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Analysis of internal dynamics in trajectory tracking problems

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Abstract

This work aims to develop a methodology to stabilize the internal dynamics motion considering the second time-derivative trajectory of the system output. For such a purpose, a partitionnement of the generalized coordinates explicit the output and the unobserved coordinates. In sequence, the equation of motion is algebraically modified resulting in a nonlinear differential equation, where states are the unobserved coordinates, and the input represent the second time-derivative of the output related to the original system. A dynamic programming and a collocation method are used to formulate the optimisation problems based on the optimal control theory. The internal dynamics is analyzed; the related optimal feedback control and feedforward control are designed using different methods. The algorithm will search for optimal trajectories of the internal dynamics that stabilizes the system in a constrained motion. The methodology is illustrated in simulation mode considering semi-passive, soft and flexible manipulators in 2D and a rotary inverted pendulum in 3D.

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  1. Mechanical Engineering Department, Federal University of Pernambuco: Universidade Federal de Pernambuco, Recife, Brazil

    Guaraci Bastos Jr.

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Bastos, G. Analysis of internal dynamics in trajectory tracking problems. Int. J. Dynam. Control 11, 2870–2885 (2023). https://doi.org/10.1007/s40435-023-01161-1

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  • DOI: https://doi.org/10.1007/s40435-023-01161-1

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