光刻机纳米级工件台系统在摩尔定律驱动下不断向更高精度发展，其中，振动和扰动的存在一直都是运动控制精度的障碍，因此开展振动抑制和扰动镇定的运动控制研究工作是具有重要理论意义和实际工程价值的。针对工件台系统中传统线性反馈控制存在的“水床效应”问题，论文提出了一种基于误差数据的自适应控制方法，可以避免这种效应的同时补偿掉能量较强的振动或扰动。该方法主要包括两部分，先是基于误差信号处理的等效扰动力建模，再是对等效扰动力在时域上做自适应补偿。针对基于误差信号处理的等效扰动力建模过程，需要先确保在经典的两自由度控制框架下，通过高精度测量技术采集到准确的误差信号，然后对其尝试多种数字信号处理方法，最终确定以“矩形窗+Welch法”的累积功率谱来提取出关键的特征信息，并将其定义为特征频率。等效扰动力就是把能量较强的主、次特征频率处振动或扰动视为周期性的，并用傅里叶级数的形式进行建模。同时考虑到闭环系统的相角和被控对象的机械共振问题，进一步完善了等效扰动力的模型。针对傅里叶级数形式的等效扰动力，寻找可以自适应各系数的控制算法。采用已有的自适应前馈抵消（AFC）框架来实现补偿，并在此基础上推导并提出了收敛速度更快、性能表现更好的递推算法（RAFC）。同时，将时域上的AFC和RAFC两种控制算法引入到两自由度控制框架中，并推广到考虑闭环系统相角和被控对象机械共振的情况。通过对比的算法仿真实验，说明了两种算法在所需的时域性能指标和频域性能指标上的提升。针对所提自适应算法的频域及稳定性进行分析。通过经典控制理论推导出了AFC类算法的传递函数，再根据推导出的传递函数，通过频域仿真实验探讨其中三个参数（增益参数、相角参数和衰减参数）对控制器性能的影响，提出指导这些参数调谐的方法论。并且，采用李雅普诺夫法和超稳定理论完成了所提算法的稳定性证明。最后，通过对一个超精密粗微叠层运动台系统进行“前馈+反馈”两自由度控制的静采实验和轨迹跟踪实验，并引入上述的AFC和RAFC算法进行验证。实验结果表明，上述基于误差数据的自适应算法能够有效补偿特定频率的振动或扰动，明显改善轨迹跟踪的性能，验证了所提算法在实际工程中的有效性。关键词：误差信号处理；等效扰动力；自适应前馈抵消；轨迹跟踪控制

The nano-scale wafer stage system of the lithography machine is constantly developing to higher precision under the drive of Moore’s Law. The existence of vibration and disturbance has always been an obstacle to the accuracy of motion control. Therefore, the research on motion control of vibration suppression and disturbance stabilization is of great theoretical significance and engineering value. Aiming at the "water-bed effect" problem of traditional linear feedback control in the workpiece stage system, the paper proposes an adaptive control method based on measured error data, which can not only avoid thie effect but also compensate for vibrations and disturbances. The method mainly includes two parts, the modeling of the equivalent disturbing force based on error signal processing, and the adaptive compensation of the equivalent disturbing force force in time domain.For the equivalent disturbing force modeling process based on error signal processing, it is necessary to first ensure that accurate error signals are measured through high-precision measurement technology under the classic two-degree-of-freedom control framework, and then try a variety of digital signal processing methods. Finally, it is confirmed to extract the key characteristic information with the cumulative power spectrum of the "rectangular window & Welch method" and define it as the characteristic frequency. The equivalent disturbing force is to regard the vibrations and disturbances at the main and secondary characteristic frequencies with strong energy as periodic, and to model it in the form of Fourier series. Further, considering the phase angle of the closed-loop system and the mechanical resonance of the plant, the equivalent disturbing force model is more accurate.For the equivalent disturbing force, a control algorithm that can adapt to each coefficient in the form of Fourier series is proposed. The existing adaptive feedforward cancellation (AFC) framework is used to realize compensation, and on this basis, a recursive adaptive feedforward cancellation (RAFC) algorithm with faster convergence speed and better performance is derived and proposed. At the same time, two control algorithms (AFC & RAFC) in the time domain, are introduced into the two-degree-of-freedom control framework, and are extended considering the phase angle of the closed-loop system and the mechanical resonance of the plant. Through the comparison of these algorithm simulation experiments, the improvement of the time domain performance index and frequency domain performance index of the two algorithms is proved.The frequency domain performance and stability of the proposed adaptive algorithm are analyzed. The transfer function of the AFC algorithm is derived through classical control theory, and then according to the derived transfer function, the influence of the three parameters (gain parameter, phase angle parameter and attenuation parameter) in it on the performance of the controller is discussed through simulation experiments. And propose a methodology to guide the tuning of these parameters. Finally, the Lyapunov method and the superstability theory are used to prove the stability of the two algorithms.Finally, the positioning and trajectory tracking experiments under the two-degree-of-freedom control (feedforward & feedback) are carried out on an ultra-precision motion stage system, and the above AFC and RAFC algorithms are introduced. Experimental results show that the above-mentioned adaptive algorithm based on measured error data can effectively compensate for vibrations or disturbances of specific frequencies, significantly improve the performance of trajectory tracking, and ensure the effectiveness of the proposed algorithm in practical engineering.