In this paper we present an energy-based algorithm to minimize limit cycles in dynamically balancing wheeled inverted pendulum (IP) machines. Because the algorithm is not based on the numerical value of parameters, performance is robust and accounts for mechanical reconfiguration and wear. The effects of phenomena such as drive-train friction, rolling friction, backlash and sensor bandwidth are well known, causing either limit cycles or instabilities in IP balancing machines and yet compensation or control design to mitigate these effects are not well known. The effects of these non-linearities can be observed in the energy behavior of IP balancing machines, hence, as a broader goal we seek to establish an energy-based framework for the investigation of non-linearities in this class of machines. We successfully demonstrate the effectiveness of our algorithm on a two-wheeled IP balancing machine, “Charlie”, developed in our laboratory. As an example we show a reduction in the amplitude of limit cycles by 95.9% in wheel angle and 89.8% in pitch over a 10 second period.
- Dynamic Systems and Control Division
Energy-Based Limit Cycle Compensation for Dynamically Balancing Wheeled Inverted Pendulum Machines
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Vasudevan, H, Dollar, AM, & Morrell, JB. "Energy-Based Limit Cycle Compensation for Dynamically Balancing Wheeled Inverted Pendulum Machines." Proceedings of the ASME 2013 Dynamic Systems and Control Conference. Volume 2: Control, Monitoring, and Energy Harvesting of Vibratory Systems; Cooperative and Networked Control; Delay Systems; Dynamical Modeling and Diagnostics in Biomedical Systems; Estimation and Id of Energy Systems; Fault Detection; Flow and Thermal Systems; Haptics and Hand Motion; Human Assistive Systems and Wearable Robots; Instrumentation and Characterization in Bio-Systems; Intelligent Transportation Systems; Linear Systems and Robust Control; Marine Vehicles; Nonholonomic Systems. Palo Alto, California, USA. October 21–23, 2013. V002T33A001. ASME. https://doi.org/10.1115/DSCC2013-3843
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