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

9813182 Kelkar本研究项目的主要目标是为欠驱动的线性和非线性非完整系统的镇定和控制建立一个统一的框架。具体地说，它旨在发展一种控制非线性欠驱动非完整系统的方法，其中将包括开环不稳定和/或非最小相位系统。作为特例，该方法也适用于线性系统。同样，该方法也将适用于完整系统。所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)，用于欠驱动非线性系统的镇定和控制。该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，从而开发了一个可以为给定的欠驱动系统生成控制器的软件工具(工具箱)。该方法基于构造一类辅助稳定系统，每个辅助稳定系统都等价于具有适当控制器选择的原始系统。给出了欠驱动二自由度机构的仿真结果。包括倒立摆小车系统，并与现有的最新结果进行了比较，以验证理论的有效性。这种方法将推动非线性系统控制和非线性控制器领域的最新发展。这一研究结果将增强对一大类实际系统的控制能力，例如处于执行器故障模式的飞机和航天器、水下机器人和两足动物运动。为了证明这一方法的可行性，将开展一系列对照实验。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. ***