A limit cycle approach for the parametric identification of hysteretic systems

This paper deals with the parametric identification of the Bouc–Wen model for smooth hysteresis. The interest of the problem stems from the fact that the Bouc–Wen model has been used experimentally to represent various hysteretic systems during the last few years. However, identifying the parameters of this model is not a trivial task due to the nonlinearity of the model. In the current literature, most methods devoted to the parametric identification of the Bouc–Wen model rely mainly on numerical simulations, and do not offer, to a large extent, a rigorous proof of the convergence of the estimated parameters to the true ones. This paper presents a new identification method that guarantees the exact determination of the parameters in the absence of perturbations. It is also shown that this method is robust with respect to a class of disturbances of practical interest. The applicability of this method is illustrated by means of experiments.  

对Preisach类的迟滞非线性神经网络建模

为了消除迟滞非线性对系统的不良影响,本文利用神经网络对Preisach类的迟滞非线性进行建模．通过引入一个特殊的迟滞因子,将多映射的迟滞非线性转换成一一映射,然后建立了基于神经网络的迟滞非线性模型．该模型结构简单,简化了辨识过程,可以调整神经网络权值以适应不同条件下的迟滞辨识．最后．应用该方法对压电执行器中的迟滞非线性建模,并与KP模型进行了比较．  

Compensation of hysteresis in piezoelectric actuator with iterative learning control

This paper presents the application of iterative learning control (ILC) to compensate hysteresis in a piezoelectric actuator. The proposed controller is a hybrid of proportional-integral-differential (PID) control, whose main function is for trajectory tracking, and a chatter-based ILC, whose main function is for hysteresis compensation. Stability analysis of the proposed ILC is presented, with the PID included in the dynamic of the piezoelectric actuator. The performance of the proposed controller is analysed through simulation and verified with experiment with a piezoelectric actuator.  

气动肌肉主动悬架系统的仿真模型与分析

以气动肌肉作为新型执行器，创建基于1／4悬架模型的汽车主动悬架系统。并运用Matlab中的Simulink模块库建立此系统的仿真模型，着重讨论仿真建模以及仿真过程中所遇到的困难，诸如气动肌肉迟滞特性的实现、高频分量对仿真结果的影响等问题。经对系统机理模型的适当变换处理，促进了仿真系统的稳定。利用获得的仿真模型对气动肌肉主动悬架系统的动态特性进行仿真研究，结果分析表明所建立的仿真模型已能满足实用的气动肌肉主动悬架系统的研究需要。  

基于迟滞算子的非平滑三明治系统自适应控制

针对一类具有非平滑的迟滞三明治系统, 提出一种基于神经网络的自适应控制方法. 首先利用神经网络做出了前端动态模块的逆系统实现前端动态模块的近似补偿, 这样将迟滞三明治系统转化成一般的迟滞非线性系统. 然后提出一个迟滞算子将迟滞的多映射转化成一一映射, 基于这个迟滞算子设计了神经网络自适应控制器, 通过Lyapunov方法证明了系统的稳定性并推导出神经网络的权值自适应调整律和控制律. 最后通过仿真验证了该方案的有效性.  

Pseudo-inverse-based adaptive control for uncertain discrete time systems preceded by hysteresis

This paper discusses the adaptive control for the uncertain discrete time linear systems preceded by hysteresis nonlinearity described by the Prandtl-Ishlinskii (PI) model. The contribution of the paper is the development of an adaptive algorithm in which a pseudo-inversion is introduced to avoid difficulties of the directly inverse construction for complex hysteresis models, especially for the unknown hysteresis case. In the developed approach, only those parameters in the formulation of the sliding mode controller are adaptively estimated. The stability in the sense that all signals in the loop remain bounded is analyzed. Simulation results show the effectiveness of the proposed algorithm.  

Inversion-free stabilization and regulation of systems with hysteresis via integral action

In this paper, we present conditions for the stabilization and regulation of the tracking error for ann$n$-dimensional minimum-phase system preceded by a Prandtl–Ishlinskii hysteresis operator. A general controller structure is considered; however, we assume that an integral action is present. The common Lyapunov function theorem is utilized together with a Linear Matrix Inequality (LMI) condition to show that, under suitable conditions, the tracking error of the system goes to zero exponentially fast when a constant reference is considered. A key feature of this LMI condition is that it does not require the hysteresis effect to be small, meaning that hysteresis inversion is not required. We use this condition together with a periodicity assumption to prove that a servocompensator-based controller can stabilize the system without using hysteresis inversion. Additionally, we draw parallels between our LMI condition and passivity-based results achieved in the literature. We then verify our LMI results in simulation, where we show that the LMI condition can accurately predict the stability margins of a system with hysteresis. Finally, we conduct experiments using a servocompensator-based controller, where we verify the stability of the system and achieve a mean tracking error of 0.5%$0.5\%$ for a 200$200$ Hz sinusoidal reference.  

Exponential stability of stochastic systems with hysteresis switching

For stochastic systems with state-dependent switching which are motivated by active regions of subsystems, the exponential stability is studied in this paper. Distinct from most of the existing references, the existence of the solution to stochastic switched systems is not given as a priori information but can be proved under some easily verified conditions. By the aid of Dynkin’s formula, Itô’s formula and exponential martingale inequality, the criteria on moment exponential stability and almost sure exponential stability of the stochastic switched system are established based on Lyapunov-like techniques. Simulation examples are presented to illustrate the validity of the results.  

Non-parametric convex identification of extended generalized Prandtl–Ishlinskii models

The Generalized Prandtl–Ishlinskii model (GPI) of hysteresis has wide applicability, partly because of its capability to model asymmetric hysteresis. It is characterized by three unknown functions. Today, GPI models are typically identified through trial and error by ad hoc methods, presuming parameterized expressions for these functions and then using nonlinear least squares to determine the parameters, with concurrent problems of convergence, a dependence on the initial parameter guess, and local minima. Except for the aggregated hysteresis input–output fit the result gives no information as to whether the functions chosen are appropriate or not. Here we present a method to circumvent these problems for a more general class of hysteresis models. First, we introduce an extended GPI model (XGPI), where an additional memoryless function is placed in parallel to the GPI model. This further widens the applicability, allowing, for example, arbitrary orientation of the hysteresis loop. For such models it is shown how its four separate mappings can be identified by convex optimization. Appropriate single-valued functions can then be fitted individually to the resulting mappings and, if necessary, the function parameters found can be fine-tuned using nonlinear least squares on input–output data. The method is applied to simulated data and experimental data from a magnetoelastic torque sensor, and the results are favorably compared to the results of another commonly used hysteresis model.  

Absolute stability analysis of linear systems with Duhem hysteresis operator

In this paper, we investigate the stability of positive and negative feedback interconnections of a linear system and a Duhem hysteresis operator. We provide sufficient conditions on the linear plant and on the Duhem operator which are based on the counterclockwise (CCW) or clockwise (CW) input–output property of the plant and hysteresis operator. We show the application of our main result in the design of a linear controller to stabilize a simple mechanical system driven by a hysteretic actuator, such as, piezo-actuator or smart material-based actuator.