文为系统设计了模拟PID控制算法、变参数PID控制算法;同时为了能获得更好的控制性能以及更多先进算法的支持,利用组件对象模型(COM)技术引入MATLAB与LabVIEW无缝集成,成功设计了基本模糊控制和模糊PID控制算法。仿真结果表明,模糊PID控制算法能更好的实现对磁悬浮球系统的控制;同时,COM技术的应用使得LabVIEW程序得到MATLAB强大的算法支持,大大缩短程序编写时间、显著提高应用程序的性能、并使得算法更易于实际工程应用。