NDLI: On Control of a Two-Link Non-Fixed-Base Inverted Pendulum With Guaranteed Uniqueness

Content Provider	The American Society of Mechanical Engineers (ASME) Digital Collection
Author	Zeng, Hairong Wu, Qiong Sepehri, Nariman
Copyright Year	2004
Abstract	A nonlinear controller with guaranteed uniqueness of Filippov’s solution is presented for controlling a two-link non-fixed-base inverted pendulum. The control system is described by differential equations with discontinuous right-hand sides, which violates the requirements of the conventional solution theories to ordinary differential equations, i.e., the vector fields must be at least Lipschitz continuous. It has been shown that Lyapunov’s second method can be used for such non-smooth systems directly under the condition of existence and uniqueness of Filippov’s solution. For this non-smooth control system with three discontinuity surfaces, the uniqueness of the solution is studied using Filippov’s solution concept. The system itself is a nonlinear, non-autonomous dynamic system without an isolated equilibrium point, which violates the assumption of Lyapunov’s stability theory. To analyze the stability of the control system, a Lyapunov-like function is constructed, which satisfies all the requirements for a Lyapunov function. Such a function can serve as an upper bound of the region in which the pendulum can be stabilized. Simulation results are presented to validate the proposed approach.
Sponsorship	Dynamic Systems and Control Division
Starting Page	1391
Ending Page	1397
Page Count	7
File Format	PDF
ISBN	0791847063
DOI	10.1115/IMECE2004-61239
Volume Number	Dynamic Systems and Control, Parts A and B
Conference Proceedings	ASME 2004 International Mechanical Engineering Congress and Exposition
Language	English
Publisher Date	2004-11-13
Publisher Place	Anaheim, California, USA
Access Restriction	Subscribed
Subject Keyword	Stability Simulation results Dynamic systems Pendulums Equilibrium (physics) Differential equations Control equipment Control systems
Content Type	Text
Resource Type	Article

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