Control of Underactuated, Nonlinear, Non-holonomic, Mechanical Systems

本研究项目的主要目标是为欠驱动线性和非线性非完整系统的稳定和控制开发一个统一的框架。特别是，它的目的是发展一种非线性欠驱动非完整系统的控制方法，其中包括开环不稳定和/或非最小相位系统。作为一个特例，该方法同样适用于线性系统。同样，该方法也将适用于完整系统。提出的研究将产生一种方法来获得一类控制器（而不是特定的控制器），用于稳定和控制欠驱动非线性系统。所提出的方法在设计难以控制的非线性系统的鲁棒控制器和容错控制器方面具有很大的潜力，导致开发了一个软件工具（工具箱），可以为给定的欠驱动系统生成控制器。该方法是建立在一类辅助稳定系统的基础上的，每一类辅助稳定系统在适当选择控制器的情况下与原始系统等效。给出了欠驱动2- dof的仿真结果。并将倒立摆小车系统与现有的最新结果进行了比较，验证了该理论。该方法将推动非线性系统和非线性控制器控制领域的发展。这项研究的结果将增强对大量现实生活系统的控制能力，例如，执行器失效模式下的飞机和航天器，水下航行器和双足运动。为了证明这种方法的可行性，将进行一系列的控制实验。每个装置将代表一类具有两个或更高自由度的欠驱动非线性机械系统。＊＊＊

9813182 Kelkar The main objective of this research project is to develop a unified framework for the stabilization and control of underactuated linear and nonlinear nonholonomic systems. In particular, it is aimed to develop a methodology for the control of nonlinear underactuated nonholonomic systems which will include open-loop unstable and/or non-minimum phase systems. As a special case, the methodology will be applicable to linear systems as well. Similarly, the methodology will also be applicable to holonomic systems. The proposed research will yield a methodology to obtain a class of controllers (and not a specific controller) for stabilization and control of underactuated nonlinear systems. The proposed method has great potential in the design of robust controllers and fault-tolerant controllers for difficult-to-control nonlinear systems, leading to the development of a software tool (toolbox) which can generate controllers for a given underactuated system. The methodology is based on the construction of a class of auxiliary stable systems each of which will be equivalent to the original system with a proper choice of controller. The simulation results for an underactuated 2-d.o.f. inverted pendulum-cart system are included and compared with the existing recent results as a validation of the theory. The methodology will advance the state-of-the-art in the area of control of nonlinear systems as well as nonlinear controllers. The results of this research will enhance ability to control a large class of real life systems, for example, aircraft and spacecraft in actuator failure mode, underwater vehicles, and biped locomotion. To demonstrate the viability of this methodology, a series of control experiments will be developed. Each apparatus will represent a class of underactuated nonlinear mechanical systems with two or higher degrees-of-freedom. ***