柔性结构前馈自适应振动主动控制中时滞和迟滞问题研究

Flexible structure widely used in engineering has the characteristics of small damping, nonlinear and uncertain model. Active control system based on feed-forward adaptive control algorithm can suppress the low frequency vibration of flexible structure with uncertain parameters. However, time-delay and nonlinear hysteresis phenomenon are inevitable in the control system, threatening the stability of active control system. The project presents systematic study of time-delay and hysteresis property related problems in feed-forward adaptive active vibration control for flexible beam and flexible thin plate. Constructing mathematic models of time-delay and nonlinear hysteresis phenomenon based on adaptive filter. Quantitatively analyzing the influence of time-delay and nonlinear hysteresis on the convergence speed, stability and control effect of feed-forward adaptive vibration control system, and providing beneficial or harmful boundary conditions. Designing a seamless switching control algorithm for elimination and utilization of time-delay and nonlinear hysteresis, and avoiding the adverse effects of possible mutation on the stability of the control system in the process of the switching. Researching the real-time accurate online identification method of time-delay and nonlinear hysteresis. Developing a general feed-forward adaptive active vibration control system based on time-delay and hysteresis phenomenon, providing the technology support for solving time-delay and hysteresis problems in multi-channel adaptive active vibration control of large complex flexible structure.

工程中广泛应用的柔性结构，具有小阻尼、非线性以及模型不确定的特点。采用前馈自适应控制算法可以实现对这类不确定参数结构低频振动的有效控制，然而在控制系统中不可避免地存在时滞和非线性迟滞现象，威胁着主动控制系统的稳定性。本申请课题以柔性梁、柔性薄板结构为研究对象，系统深入地研究前馈自适应振动主动控制中时滞和迟滞相关问题。建立时滞和迟滞的自适应滤波结构数学模型；定量分析时滞和迟滞特性对前馈自适应振动控制系统收敛速度、稳定性和控制效果的影响，确定时滞和迟滞利害影响的边界条件，设计时滞和迟滞消除与利用无缝切换控制算法，并解决切换过程中可能发生的突变对系统稳定性的影响；研究对时滞和迟滞非线性模型实时精确在线辨识方法；开发基于时滞和迟滞的通用前馈自适应振动主动控制系统，为解决大型复杂柔性结构多通道振动主动控制的时滞与迟滞问题提供重要的技术理论支持。

本项目针对前馈自适应振动主动控制系统中普遍存在的时滞和迟滞现象进行基础研究，解释了时滞和迟滞对前馈自适应控制系统影响的物理机理；建立了基于全通滤波器与AR模型相结合的自适应时滞预测模型，和基于迟滞 Backlash 算子与横向滤波结构相结合的自适应迟滞模型。开发了基于滤波-U最小均方算法和非线性迟滞在线建模和动态补偿的前馈自适应振动控制算法，核心算法包括三个关键模块：基于IIR滤波器的自适应主动控制器模块、次级通道在线建模模块、迟滞在线建模和动态补偿模块，实现了对包含时滞和迟滞特性的次级通道的在线建模，完成在前馈自适应振动控制系统中实时精确地动态辨识描述时滞和迟滞特性的目标，并对非线性迟滞进行了动态线性化。将研究理论成果应用到自适应控制器的设计中，开发了基于次级通道在线建模的多通道振动主动控制算法。.为了验证研究成果的有效性，本项目以压电智能悬臂薄板结构为试验对象，搭建柔性结构自适应主动控制实验平台。并进行了包括时滞和迟滞环节在线辨识试验、柔性薄板多通道自适应振动主动控制试验的所有研究成果的试验验证，取得了预期的控制效果。