Feedback Design Methods for Nonlinear Systems

本研究基于对经典根轨迹理论的非线性改进，发展了一种非线性系统的反馈设计方法。例如，这种提出的非线性“频域”方法能够以系统的方式设计“超前-滞后”补偿器、用于设定值控制的非线性PD控制器、用于干扰解耦的闭环系统稳定的反馈策略，或者甚至是基于经典控制概念的非线性类似于相对度或非线性“最小相位”性质的渐近跟踪和干扰抑制。在一定的正则性条件下，该方法已成功地应用于大的标量、仿射(控制)“最小相位”非线性系统的镇定。然而，许多感兴趣的应用是多变量的，有时不是仿射的，并且经常具有奇异性。这项工作将系统地发展和扩展这种设计方法，以便包括这样的系统，必要时借鉴几何控制、动力系统和经典控制中的技术。

This research involves the development of a feedback design methodology for nonlinear systems, based on a nonlinear enhancement of classical root-locus theory. This proposed nonlinear "frequency domain" methodology, for example, is capable of designing, in a systematic way, stabilizing "lead-lag" compensators, nonlinear PD controllers for set-point control, feedback strategies for disturbance decoupling with closed-loop stability or perhaps even asymptotic tracking and disturbance rejection for a broad class of nonlinear systems, based on nonlinear analogues of classical control concepts such as relative degree or nonlinear "minimum phase" properties. This methodology has been successfully employed for stabilization in the large of scalar, affine (in the control) "minimum phase" nonlinear systems under certain regularity conditions. However, many applications of interest are multivariable, sometimes not affine, and very often have singularities. This work will systematically develop and extend this design methodology so as to include such systems, drawing where necessary on techniques in geometric control, dynamical systems and classical control.