Neural model-based adaptive control for systems with unknown Preisach-type hysteresis

An adaptive control scheme is presented for systems with unknown hysteresis. In order to handle the case where the hysteresis output is unmeasurale, a novel model is firstly developed to describe the characteristic of hysteresis. This model is motivated by Preisach model but implemented by using neural networks (NN). The main advantage is that it is easily used for controller design. Then, the adaptive controller based on the proposed model is presented for a class of SISO nonlinear systems preceded by unknown hysteresis, which is estimated by the proposed model. The hws for model updating and the control hws for the neural adaptive controller are derived from Lyaptmov stability theorem, therefore the semi - global stability of the closed-loop system is guaranteed. At last, the simulation results are illuswated.     

Adaptive narrow band disturbance rejection applied to an active suspension—an internal model principle approach

This paper presents a methodology for feedback adaptive control of active vibration systems in the presence of time varying unknown narrow band disturbances. A direct adaptive control scheme based on the internal model principle and the use of the Youla-Kucera parametrization is proposed. This approach is comparatively evaluated with respect to an indirect adaptive control scheme based on the estimation of the disturbance model. The comparative evaluation is done in real time on an active suspension system.     

改进的内模跟踪控制对随机噪声抑制的研究与仿真

对于存在随机噪声和干扰的系统,传统的内模跟踪控制是无法解决这类问题的。将自适应滤波器引入到内模控制的结构中,很好地解决了内模控制在抑制随机噪声方面的不足。针对被控对象的模型和系统性能指标,同时考虑到系统的随机噪声设计自适应滤波器,从而构建自适应控制器。通过自适应控制器和基于内模原理设计的伺服补偿器对被控对象进行跟踪控制。提出的方法综合了内模控制和自适应滤波的优点,使控制系统达到满意的跟踪控制效果,对常规谐波扰动和随机噪声都有良好的抑制作用。仿真结果表明提出的设计方法能够实现系统的无静差跟踪,并且具有良好的抗噪性和稳定性。     

On the Control of Plants with Hysteresis: Overview and a Prandtl-Ishlinskii Hysteresis Based Control Approach

The development of control techniques to mitigate the effects of unknown hysteresis preceding with plants has recently re-attracted significant attention. In this paper, we first give a brief review of presently developed hysteresis models and hysteresis compensating control methods. Then, with the use of the Prandtl-Ishlinskii hysteresis model, we propose a robust adaptive control scheme. The novelty is that the model of hysteresis nonlinearities is firstly fused with the available control techniques without necessarily constructing a hysteresis inverse. The global stability of the adaptive system and tracking a desired trajectory to a certain precision are achieved. Simulations performed on a nonlinear system illustrate and clarify the approach.     

Adaptive backstepping‐based control design for uncertain nonlinear active suspension system with input delay

This paper addresses the control problem of adaptive backstepping control for a class of nonlinear active suspension systems considering the model uncertainties and actuator input delays and presents a novel adaptive backstepping‐based controller design method. Based on the established nonlinear active suspension model, a projector operator–based adaptive control law is first developed to estimate the uncertain sprung‐mass online, and then the desirable controller design and stability analysis are conducted by combining backstepping technique and Lyapunov stability theory, which can not only deal with the actuator input delay but also achieve better dynamics performances and safety constraints requirements of the closed‐loop control system. Furthermore, the relationship between the input delay and the state variables of this vehicle suspension system is derived to present a simple and effective method of calculating the critical input delay. Finally, a numerical simulation investigation is provided to illustrate the effectiveness of the proposed controller.     

Adaptation‐Enhanced Model‐Based Control with Charge Feedback for Piezo‐Actuated Stage

This paper proposes a new control design to compensate for the residual control error from charge feedback control. A part of the applied voltage is consumed by the hysteresis effect because of the nature of the piezoelectric material; moreover, this effect is difficult to overcome because it is rate dependent. This work utilizes a piezoelectric electromechanical model to propose a precompensation algorithm for a piezoelectric actuator. A nonlinear compensator can be used to treat both the hysteresis nonlinearity and the rate dependency of the system, and the adjustable parameters are specified through adaptive identification with only basic system information. The proposed design can position a piezoelectric stage with a magnifying mechanism within a few nanometers of a target, and the leftover hysteresis phenomenon is negligible.     

连续回滞系统的模型参考自适应控制

采用Stop和Play算子表示的Prandtl-Ishlinskii回滞模型描述回滞特性，该模型便于实现控制器的设计．考虑带有未知回滞驱动且以状态空间形式表示的连续时间线性动态系统，给出了模型参考白适应控制设计方案．控制策略保证闭环系统的全局稳定性和期望的跟踪精度，有效地抑制回滞产生的不精确和振荡现象．数值仿真结果表明了控制算法的有效性．     

Zero-error tracking control of uncertain nonlinear systems in the presence of actuator hysteresis

In this paper, the problem of adaptive tracking control is addressed for a class of nonlinear systems with unknown constant parameters and unknown actuator nonlinearity. The actuator nonlinearity is modelled as the backlash-like hysteresis, which is described by a differential model. The prior knowledge on the control gain sign is not required, and only the assumption on the reference signal is made. By combining the adaptive backstepping technique with the Nussbaum gain approach, an adaptive compensation controller design approach is developed. It is proved that the proposed control approach can guarantee that all the signals in the closed-loop system are bounded, and the tracking error can converge to zero asymptotically despite the presence of the actuator hysteresis. Two simulation examples are included to illustrate the effectiveness of the proposed approach.     

Constraint adaptive output regulation of output feedback systems with application to electrostatic torsional micromirror

This paper studies a constraint adaptive output regulation design for a class of nonlinear systems with an unknown exosystem by output feedback control. First, by introducing an internal model with some known design parameter, our concerned problem may be formulated as a specific regulation problem with output constraint. Then, the barrier Lyapunov function technique is further integrated to approach the problem. It is shown that such a constraint adaptive output regulation problem is solvable without constraint violation. In particular, the constructed regulator cannot only keep the boundedness of the closed‐loop system signals but also guarantees the parameter convergence for the unknown parameter vector in the exosystem. As an application, it is illustrated that our result is applicable in tracking the control of an electrostatic torsional micromirror with physical geometry constraint. Copyright © 2013 John Wiley & Sons, Ltd.     

Adaptive control of system involving complex hysteretic nonlinearities: a generalised Prandtl–Ishlinskii modelling approach

In this article an adaptive control approach is proposed for a class of nonlinear systems preceded by unknown hysteretic nonlinearities, which is described by a generalised Prandtl–Ishlinskii (P-I) model. The main feature is that the generalised P-I hysteresis model is counted in the controller design without constructing a hysteresis inverse. The developed controller guarantees the global stability of the system and tracking a desired trajectory to a certain precision is achieved. The effectiveness of the proposed control approach is demonstrated through simulation example.     

直接多模型自适应控制器设计——LMI方法

本文将线性矩阵不等式(LMI)方法引入直接多模型自适应控制, 将直接多模型控制器的 设计过程转化为求解线性矩阵不等式的可行解问题,同时给出在不同不确定参数范围内的多 个状态反馈控制器,并由此构成直接多模型自适应控制器．同时将直接多模型自适应控制推 广到多输入多输出被控对象的设定值跟踪问题,并给出稳定性分析结果．     

Robust adaptive control of a class of nonlinear systems including actuator hysteresis with Prandtl-Ishlinskii presentations

This paper deals with robust adaptive control of a class of nonlinear systems preceded by unknown hysteresis nonlinearities. By using a Prandtl-Ishlinskii model with play and stop operators, we attempt to fuse the model of hysteresis with the available control techniques without necessarily constructing a hysteresis inverse. A robust adaptive control scheme is therefore proposed. The global stability of the adaptive system and tracking a desired trajectory to a certain precision are achieved. Simulation results attained for a nonlinear system are presented to illustrate and further validate the effectiveness of the proposed approach.     

Adaptive regulation—Rejection of unknown multiple narrow band disturbances (a review on algorithms and applications)

The paper addresses the problem of attenuation (rejection) of unknown and time varying multiple narrow band disturbances without measuring them. In this context the disturbance model is unknown and time varying while the model of the plant is known (obtained by system identification) and almost invariant. This requires to use an adaptive feedback approach. The term “adaptive regulation” has been coined to characterize this control paradigm. Application domains include: mechanical and mechatronics systems, active vibration and noise suppression systems, some types of bio-chemical reactors.The paper reviews the various techniques proposed for solving this problem. It will focus on the presentation of the direct and indirect adaptive regulation strategies using the internal model principle and the Youla–Kucera parametrization which have been extensively used in applications.The paper also reviews a number of applications including: active suspension systems, active vibration control systems, active noise control, bio-chemical reactors, distributed flexible mechanical structures and Blu-ray disc drives. Real time results obtained on various applications will illustrate the methodology.     

Decentralized adaptive stabilization in the presence of unknown backlash-like hysteresis

Due to the difficulty of handling both hysteresis and interactions between subsystems, there is still no result available on decentralized stabilization of unknown interconnected systems with hysteresis, even though the problem is practical and important. In this paper, we provide solutions to this challenging problem by proposing two new schemes to design decentralized output feedback adaptive controllers using backstepping approach. For each subsystem, a general transfer function with arbitrary relative degree is considered. The interactions between subsystems are allowed to satisfy a nonlinear bound with certain structural conditions. In the first scheme, no knowledge is assumed on the bounds of unknown system parameters. In case that the uncertain parameters are inside known compact sets, we propose an alternative scheme where a projection operation is employed in the adaptive laws. In both schemes, the effects of the hysteresis and the effects due to interactions are taken into consideration in devising local control laws. It is shown that the designed local adaptive controllers can ensure all the signals in the closed-loop system bounded. A root mean square type of bound is obtained for the system states as a function of design parameters. This implies that the transient system performance can be adjusted by choosing suitable design parameters. With Scheme II, the proposed control laws allow arbitrarily strong interactions provided their upper bounds are available. In the absence of hysteresis, perfect stabilization is ensured and the L₂ norm of the system states is also shown to be bounded by a function of design parameters when the second scheme is applied.     

具有Preisach类型磁滞输入的不确定非线性系统 自适应神经网络控制

本文针对一类执行器受Preisach磁滞约束的不确定非线性系统, 提出一种基于神经网络的直接自适应控制 方案, 旨在解决系统的预定精度轨迹跟踪问题. 由于Preisach算子与系统动态发生耦合, 导致算子输出信号不可测 量, 给磁滞的逆补偿造成了困难. 为解决此问题, 本文首先将Preisach模型进行分解, 以提取出控制命令信号用于 Backstepping递归设计, 并在此基础上融合一类降阶光滑函数与直接自适应神经网络控制策略, 形成对磁滞非线性 和被控对象非线性的强鲁棒性能, 且所设计方案仅包含一个需要在线更新的自适应参数, 同时可保证Lyapunov函数 时间导数的半负定性. 通过严格数学分析, 已证明该方案不仅保证闭环系统所有信号均有界, 而且输出跟踪误差随 时间渐近收敛到用户预定区间. 基于压电定位平台的半物理仿真实验进一步验证了所提出控制方案的有效性.     

迟滞非线性动态系统神经网络自适应控制

为了减轻非线性动态系统中未知迟滞(Hysteresis)的不良影响，该文提出了一类Backlash型迟滞模型。将有限数量不同宽度的Backlash(Matlab／Simulink)算子进行叠加，来仿真执行器中的迟滞非线性动态。用此模型，提出了基于径向基函数神经网络的自适应控制方案，以控制伴有未知迟滞的非线性动态系统。该方案采用了动态逆的思想及伪控制的概念。利用Lyapunov稳定理论，设计了两个鲁棒控制项，保证动态系统的稳定性、系统中所有信号有界和误差收敛到起点的领域内。通过Matlab／Simulink仿真实验，证明了所提出方案的有效性。     

Robust tracking control for operator-based uncertain micro-hand actuator with Prandtl–Ishlinskii hysteresis

Since the hysteresis property inherently exists in the rubber material, it is necessary to deal with the control issues for the micro-hand by considering the hysteresis property. Therefore, in this paper, the robust tracking control for the micro-hand systems is discussed from the aspect of the Prandtl–Ishlinskii hysteresis property which is more applicable for the real applications. Firstly, a new model is obtained by combining the dynamic model of the micro-hand with Prandtl–Ishlinskii hysteresis property. Secondly, a new stability condition based on bounded input and bounded output stability is proposed for the Prandtl–Ishlinskii hysteresis modeled micro-hand system from two different cases. Thirdly, by designing the robust controllers based on the internal model control method, the tracking performance can be improved by eliminating the effect from the disturbance. Finally, simulation is used to further demonstrate the effectiveness of the proposed design scheme.     

A multivariable MRAC scheme with application to a nonlinear aircraft model

This paper revisits the multivariable model reference adaptive control (MRAC) problem, by studying adaptive state feedback control for output tracking of multi-input multi-output (MIMO) systems. With such a control scheme, the plant-model matching conditions are much less restrictive than those for state tracking, while the controller has a simpler structure than that of an output feedback design. Such a control scheme is useful when the plant-model matching conditions for state tracking cannot be satisfied. A stable adaptive control scheme is developed based on LDS decomposition of the high-frequency gain matrix, which ensures closed-loop stability and asymptotic output tracking. A simulation study of a linearized lateral-directional dynamics model of a realistic nonlinear aircraft system model is conducted to demonstrate the scheme. This linear design based MRAC scheme is subsequently applied to a nonlinear aircraft system, and the results indicate that this linearization-based adaptive scheme can provide acceptable system performance for the nonlinear systems in a neighborhood of an operating point.     

Hybrid systems in automotive control

This paper deals with robust adaptive control for a class of perturbed strict-feedback non-linear systems preceded by unknown hysteresis non-linearities. By using the Prandtl-Ishlinskii model with play and stop operators and the properties of this model, a robust adaptive control scheme is proposed to mitigate effects of the preceded hysteresis. The global uniform ultimate boundedness of the closed-loop system is achieved, and the effectiveness of the proposed control approach is demonstrated through simulation examples.     

Adaptive Pseudo Inverse Control for a Class of Nonlinear Asymmetric and Saturated Nonlinear Hysteretic Systems

This paper aims at eliminating the asymmetric and saturated hysteresis nonlinearities by designing hysteresis pseudo inverse compensator and robust adaptive dynamic surface control (DSC) scheme. The “pseudo inverse” means that an on-line calculation mechanism of approximate control signal is developed by applying a searching method to the designed temporary control signal where the true control signal is included. The main contributions are summarized as: 1) to our best knowledge, it is the first time to compensate the asymmetric and saturated hysteresis by using hysteresis pseudo inverse compensator because the construction of the true saturated-type hysteresis inverse model is very difficult; 2) by designing the saturated-type hysteresis pseudo inverse compensator, the construction of true explicit hysteresis inverse and the identifications of its corresponding unknown parameters are not required when dealing with the saturated-type hysteresis; 3) by combining DSC technique with the tracking error transformed function, the “explosion of complexity” problem in backstepping method is overcome and the prespecified tracking performance is achieved. Analysis of stability and experimental results on the hardware-in-loop platform illustrate the effectiveness of the proposed adaptive pseudo inverse control scheme.