Romero Pérez, Julio ArielMiguel-Escrig, OscarSánchez Moreno, JoséDormido Canto, Sebastián2026-01-142026-01-142025-12-09Romero-Pérez, J.-A., Miguel-Escrig, O., Sánchez-Moreno, J., & Dormido-Bencomo, S. (2026). Identification of multiple frequency response points using gain-changing nonlinear feedback experiments. European Journal of Control, 87. https://doi.org/10.1016/J.EJCON.2025.1014370947-3580https://doi.org/10.1016/j.ejcon.2025.101437https://hdl.handle.net/20.500.14468/31408The registered version of this article, first published in “European Journal of Control, 87", is available online at the publisher's website: https://doi.org/10.1016/j.ejcon.2025.101437La versión registrada de este artículo, publicado por primera vez en “European Journal of Control, 87", está disponible en línea en el sitio web del editor: https://doi.org/10.1016/j.ejcon.2025.101437Relay feedback experiments are well known for providing valuable information about system dynamics, which can be used for automatic PID controller tuning. The estimation of frequency response points from data obtained in such experiments is typically based on describing function theory, which assumes purely sinusoidal closed-loop responses and neglects higher-order harmonics. However, this assumption is often violated in low-order systems with poor filtering characteristics, resulting in reduced estimation accuracy. To address this issue, several alternatives, such as the saturation relay and pre-load relay, have been proposed in the literature, offering improved estimation performance. In this work, it is introduced a gain-changing nonlinear scheme for frequency points identification that enhances the accuracy of existing approaches. The experiments follow a similar structure to standard relay feedback tests, thus preserving their well-known advantages while significantly reducing estimation errors. Furthermore, by incorporating calculated time delays and dynamically adjusting the gain-changing parameters, the method generates multiple closed-loop oscillation conditions to identify several frequency response points, all while keeping the output amplitude within safe operational limits. Simulation results demonstrate a substantial improvement in estimation accuracy compared to both traditional and enhanced relay-based methods, offering a precise and practical solution for frequency response identification in industrial process control.eninfo:eu-repo/semantics/openAccess1203.17 InformáticaartículoIdentificationExperimentRelayGain-changing