An Improved Technique for Modeling and Control of Flexible Structures
Krauss, Ryan Walter
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Control design for flexible robots is a challenging problem. Part of the difficulty comes from a lack of controls-focused modeling tools. Practical flexible robots have several aspects that make them difficult to model: continuous elements, complicated actuators, multiple feedback loops, non-collocated sensors and actuators, and the ability to take on arbitrary three-dimensional poses. Even if existing techniques for modeling flexible structures could model the closed-loop response of a hydraulically-actuated flexible robot with a vibration suppression controller, how would such a model be used for control design? This work presents the development of a modeling approach that meets the needs of a controls engineer. The approach is based on the transfer matrix method (TMM). The TMM has been expanded in several ways to enable it to accurately model practical flexible robots. Quantitative agreement is shown between model and experiment for the interaction of a hydraulic actuator and a flexible structure as well as for the closed-loop response of a system with vibration suppression. Once the ability to model the closed-loop response of the system has been demonstrated, this work focuses on using the model for control design. Control design is facilitated by symbolic implementation of the TMM, which allows closed-form expressions for the closed-loop response of the system to be found without discretization. These closed-form expressions will be transcendental transfer functions for systems with continuous elements. These transfer functions can then be used in various optimization approaches for designing the closed-loop system response.