Multi-Predictor Based Scheme for the Stabilization of Delayed First-Order Systems

https://doi.org/10.58571/CNCA.AMCA.2024.061

Resumen: The stabilization and control of continuous linear systems with delay are significant challenges, as well as the complexity of their analysis, which offers important research opportunities. This article presents a prediction-based scheme to control a first-order system with an unstable pole and any size of time delay. Moreover, the necessary and sufficient conditions are provided to ensure the stability of the closed-loop system with static output feedback. To implement the strategy, a scheme based on an observer-predictor is developed to mitigate the impact of the delay. This method involves partitioning the time delay into a serie of sub-predictors, where each one estimates the signal with its assigned portion of the delay. This approach ensures an accurate estimation of the complete desired signal, allowing the application of a classical controller using the signal before been delayed to stabilize the system. The main contribution of this work is to establish a minimum number of sub-predictors such that the closed-loop system can be stabilized regardless of the delay size. Finally, an example with simulation is presented to illustrate the obtained results.

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Cabañez Vilchis, A.D., Urquiza Castro, A., Vazquez Guerra, R.J., Del Muro Cuéllar, B. & Marquez Rubio, J.F. (2024). Multi-Predictor Based Scheme for the Stabilization of Delayed First-Order Systems. Memorias del Congreso Nacional de Control Automático 2024, pp. 356-361. https://doi.org/10.58571/CNCA.AMCA.2024.061

Palabras clave

Stability, delay, unstable systems, predictor, observer

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