Feedback Design Methods for Nonlinear Systems

这项研究涉及的反馈设计的发展 非线性系统的方法，基于非线性增强的 经典根轨迹理论 这种非线性“频率 例如，“域”方法能够设计， 系统方法，稳定“超前-滞后”补偿器，非线性PD 设定点控制的控制器，干扰的反馈策略 解耦与闭环稳定性或甚至渐近 跟踪和干扰抑制的一个广泛的一类非线性 系统，基于经典控制概念的非线性模拟 例如相对度或非线性“最小相位”特性。 这 方法已成功地用于稳定 大标量仿射（在控制中）“最小相位”非线性 在一定的规则性条件下。 但不少 感兴趣的应用是多变量的，有时不是仿射的， 经常有奇点。 这项工作将系统地发展 并扩展该设计方法以便包括这样的系统， 在必要时绘制几何控制、动态 系统与经典控制

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.