Abstract
In this paper a sliding mode control with variable gains is proposed. Such a controller has chatteringeffect reduction without detriment to the robustness properties of the sliding modes. The key idea behind the control design is that the variable gains magnitude is proportional to the trajectory tracking error magnitude. Also, this design establishes a connection between both the first and the second order sliding modes control. It is demonstrated that the proposed controller does not overestimates disturbances, which significantly reduces the control energy used. Finally, a stability analysis in the sense of Lyapunov is developed to demonstrate finite time convergence to the origin; simulations experiments are carried out to show the effectiveness and robustness of the proposed controller.
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Recommended by Associate Editor Juhoon Back under the direction of Editor Jessie (Ju H.) Park. This work was partially supported by the FORDECYT-CONACYT under grant 000000000292399 and the National Laboratory of Vision Optics of the National Council of Science and Technology in Mexico (CONACYT) agreement number 293411.
Sergio Alvarez-Rodríguez received the post-graduated degree in mechatronics engineering from Centro Nacional de Investigación y Desarrollo Tecnológico, México, in 2007 and the Ph.D. degree in Science and Technology from Universidad de Guadalajara, México, in 2014, from February 2016 to July 2017 he made a post-doctoral stay at Optical Research Center, AC. He is currenlty 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 the B.S degree in Electronic Engineering with honors from the Instituto Tecnológico de Saltillo, México in 2000; the M.S. degree in Automatic Control from CINVESTAV-IPN, Mexico City, in 2010; and the 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. From November 2014 to July 2016, he was a post-doctoral researcher with the Centro de Investigacién y de Estudios Avanzados del Instituto Politécnico Nacional, Mexico City. Since August 2016, he has been full time researcher and 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. He is especially interested in: artificial vision, theory and applications of intelligent systems, nonlinear control, design, conception and control of UAVs. Dr. Flores has published more than 30 papers in the areas of control systems, computer vision and robotics. He has been member of the Sistema Nacional de Investigadores since 2014.
Noé Alcalá Ochoa received his BSc degree in physics with a major in mathematics from the Universidad Michoacana México, in 1986, and his MSc and PhD degrees from Optical Research Center (CIO), México, in 1990 and 1997, respectively. Since then, he has been a researcher at CIO. His main research interests include nondestructive optical testing (ESPI, moiré, interferometry, profilometry), optical superresolution, and microscopy.
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Alvarez-Rodríguez, S., Flores, G. & Ochoa, N.A. Variable Gains Sliding Mode Control. Int. J. Control Autom. Syst. 17, 555–564 (2019). https://doi.org/10.1007/s12555-018-0095-9
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DOI: https://doi.org/10.1007/s12555-018-0095-9