随着超精密运动系统的发展,其精度和速度指标之间的矛盾愈加尖锐。结构拓扑形式、电机布局及控制器作为超精密运动系统的主要设计元素,决定着运动系统的主要运动性能指标。集成优化设计方法充分考虑结构与控制之间的耦合关系,对于超精密运动系统运动指标的提升具有重要的学术研究意义和工程应用价值。本文以超精密运动系统为研究对象,首先,研究超精密运动系统结构与控制集成优化多级分解方法,实现复杂优化问题的有效降维;其次,研究目标及约束建模方法、结构动力学建模及控制器设计方法,实现高效高精度优化建模;最后,研究复杂优化问题的求解方法,解决计算精度及收敛性问题。针对集成优化问题中的建模及数值求解难点,提出了一种结构与控制集成优化问题的多级分解方法。利用超精密运动系统的性能变量将复杂优化问题分解为系统级优化问题及结构与控制器子系统级优化问题,实现了设计变量的有效降维。采用电机布局优化问题内嵌结构拓扑优化问题的层级关系解决了二者对求解算法的尖锐矛盾。为体现各层级优化问题的耦合关系,基于最优敏度向量及约束裕度实现了控制器及结构子系统级优化问题向系统级优化问题的信息传递。确立了各层级优化问题的建模和求解条件,有效指导后续方法研究。针对现有目标/约束函数难以计算多性能点时域瞬态响应的难题,提出了一种综合频域和时域特点的目标/约束建模方法。针对电机推力解析模型精度不足的问题,提出了以电机推力解析模型与有限元计算方法相结合的方法。针对结构动力学建模需求,建立了一种电机布局可变的高效高精度结构拓扑材料插值模型及组件非干涉约束条件。针对超精密运动系统结构柔性的影响,提出了以过驱动为核心的控制器设计方法,实现了全局振动抑制的同时保有其通用性。针对各层级优化问题的模型特点及求解条件,提出了复杂非线性优化问题的求解算法。针对高阶结构模态造成的计算收敛问题,采用约束多阶模态的可控性gramians对角线元素取值的方法,从根本上减少对柔性模态的激发程度。针对灵敏度计算困难的问题,结合特征值问题求导方法和复变量求导方法实现了灵敏度的半解析表达,提高了计算精度及收敛性。将所提方法应用于光刻机工件台的微动台系统设计中,利用数值计算结果及实验结果验证本文所提方法的有效性。
As the requirements for precision and velocity in ultra-precision motion systems are getting higher, contradictions between these two aspects are getting more serious. Structural topology, actuator configuration and controller design are the determining factors in ultra-precision motion systems. The integrated optimization method takes full consideration of couplings between structural topology, actuator configuration and controller design. Exploring the integrated optimization method of structural and control design in ultra-precision motion systems has its value in both academic research and engineering applications. In this thesis, ultra-precision motion systems are taken as the research objects, a multi-level decomposition method is firstly studied to reduce modelling and solving difficulties. Then, methods of design objective/constraints modelling and structural dynamics modelling are proposed, together with a controller design method, to achieve high modelling accuracy and efficiency. Finally, methods on solving complex optimization problems are proposed to improve computational accuracy and convergence.The integrated optimization of structural and control design in ultra-precision motion systems is a complex high-nonlinear problem with large-scale design variables, which makes it difficult to solve directly by using numerical methods. To deal with this, a multi-level decomposition method is proposed. By utilizing design variables that could determine the moving performance of ultra-precision motion systems, the original optimization is decomposed into a system-level optimization, a structural subsystem-level optimization and a control subsystem-level optimization, which reduces the dimension of design variables to a great extent. The structural topology optimization is nested in the actuator configuration optimization in order to overcome contradictions in their requirements for numerical methods. To reflect couplings between optimizations, the optimum sensitivity derivatives and constraint margin are adopted to transfer information between the system-level optimization and subsystem-level optimizations. Conditions on optimization modelling and solving are derived based on the decomposition method, which could offer guidance on the further research.To overcome difficulties in directly solving the time-domain responses at multiple positions, a method of design objective/constraints modelling is proposed to combine advantages of both the time-domain modelling method and the frequency-domain modelling method. To improve the modelling accuracy of actuators forces, the analytical model and the finite element model are combined in calculating actuator forces. A material interpolation model with high accuracy and high efficiency is proposed, together with a new method to represent non-overlapping constraints of actuators. To suppress the vibration caused by structural flexible modes, a new control design method based on over-actuation is proposed which could reduce responses of the flexible modes in a global sense while holding its generality in ultra-precision motion systems.Based on the multi-level decomposition method and conditions on problem solving, numerical methods of solving the complex non-linear problems are studied. Design constraints on modal controllability gramians of the higher modes are proposed to prevent them from exciting, which could reduce their effects on convergence during optimization. To improve computational accuracy and convergence, the eigensensitivity analysis method and the complex-step derivative approximation method are combined to calculate sensitivities in the structural topology optimization. In the end, the proposed method is adopted in designing a fine stage in the wafer stage. The effectiveness of the proposed method is verified by numerical and experimental results.