摘要
随着纳米科学和纳米技术的飞速发展,压电陶瓷驱动的微位移平台逐渐成为精密制造装备中实现微观操作和加工的核心部件。但是压电陶瓷驱动器存在复杂的非线性磁滞效应,会造成系统精度超差,易产生振荡,甚至闭环系统的不稳定。此外,压电陶瓷驱动微位移平台是含输入磁滞非线性的动力学系统,现有数学模型无法精确描述这种复杂动力学特性,造成基于精确数学模型的控制与优化策略难以直接应用。这给磁滞补偿控制器的设计带来了极大的挑战。
本学位论文以压电陶瓷驱动微位移平台为对象,深入研究磁滞非线性补偿控制的理论与方法,旨在消除压电陶瓷驱动器的磁滞效应对驱动精度的影响,实现压电陶瓷驱动微位移平台的纳米精度运动控制,扩展压电陶瓷驱动器在精密制造装备中的应用。本论文从系统建模、控制器设计和实验验证三个层次展开,主要研究内容如下：
提出了增强型Prandtl-Ishlinskii(P-I)磁滞模型和基于此模型的直接逆磁滞补偿方法。针对传统P-I模型只能描述对称磁滞特性的不足,将非线性输入函数引入到传统P-I磁滞建模中,提出一种既能表征对称磁滞特性也能表征非对称磁滞特性的增强型P-I模型,并验证了所提模型的消除属性和一致性属性。在此基础上,直接应用增强型P-I模型描述压电陶瓷驱动器的逆磁滞曲线,将辨识的增强型P-I模型串入到压电陶瓷微驱动平台实现逆磁滞补偿。实验结果验证了增强型P-I模型和基于此模型的直接逆磁滞补偿控制方法的有效性。
从电路特性、磁滞效应、压电效应和机械振动等多场耦合特性分析入手,提出了完整表征压电陶瓷驱动微位移平台的综合机电动力学模型。为便于模型参数辨识,将综合动力学模型表征为含输入磁滞驱动的三阶线性系统,进而采用线性动力学部分与磁滞非线性部分分离的方法辨识模型参数。为验证模型的有效性,采用增强型P-I模型作为实例描述输入磁滞非线性。实验结果证明了所提的综合动力学模型很好的表征了压电陶瓷驱动微位移平台的动态特性和磁滞效应。为后续鲁棒控制器的设计提供了模型基础。
设计了无需磁滞逆模型的鲁棒自适应控制器。在建立的系统综合机电动力学模型的基础上,给出了一种磁滞分解的方法表征磁滞非线性效应,将磁滞非线性描述成输入信号的线性函数和依赖于输入信号的有界非线性扰动。结合滑模控制和自适应控制的优点,设计了基于磁滞分解而无需磁滞逆模型的鲁棒自适应控制算法,其中,滑模控制器补偿有界扰动、未知非线性和未建模动态,自适应算法消除系统模型参数的不确定性或不精确性。利用Lyapunov函数法证明了闭环控制系统的全局稳定性,并通过实验证明了所设计的控制器实现了压电陶瓷驱动平台的快速纳米精度运动。
设计了含估计逆磁滞模型补偿的鲁棒自适应控制器。针对一类含输入非对称Backlash磁滞非线性驱动的非线性系统,分析了非对称Backlash磁滞非线性的特性,构造了非对称Backlash的估计逆模型,给出了基于此估计逆模型的补偿误差的解析表达式,并将补偿误差分解成参数化的部分和非参数化的有界干扰。在此基础上,设计鲁棒自适应控制算法。所设计的控制器保证了整个闭环系统的稳定性和理想的跟踪精度。仿真实验证明了该控制方法的正确性和有效性。
Along with the rapid development of nanoscience and nanotechnology, piezoceramic actuated micro/nanopositioning stages are becoming a promising technique in many precision manufacturing equipments. However, piezoceramic actuators suffer from the inherent hysteresis effect because of loss phenomena taking place inside piezo-ceramic materials. The hysteresis effect exhibits complex nonlinear characteristics, which usually introduces undesirable inaccuracies or oscillations and even instability. Interest in studying piezoceramic actuated micro/nanopositioning stages with actuator hysteresis is also motivated by the fact that they are complex dynamic systems with un-known non-smooth nonlinearities for which traditional model-based control methods are insufficient and thus require the comprehensive dynamic model of the controlled stage. Development of control techniques to mitigate the effects of hysteresis is a quite challenging task and recently attracts significant attentions.
To address such challenges, this dissertation presents a comprehensive model-ing, controller design and experimental evaluation for piezoceramic actuated micro/-nanopositioning stages with unknown hysteresis nonlinearity. With the emerging ap-plications of smart material based actuated systems, the results of the dissertation will enrich the theory and methodology of hysteresis compensation and control, and ad-vance the state of nanomanufacturing in both theoretic and practical aspects. The main research contents and achievements are listed as follows.
A modified Prandtl-Ishlinskii(P-I) hysteresis model with a nonlinear input func-tion is developed to describe the symmetric as well as asymmetric hysteresis loops on the basis of the classical P-I hysteresis model. The essential wiping-out and con-gruency properties for the validity of the developed hysteresis model are addressed. With the modified P-I model, a new real-time inverse hysteresis compensation method is proposed. Different from the commonly design procedures for inverse hysteresis compensation, the proposed method directly utilizes the modified P-I model to cap-ture the inverse hysteresis effect of the piezoelectric actuators. Then, the identified hysteresis model is cascaded in the feedforward path for direct inverse hysteresis can-celation. Experimental results on a piezoceramic actuated positioning stage verify the effectiveness of the feedforward controller along with the modified P-I model.
A general electromechanical model is proposed to characterize dynamic behaviors of the piezoceramic actuated micro/nanopositioning stage, including nonlinear elec-tric behavior, voltage-charge hysteresis, piezoelectric effect, and frequency response of the stage. To identify the parameters of the general model, the adopted approach is to express the general model into a third-order linear plant preceded by an input hys-teresis nonlinearity. Then, the linear parameters and the hysteresis term can be iden-tified separately. To validate the proposed model, the modified P-I model is adopted as an illustration to describe the hysteresis nonlinearity, which is also confirmed by experimental results.
A robust adaptive control approach is developed for a reduced dynamic model of the piezoceramic actuated stage with unknown parameters and hysteresis nonlinearity. In-stead of constructing the inverse of the hysteresis model to cancel the hysteresis effect, the hysteresis decomposition approach is adopted in the control scheme to express the hysteresis effect as an approximate linear relationship with unknown but bounded nonlinear term. In the developed robust adaptive approach, a sliding mode controller is designed to remedy the unknown hysteresis nonlinearity and disturbances, while a discontinue projection-based adaptive control law is utilized to handle the parameters uncertainties of the dynamic plant. The global stability of the chosen control laws is established by the Lyapunov function method. Experimental tests on a prototype plat-form with different motion trajectories are conducted to validate the feasibility and effectiveness of the proposed robust control approach.
With the estimated inverse hysteresis compensation, a robust adaptive controller is developed for a class of nonlinear systems with unknown asymmetric input backlash. Considering the characteristics of the asymmetric backlash nonlinearity, an analytical expression of the estimated inverse compensation error for asymmetric backlash is ob- tained, which can be expressed as a parametrizable part with a bounded unparametriz-able disturbance. With the analytical expression of the inverse compensation error, a corresponding controller is designed by using the robust adaptive control approach. The proposed controller ensures the boundedness of the closed-loop signals, and yields desired tracking precision. The simulation results demonstrate significantly enhanced tracking performance when the estimated inverse of the asymmetric Backlash model is considered in the closed-loop control system.
引文
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