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PID Principles to Obtain Adaptive Variable Gains for a Bi-order Sliding Mode Control


A new model to obtain adaptive variable gains for a bi-order Sliding Mode Control is proposed in this work. The variable gains for the controller are designed to dynamically adapt their values, using principles of the well-known Proportional-Integral-Derivative control technique, where the magnitude of the tracking error is the signal feedback. According the way to tune parameters, it can become a first-order or a second-order controller. This design takes into account the actuators constraints (operational limits of the plant to control). As a result of the adaptive properties of the proposed scheme, the new controller significantly reduces the energy consumption in control processes, and it rejects the so called chattering-effect, simultaneously maintaining the main robust properties of the Sliding Mode strategy. In order to show the feasibility and effectiveness of the proposed design, simulation results are presented, where the performance of the proposed controller is compared with the conventional Sliding Modes of order one and two, and also with the classical PID controller. A strong stability analysis in the sense of Lyapunov is presented, showing global exponential stability for the equilibrium point of the closed-loop control system when the proposed control design is used.

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Corresponding author

Correspondence to Sergio Alvarez-Rodríguez.

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Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Recommended by Associate Editor Guangdeng Zong under the direction of Editor Hamid Reza Karimi. This work was partially supported by the FORDECYT-CONACYT under grant 292399 of the National Council of Science and Technology in Mexico (CONACYT).

Sergio Alvarez-Rodríguez received his post-graduated degree in mechatronics engineering from Centro Nacional de Investigación y Desarrollo Tecnológico, México, in 2007. He received a Ph.D. degree in Science and Technology from Universidad de Guadalajara, México, in 2014, and from February 2016 to July 2017 he made a post-doctoral stay at Optical Research Center, AC. He is currenlty a full time researcher professor at TecMM, Lagos de Moreno, Jalisco, México. His areas of interest are on robotics, control theory, and sensors for instrumentation.

Gerardo Flores received his B.S. degree in Electronic Engineering with honors from the Instituto Tecnológico de Saltillo, México in 2000; an M.S. degree in Automatic Control from CINVESTAV-IPN, Mexico City, in 2010; and a Ph.D. degree in Systems and Information Technology from the Heudiasyc Laboratory of the Université de Technologie de Compiègne — Sorbonne Universités, France in October 2014. Since August 2016, he has been a full time researcher and the head of the Perception and Robotics LAB with the Center for Research in Optics, León Guanajuato, Mexico. His research interests are focused on the theoretical and practical problems arising from the development of autonomous robotic systems and vision systems. Dr. Flores has published more than 40 papers in the areas of control systems, computer vision and robotics.

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Alvarez-Rodríguez, S., Flores, G. PID Principles to Obtain Adaptive Variable Gains for a Bi-order Sliding Mode Control. Int. J. Control Autom. Syst. 18, 2456–2467 (2020).

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  • Chattering-effect
  • Lyapunov stability approach
  • PID control
  • sliding mode control