对迟滞三明治系统基于Duhem算子的自适应控制

对具有迟滞非线性的三明治系统,设计了基于Duhem算子的神经网络自适应控制器.首先对前端动态子系统进行近似补偿;然后用Duhem算子描述所提出的迟滞状态,用神经网络逼近迟滞状态与迟滞输出的关系,实现对迟滞非线性的建模.基于该迟滞模型并采用伪控制技术设计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.     

基于压电陶瓷微位移执行器的精密定位技术研究

阐述了压电陶瓷微位移执行器的驱动原理,介绍了执行器的性能与应用情况;利用自行设计的输出特性测试系统,对WTYD0808042压电陶瓷微位移执行器进行了相关实验研究,分析了执行器的非线性和迟滞特性;采用Duhem算子建立了压电执行器的迟滞模型,利用建立的Duhem模型作为PID反馈控制的前馈环节进行闭环精密定位控制的研究。实验结果表明:该模型能够有效降低非线性和迟滞特性对压电执行器位移输出精度的影响,提高执行器的动态响应特性。     

ULTRA‐FINE TRACKING CONTROL ON PIEZOELECTRIC ACTUATED MOTION STAGE USING PIEZOELECTRIC HYSTERETIC MODEL

The tracking control accuracy of the piezoelectric actuator (PEA) is limited due to its inherent hysteresis nonlinearity. A new piezoelectric‐actuator model is synthesized based on two first‐order transfer systems in parallel with two tuned parameters determined from one experiment. Two open‐loop tracking controllers are implemented with the proposed model to compensate the hysteresis of linear positioning. Numerical simulations and experimental tests on the tracking of sinusoidal and triangular waveforms with signal frequencies ranging from 1Hz to 30 Hz are revisited and compared with the conventional Bouc‐Wen and Duhem models. Experimental results reveal that the RMS tracking error can be reduced to less than 2% of the maximum traveling distance without any feedback sensor. When a piezoelectric actuated on a two Degree‐Of‐Freedom (DOF) monolithic motion stage was employed, the RMS tracking error was 50 nm within the measured sensor accuracy.     

Stability of systems with the Duhem hysteresis operator: The dissipativity approach

In this paper, we discuss the dissipativity property of the counterclockwise Duhem operator. Sufficient conditions on the functions which define the Duhem operator are given such that the Duhem operator has counterclockwise input–output dynamics. In particular, an explicit construction of the storage functions satisfying the counterclockwise dissipation inequality is given. The constructed storage function is also related to the underlying anhysteresis function which is commonly used to describe hysteresis in magnetic materials. The results can thus facilitate analysis of systems with the counterclockwise Duhem operator via the dissipativity approach.     

A hysteresis functional link artificial neural network for identification and model predictive control of SMA actuator

In this paper, a modified Hysteresis Functional Link Artificial Neural Network (HFLANN) is proposed to identify and control a Shape Memory Alloy (SMA) actuator, which has an inherent hysteresis phenomenon. In this structure, a hysteresis operator combined with the Functional Link Artificial Neural Network (FLANN) to employ the hysteresis phenomenon and the dynamic of the SMA actuator. The hysteresis operator is introduced to capture the SMA hysteresis. And the FLANN is employed to approximate the dynamic of the system. In identification problem, the FLANN parameters are trained by Particle Swarm Optimization technique. For control problem, a Model Predictive Controller based HFLANN is derived to control the system. The identification results show that the HFLANN can employ for the SMA dynamic. The simulation and experimental results demonstrated the effectiveness of the proposed algorithm. The SMA hysteresis phenomenon is compensated completely by proposed controller.     

A Survey of the Hysteretic Duhem Model

The Duhem model is a simulacrum of a complex and hazy reality: hysteresis. Introduced by Pierre Duhem to provide a mathematical representation of thermodynamical irreversibility, it is used to describe hysteresis in other areas of science and engineering. Our aim is to survey the relationship between the Duhem model as a mathematical representation, and hysteresis as the object of that representation.     

Modeling and H_∞ Robust Control of a Smart Structure with Rate-dependent Hysteresis Nonlinearity

The performance of smart structures in trajectory tracking under sub-micron level is hindered by the rate-dependent hysteresis nonlinearity.In this paper,a Hammerstein-like model based on the support vector machines(SVM)is proposed to capture the rate-dependent hysteresis nonlinearity.We show that it is possible to construct a unique dynamic model in a given frequency range for a rate-dependent hysteresis system using the sinusoidal scanning signals as the training set of signals for the linear dynamic subsystem of the Hammerstein-like model.Subsequently,a two-degree-of-freedom(2DOF)H∞robust control scheme for the ratedependent hysteresis nonlinearity is implemented on a smart structure with a piezoelectric actuator(PEA)for real-time precision trajectory tracking.Simulations and experiments on the structure verify both the efectiveness and the practicality of the proposed modeling and control methods.     

Operator-based robust control for nonlinear uncertain systems with unknown backlash-like hysteresis

In this paper, operator based robust control for nonlinear uncertain system with unknown backlash-like hysteresis is considered. In detail, a continuous backlash-like hysteresis operator is proved to be corresponding to a one-to-one operator, that is, it is suitable to be used in operator theoretic based control theory. Moreover, an internal model control (IMC) structure with one parallel compensating operator is proposed for nonlinear uncertain system with unknown backlash-like hysteresis. Based on the proposed control scheme, the designed system is robustly stable and the desired output tracking performance can be realized simultaneously. Finally, a simulation example about nonlinear plant preceded by backlash is given to show the design procedure of the proposed method.     

微位移系统中压电陶瓷驱动器迟滞建模

针对超精密微位移系统中压电陶瓷驱动器的迟滞非线性问题,提出了一种基于遗传反向传播(BP)神经网络的压电陶瓷迟滞非线性建模方法.通过电涡流位移传感器获取压电陶瓷驱动器不同电压值下所对应的位移值;利用六次多项式拟合获得迟滞的数学模型,从而建立基于遗传BP神经网络的迟滞,模型.实验结果显示:该迟滞模型在神经网络测试下的最大误差为0.082 1 μm,平均绝对误差为0.0158 μm.表明,所建的迟滞模型能够较精确地反映出压电陶瓷驱动器的迟滞特性,同时为微位移控制系统设计提供了一定的理论基础.     

Semilinear Duhem model for rate-independent and rate-dependent hysteresis

The classical Duhem model provides a finite-dimensional differential model of hysteresis. In this paper, we consider rate-independent and rate-dependent semilinear Duhem models with provable properties. The vector field is given by the product of a function of the input rate and linear dynamics. If the input rate function is positively homogeneous, then the resulting input-output map of the model is rate independent, yielding persistent nontrivial input-output closed curve (that is, hysteresis) at arbitrarily low input frequency. If the input rate function is not positively homogeneous, the input-output map is rate dependent and can be approximated by a rate-independent model for low frequency inputs. Sufficient conditions for convergence to a limiting input-output map are developed for rate-independent and rate-dependent models. Finally, the reversal behavior and orientation of the rate-independent model are discussed.