Nonlinear Repetitive Control

眼镜镜片的高速钻石车削、凸轮轴和活塞的非圆加工、原子力显微镜(AFM)的高速扫描和振动探测以及金属轧制都是可以受益于重复控制算法的工业过程的例子。受光学车削和原子力显微镜控制中的非线性的启发，本研究项目解决了非线性重复控制的基本挑战。除了研究周期运动存在的基本理论、稳定性结果和设计方法外，还研究了光学转弯和原子力显微镜控制中的具体非线性问题。该项目涉及与DAC Vision，Inc.的合作，以了解聚碳酸酯眼镜镜片的钻石车削。这一过程需要准周期的刀具轨迹，并受到显著的非线性致动器的影响。在对单输入单输出(SISO)重复控制系统的非线性周期运动的性质进行初步研究之后，将研究其在多输入多输出(MIMO)系统中的推广，与正常双曲流形理论的可能联系，以及非线性重复控制中混沌的开始。DAC Vision钻石车削过程的建模和仿真将在同一时期完成，随后将在DAC的机器上进行控制器的控制设计和实现。UCSB研究生控制实验室的教学开发与教育控制实验供应商Magic Moments的合作也是该项目的一部分。PI将把重复控制设计融入到这个教学实验室中，以实现磁悬浮转子的平衡。在这个计划的后面，原子力显微镜(AFM)中的重复控制问题将被解决，目的是提高这些设备的成像速度。需要解决的具体问题是攻丝模式下原子力显微镜的控制。在高点击和高扫描速度下，AFM可能会进入混乱的运动，从而显著降低图像质量。这项研究的目的之一是控制混沌的开始，从而提高系统的性能。

High-speed diamond turning of eyeglass lenses, noncircular machining of camshafts and pistons, high-speed scanning and vibratory probing in atomic force microscopy (AFM), and metal rolling are examples of industrial processes which can benefit from repetitive control algorithms. Motivated by the nonlinearities in optical turning and AFM control, this research project addresses basic challenges in nonlinear repetitive control. In addition to research on basic theory involving the existence of periodic motions, stability results, and design methods, specific nonlinear problems in optical turning and AFM control are addressed. The project involves collaborations with DAC Vision, Inc. to understand the diamond turning of polycarbonate eyeglass lenses. The process requires quasi-periodic tool trajectories and suffers from significant actuator nonlinearly. Following the initial investigations into the nature of nonlinear periodic motions in single-input single-output (SISO) repetitive control systems, extension to MIMO systems, possible connections with normally hyperbolic manifold theory, and the onset of chaos in nonlinear repetitive control will be investigated. Modeling and simulation of the DAC Vision diamond turning process will be accomplished in this same period followed by control design and implementation of controllers on DAC's machines. Instructional development in UCSB's graduate control lab in collaboration with Magnetic Moments, a supplier of educational control experiments is also a part of this project. The PI will incorporate repetitive control design into this teaching lab for the outbalancing of a magnetically suspended rotor. Later in this program, repetitive control problems in atomic force microscopy (AFM) are to be addressed with the aim of improving the imaging speed of these devices. The specific problem to be addressed is the control of AFM's in tapping mode. At high tapping and scan rates, AFM's can enter into chaotic motions that degrade image quality significantly. One of the aims of this research is to control the onset of chaos and thus improve system performance.