Linear Algebra Based Control: Application to a second order chained form system

Authors

  • Leandro Pedro Faustino Rodriguez Aguilar Instituto de Ingeniería Química, Universidad Nacional de San Juan (UNSJ), CONICET, Av. Lib. San Martín Oeste 1109, San Juan J5400ARL, Argentina https://orcid.org/0000-0002-8267-6711
  • María Cecilia Fernández Puchol Instituto de Ingeniería Química, Universidad Nacional de San Juan (UNSJ), CONICET. https://orcid.org/0000-0002-9311-1556
  • Mabel Cristina Sánchez Planta Piloto de Ingeniería Química, Universidad Nacional del Sur, CONICET https://orcid.org/0000-0002-0647-2717
  • Gustavo Javier Scaglia Instituto de Ingeniería Química, Universidad Nacional de San Juan (UNSJ), CONICET. https://orcid.org/0000-0002-0188-0017

Keywords:

non-holonomic system, linear algebra, nonlienar tracking control, positioning

Abstract

Control of underactuated systems with non-holonomic constraints has been an issue of interest in recent years. These systems are hard to control because their linearization makes them uncontrollable and current approaches generally involve complex calculations. In this manuscript, a controller for trajectory tracking and positioning for a second-order chained form system using a simple approach based on linear algebra is proposed. The control law is formulated by setting two of the six variables trajectories, while the other four are calculated assuming the equations system has an exact solution, and ensuring the error tends to zero. The stability of the proposed control system is demonstrated through the Khalil Lemma, and simulations show the performance of the controller.

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Author Biographies

Leandro Pedro Faustino Rodriguez Aguilar, Instituto de Ingeniería Química, Universidad Nacional de San Juan (UNSJ), CONICET, Av. Lib. San Martín Oeste 1109, San Juan J5400ARL, Argentina

Leandro Rodriguez received the Food Processing Engineering degree from the National University of San Juan – Argentina, in 2008. Then, he received the Ph.D. in Chemical Engineering from the National University of the South – Argentina, in 2015. At this time, he is dedicated to process engineering, specifically to optimization and control of multivariable nonlinear systems. His main research interests include modeling, state estimation, optimization, sensor location and trajectory tracking control of chemical process and water systems.

María Cecilia Fernández Puchol, Instituto de Ingeniería Química, Universidad Nacional de San Juan (UNSJ), CONICET.

Cecilia Fernández received the Food Processing Engineering degree from the National University of San Juan - Argentina, in 2014. Then she received the Doctorate in Chemical Engineering - Mention Clean Processes degree from the National University of San Juan - Argentina, in 2019. At this time, she is dedicated to process engineering, specifically to optimization and control of multivariable non-linear processes. Her main research interests include modeling, state estimation, and trajectory tracking control of biochemical processes.

Mabel Cristina Sánchez, Planta Piloto de Ingeniería Química, Universidad Nacional del Sur, CONICET

Mabel Sánchez received the Chemical Engineering degree from the National University of the South, Argentina, in 1982, and the Ph.D. in Chemical Engineering from the National University of the South, Argentina, in 1996. She is a Research Fellow of the Council for Scientific and Technological Research, Argentina, since 2001. She leads different technological projects and at this time, she is dedicated to process engineering, specifically to monitoring and statistical process control of nonlinear systems. Her main research interests include robust state estimation, sensor network design, and statistical process control of chemical process and water systems.

Gustavo Javier Scaglia, Instituto de Ingeniería Química, Universidad Nacional de San Juan (UNSJ), CONICET.

Gustavo Scaglia received the Eng. degree in Electronic Engineering with orientation in Control Systems from the National University of San Juan, Argentina, in 1999, and the Ph.D in Control Systems from the Institute of Automatic Control at the National University of San Juan, Argentina in 2006, his work was about a new tracking trajectories algorithms. He is a Research Fellow of the Council for Scientific and Technological Research, Argentina, since 2011. He leads different technological projects and his current scientific research at the Engineering Chemical Institute from National University of San Juan. His main interests are algorithms for tracking trajectories, nonlinear and adaptive control theory, and mechanical and chemical process.

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Published

2021-03-29

How to Cite

Rodriguez Aguilar, L. P. F., Fernández Puchol, M. C., Sánchez, M. C., & Scaglia, G. J. (2021). Linear Algebra Based Control: Application to a second order chained form system. IEEE Latin America Transactions, 19(9), 1435–1442. Retrieved from https://latamt.ieeer9.org/index.php/transactions/article/view/4527

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