RESEARCH INITIATION AWARD: Stable Inversion and Output Tracking for Nonlinear Nonminimum Phase Systems

9410646陈这个项目研究了一个具有挑战性的非线性控制问题。它旨在为设计适用于非最小相位非线性系统的输出跟踪控制器提供一种系统的综合方法。该控制器不仅提供了稳定的渐近跟踪，而且还确保了暂态误差将在预定的范围内。这是通过使用一种新的稳定反演方法实现的。在该方法中，首先对非最小相位系统进行稳定逆，以获得期望的(且稳定的)状态和精确映射到参考轨迹的输入轨迹。由此，将非最小相位控制问题转化为最小相位问题。然后设计了一个反馈控制器来稳定闭环系统，并确保对某些类型的不确定性具有鲁棒性。这一研究有望对跟踪问题以及对非线性系统的基本理解做出重要贡献。所开发的新程序可应用于许多工程问题，如飞机控制、火箭控制、医疗设备、无损评估等，产生了优越的性能和经济效益。***

9410646 Chen This project investigates a challenging problem in nonlinear control. It aims to provide a systematic synthesis procedure for designing output tracking controllers that apply to nonminimum phase nonlinear systems. Not only does the controller provide stable asymptotic tracking, it also ensures that the transient error will be within a prespecified bound. This achieved by using a novel approach of stable inversion. In this approach, the nonminimum phase system is first stably inverted to obtain desired (and stable) state and input trajectories that map exactly into the reference trajectory. With this, the nonminimum phase control problem is converted into a minimum phase one. Then a feedback controller is designed to stabilize the closed- loop system and to ensure robustness to certain types of uncertainties. This research is expected to make significant contributions to the tracking problem as well as the basic understanding of nonlinear systems. The new procedures developed can be applied to many engineering problems, such as aircraft control, rocket control, medical equipment, nondestructive evaluation, leading to superior performance and economic benefits. ***