Control of Linear Time-Delay Actuators Based on Virtual Reference Trajectory

Gómez-Rosas, Carlos; Portillo-Vélez, Rogelio de J.; Fernández-Anaya, Guillermo; Vásquez-Santacruz, J. Alejandro; Marín-Urías, Luis F.; Alazki, Hussain

doi:10.3390/act15070391

Open AccessArticle

Control of Linear Time-Delay Actuators Based on Virtual Reference Trajectory

by

Carlos Gómez-Rosas

¹

,

Rogelio de J. Portillo-Vélez

^1,2,*

,

Guillermo Fernández-Anaya

³

,

J. Alejandro Vásquez-Santacruz

^1,2

,

Luis F. Marín-Urías

^1,2

and

Hussain Alazki

⁴

¹

Faculty of Construction and Habitat Engineering, Universidad Veracruzana, Boca del Río 94294, Veracruz, Mexico

²

Faculty of Electric and Electronics Engineering, Universidad Veracruzana, Boca del Río 94294, Veracruz, Mexico

³

Mathematics and Physics Department, Universidad Iberoamericana Ciudad de México, Mexico City 01219, Mexico

⁴

Engineering Faculty, Universidad Autónoma del Carmen, Ciudad del Carmen 24180, Campeche, Mexico

^*

Author to whom correspondence should be addressed.

Actuators 2026, 15(7), 391; https://doi.org/10.3390/act15070391

Submission received: 6 June 2026 / Revised: 29 June 2026 / Accepted: 9 July 2026 / Published: 11 July 2026

(This article belongs to the Special Issue New Control Schemes for Actuators—3rd Edition)

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Abstract

A control approach for linear actuators with time delay is introduced. The novelty of the proposal is the inclusion of a virtual reference trajectory (VRT) without modifying the controller architecture, allowing the stability margin of a single-delay actuator controller to be increased; in the ideal case, the proposed approach can render stability independent of delay. Moreover, a slight modification of the dynamics of the virtual trajectory allows the closed-loop system to be expressed as a neutral time-delay system. Therefore, its stability analysis is performed using the Lyapunov–Krasovskii approach, yielding theoretical conditions that allow the critical time delay to be computed. Numerical simulations and experiments on the control of a DC motor actuator with a control input time delay validate our proposal.

Keywords: linear actuator; time delay; control; stability; virtual reference trajectory

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MDPI and ACS Style

Gómez-Rosas, C.; Portillo-Vélez, R.d.J.; Fernández-Anaya, G.; Vásquez-Santacruz, J.A.; Marín-Urías, L.F.; Alazki, H. Control of Linear Time-Delay Actuators Based on Virtual Reference Trajectory. Actuators 2026, 15, 391. https://doi.org/10.3390/act15070391

AMA Style

Gómez-Rosas C, Portillo-Vélez RdJ, Fernández-Anaya G, Vásquez-Santacruz JA, Marín-Urías LF, Alazki H. Control of Linear Time-Delay Actuators Based on Virtual Reference Trajectory. Actuators. 2026; 15(7):391. https://doi.org/10.3390/act15070391

Chicago/Turabian Style

Gómez-Rosas, Carlos, Rogelio de J. Portillo-Vélez, Guillermo Fernández-Anaya, J. Alejandro Vásquez-Santacruz, Luis F. Marín-Urías, and Hussain Alazki. 2026. "Control of Linear Time-Delay Actuators Based on Virtual Reference Trajectory" Actuators 15, no. 7: 391. https://doi.org/10.3390/act15070391

APA Style

Gómez-Rosas, C., Portillo-Vélez, R. d. J., Fernández-Anaya, G., Vásquez-Santacruz, J. A., Marín-Urías, L. F., & Alazki, H. (2026). Control of Linear Time-Delay Actuators Based on Virtual Reference Trajectory. Actuators, 15(7), 391. https://doi.org/10.3390/act15070391

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Control of Linear Time-Delay Actuators Based on Virtual Reference Trajectory

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