压电倾斜镜迟滞动力学建模及宽频域高精度跟踪控制

Piezoelectric fast steering mirror (PFSM) is a complex strong coupling system that integrates optics, mechanics, electrics and control. The factors of hysteresis nonlinearity, resonance and all disturbances will restrict the positioning accuracy and closed-loop bandwidth of PFSM system, even introduce instability. Different from traditional studies which are mostly devoted to certain disturbances, a comprehensive study of hysteresis, resonance and disturbances is conducted to realize high precision tracking control in the broadband frequencies which is over the resonance of PFSM. The entire research process is based on theoretic analysis, computer simulation and experiment verification. First, combining the P-I model method with support vector machine, a rate-dependent asymmetric hysteresis model is established which is inverse-needless and controller-oriented. Then, considering both the linear and nonlinear parts, the PFSM is precisely modeled as a multi-segment hysteresis dynamic model, and the PFSM resonance compensation is conducted based on the approach of resonance suppression and adaptive filters. Finally, with the corresponding disturbance observes for each factor, a robust slide-mode adaptive controller is designed in which the parameters of model and controller can be estimated and updated online. The bandwidth of 500Hz and tracking precision of 1 micro radian of the stable control system can be realized. This research will solve the key fundamental problems in the high precision tracking application of PFSM over broadband frequencies, and has important academic values in terms of dynamic hysteresis modeling and control strategy research.

压电倾斜镜(PFSM)是集光、机、电、控于一体的强耦合复杂系统，迟滞非线性、机械谐振和其他各种干扰等都会影响PFSM定位精度和闭环带宽，甚至引起不稳定。传统研究多致力于抑制部分干扰因素，而本项目综合研究迟滞、谐振和其他干扰，以达到在高于PFSM谐振频率的宽频域内实现高精度跟踪控制。在理论、仿真与实验的基础上，首先基于支持向量机和P-I模型的结合，建立无需求逆面向控制的率相关非对称迟滞模型；然后综合分析线性与非线性部分，构建PFSM多环节迟滞动力学综合模型，并采用谐振抑制和自适应滤波等方法进行谐振补偿；最后针对各干扰因素设计对应的扰动观测器，并设计鲁棒滑模自适应控制算法，在线估计和更新模型参数与控制器参数，保证系统稳定，实现高于500Hz小于1微弧度的PFSM稳定跟踪控制。本项目的研究将解决PFSM宽频域高精度跟踪控制应用的关键基础问题，在动态迟滞建模、控制策略研究方面具有重要学术价值。

本项目针对压电倾斜镜系统本身存在的迟滞非线性、动态谐振和各种干扰，开展了应用基础研究。主要围绕压电迟滞非线性的建模与辨识、PFSM的迟滞动力学建模、高精度跟踪控制器设计三个方面展开，实现了压电倾斜镜系统的宽频域高精度跟踪控制。具体研究内容与重要结果包括：①研究了压电致动器的非对称率相关迟滞非线性。构建了非对称率相关Bouc-Wen迟滞模型、Prandtl-Ishlinskii迟滞模型、Duhem神经网络迟滞模型，并研究了模型的在线实现与参数辨识方法。②研究了PFSM的迟滞与谐振等动态特性。分析了PFSM系统中高压放大器、压电执行器、倾斜镜本体、角度传感器等环节的传递函数及其耦合关系，建立了PFSM系统的多环节迟滞动力学综合数学模型和参数辨识方法。③研究了PFSM的鲁棒滑模跟踪控制方法。构造了系统的鲁棒稳定条件，设计了PFSM的复合控制器。并对控制策略进行改进和优化，设计了PFSM系统的鲁棒滑模控制器及在线实现方法。本项目研究了PFSM系统在跟踪控制应用中的关键基础问题，提出的动态迟滞建模与控制策略设计等理论与方法为压电倾斜镜和其他超精密定位装置的自主研发提供了重要理论和技术支撑。