Rotor imbalance suppression by optimal control
Abstract
An imbalanced rotor is considered. A system of moving balancing masses is given. We determine the optimal movement of the balancing masses to minimize the imbalance on the rotor. The optimal movement is given by an open‐loop control solving an optimal control problem posed in infinite time. By methods of the Calculus of Variations, the existence of the optimum is proved and the corresponding optimality conditions have been derived. Asymptotic behavior of the control system is studied rigorously. By Łojasiewicz inequality, convergence of the optima as time towards a steady configuration is ensured. An explicit estimate of the convergence rate is given. This guarantees that the optimal control stabilizes the system. In case the imbalance is below a computed threshold, the convergence occurs exponentially fast. This is proved by the Stable Manifold Theorem applied to the Pontryagin optimality system. Moreover, a closed‐loop control strategy based on Reinforcement Learning is proposed. Numerical simulations have been performed, validating the theoretical results.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Sep 24, 2021
- Source ID
- 10.1002/oca.2780
Entities
People
- Darío Pighin
- Matteo Gnuffi
- Noboru Sakamoto
Organizations
- Air Force Office of Scientific Research
- Alexander von Humboldt Foundation
- Autonomous University of Madrid
- Basque Government
- German Research Foundation
- Japan Society for the Promotion of Science
- Marie Skłodowska-Curie Actions
- Nanzan University