PID Passivity-Based Control of Nonlinear Systems with Applications. Romeo Ortega

DDC 629.8/36–dc23

      LC record available at https://lccn.loc.gov/2021024088 LC ebook record available at https://lccn.loc.gov/2021024089

      Cover Design: Wiley

      Cover Image: © marty8801/iStock/Getty Images

      To the memory of my mother – Romeo.

      To the memory of my mother; and to Salua, Patricia, Liliana and Vianca with all my love – José Guadalupe.

      To Celia with all my love. To my parents, Diana and Mario – Pablo.

      To Delfina, Phoebe and Cristina – Alejandro.

Author Biographies

      Romeo Ortega was born in Mexico. He obtained his BSc in Electrical and Mechanical Engineering from the National University of Mexico, Master of Engineering from Polytechnical Institute of Leningrad, USSR, and the Docteur D‘Etat from the Polytechnical Institute of Grenoble, France in 1974, 1978 and 1984 respectively.

      He then joined the National University of Mexico, where he worked until 1989. He was a Visiting Professor at the University of Illinois in 1987–1988 and at McGill University in 1991–1992, and a Fellow of the Japan Society for Promotion of Science in 1990–1991. He was a member of the French National Research Council (CNRS) from June 1992 to July 2020, where he was a “Directeur de Recherche” in the Laboratoire de Signaux et Systemes (CentraleSupelec) in Gif‐sur‐Yvette, France. Currently, he is a full time Professor at ITAM in Mexico. His research interests are in the fields of nonlinear and adaptive control, with special emphasis on applications.

      He has published five books and more than 350 scientific papers in international journals, with an h‐index of 84. He has supervised more than 35 PhD thesis. He is a Fellow Member of the IEEE since 1999 (Life 2020) and an IFAC Fellow since 2016. He has served as chairman in several IFAC and IEEE committees and participated in various editorial boards of international journals. He is currently Editor in Chief of International Journal of Adaptive Control and Signal Processing and Senior Editor of Asian Journal of Control.

José Guadalupe Romero was born in Tlaxcala, Mexico in 1983. He received the BS degree in electronic engineering from the University of Zacatecas, Zacatecas, Mexico, in 2006 and the MSc degree in robotics and advanced manufacturing from the Centre for Research and Advanced Studies, National Polytechnic Institute (CINVESTAV), Mexico, in 2009. He obtained the PhD degree in Control Theory from the University of Paris‐Sud XI, France in 2013.

      He was a postdoctoral fellow at Schneider electric and EECI in Paris France and at the Laboratoire d'Informatique, de Robotique et de Microélectronique de Montpellier (LIRMM) in 2014 and 2015, respectively. Currently, he is an associate professor and researcher at the Digital Systems Department at the Instituto Tecnológico Autónomo de México (ITAM) and since 2019 he is the Director of undergraduate mechatronics engineering program.

      His research interests are focused on nonlinear and adaptive control, stability analysis and the state estimation problem, with application to mechanical systems, aerial vehicles, mobile robots and multi‐agent systems.

      Pablo Borja was born in Mexico City, Mexico. He obtained the B.Eng. in Electrical and Electronic Engineering and the M.Eng. from the National Autonomous University of Mexico in 2011 and 2014, respectively, and the PhD in Control Systems from the University Paris Saclay, France, in 2017.

From 2017 to 2018, he was a postdoctoral researcher member of the Engineering and Technology Institute Groningen (ENTEG) at the University of Groningen (RUG). Since 2018 he is a fellow of the Faculty of Science and Engineering and ENTEG member at the RUG. His research interests encompass the control and analysis of nonlinear systems, passivity‐based control, control of physical systems, passivity and its role in control theory, and model reduction.

      Alejandro Donaire received the Electronic Engineering and PhD degrees in 2003 and 2009, respectively, from the National University of Rosario, Argentina. His work was supported by the Argentine National Council of Scientific and Technical Research, CONICET. In 2009, he joined the Centre for Complex Dynamic Systems and Control at The University of Newcastle, Australia, and in 2011, he received the Postdoctoral Research Fellowship of the University of Newcastle, Australia. From 2015 to March 2017 he was with the PRISMA Lab at the University of Naples Federico II, and from 2017 to 2019 with the Institute for Future Environments, School of Electrical Engineering and Computer Science, Queensland University of Technology, Australia. In 2019, he joined the School of Engineering, The University of Newcastle, Australia, where he conducts his academic activities. His research interests include nonlinear and energy‐based control theory with application to electrical drives, multi‐agent systems, robotics, smart micro‐grids networks, marine and aerospace mechatronics, and power systems.

Preface

It is widely recognized that proportional‐integral‐derivative (PID) control offers the simplest and yet most efficient solution to many real‐world control problems. It is said to be a universal controller in the sense that the integral action takes care of the past, the proportional one of the present, and the derivative term has a predictive effect. Since the invention of PID control in 1910, the popularity of PID control has grown tremendously (Ang et al., 2005; Åstrom and Hägglund, 1995, 2006; Samad, 2017).

      It is interesting to quote a 2018 report of Karl Åstrom (Åstrom, 2018) where he points out the following:

       In spite of the predictions that other control techniques, e.g. model predictive control (MPC), will make, the PID obsolete, more than 90% of industrial controllers are still implemented based around PID algorithms.

       In a report of Bill Bialkowski of the Canadian consulting company Entech, it is indicated that out of 3000–5000 control loops in the paper mill industry, 97% use proportional‐derivative (PI) and the remaining 3% are MPC, adaptive, etc.

       In the same report it is indicated that, out of the 50% of the PIDs that do not work well, 30% are due to bad tuning.

Indeed, it is very well known that PID controllers yield, in general, a satisfactory performance provided they are well tuned. The need to fulfill this requirement has been the major driving force of the research on PID control, with the vast majority of the reports related to the development of various PID tuning techniques, which are customarily based on a linear approximation of the plant around a fixed operating point (or a given trajectory). When the range of operation of the system is large, the linear approximation is invalidated and the procedure to tune the gains of PID regulators is a challenging task. Although gain scheduling, auto tuning, and adaptation provide some help to overcome this problem, they suffer from well‐documented drawbacks that include being time‐consuming and fragility of the design. The interested reader is referred to Ang et al. (2005) for a recent, detailed account of the various trends and topics pertaining to PID tuning.

      The present book is devoted to the study of PID passivity‐based control (PBC), which provides a solution to the tuning problem of PID control of nonlinear systems. The underlying principle for the operation of PID‐PBC is, as the name indicates, the property of passivity, which is a fundamental property of dynamical systems. One of the foundational results