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

interconnection of two passive systems ensures convergence of the output to zero and stability (in the sense) of the closed‐loop. On the other hand, it is well‐known (van der Schaft, 2016) that PID controllers are (output strictly) passive systems – for all positive PID gains. Therefore, wrapping the PID around a passive output yields a stable system for all PID gains. Clearly, this situation simplifies the gain‐tuning task, since the designer is left with the only task of selecting, among all positive gains, those that ensure the best transient performance.

      PID‐PBCs have been successfully applied to a wide class of physical systems, see e.g. Aranovskiy et al. (2016), Castaños et al. (2009), Cisneros et al. (2015, 2016), De Persis and Monshizadeh (2017), Hernández‐Gómez et al. (2010), Meza et al. (2012), Romero et al. (2018), Sanders and Verghese (1992), and Talj et al. (2010). However, their application has mainly been restricted to academic circles. It is the authors' belief that PID‐PBCs have an enormous potential in engineering practice and should be promoted among practitioners. The main objective of the book is then to give prospective designers of PID‐PBCs the tools to successfully use this technique in their practical applications. Toward this end, we provide a basic introduction to the theoretical foundations of the topic, keeping the mathematical level at the strict minimum necessary to cover the material in a rigorous way, but at the same time to make it accessible to an audience more interested in its practical application. To fulfill this objective, we have skipped technically involved theoretical proofs – referring the interested reader to their adequate source – and we have included a large number of practical examples.

      We are aware that aiming at penetrating current engineering practice is a very challenging task. It is our strong belief that combining the unquestionable dominance of PIDs in applications with the fundamental property of passivity, which in the case of physical systems captures the universal feature of energy conservation, yields an unbeatable argument to justify its application.

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      2 S. Aranovskiy, R. Ortega, and R. Cisneros. A robust PI passivity‐based control of nonlinear systems and its application to temperature regulation. International Journal of Robust and Nonlinear Control, 26(10): 2216–2231, 2016.

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      7 R. Cisneros, M. Pirro, G. Bergna‐Díaz, R. Ortega, G. Ippoliti, and M. Molinas. Global tracking passivity‐based PI control of bilinear systems and its application to the boost and modular multilevel converters. Control Engineering Practice, 43(10): 109–119, 2015.

      8 R. Cisneros, R. Gao, R. Ortega, and I. Husain. PI passivity‐based control for maximum power extraction of a wind energy system with guaranteed stability properties. International Journal of Emerging Electric Power Systems, 17(5): 567–573, 2016.

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      11 M. Hernández-Gómez, R. Ortega, F. Lamnabhi‐Lagarrigue, and G. Escobar. Adaptive PI stabilization of switched power converters. IEEE Transactions on Control Systems Technology, 18(3): 688–698, 2010.

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      14 J. G. Romero, A. Donaire, R. Ortega, and P. Borja. Global stabilisation of underactuated mechanical systems via PID passivity‐based control. Automatica, 96(10): 178–185, 2018.

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      17 R. Talj, D. Hissel, R. Ortega, M. Becherif, and M. Hilairet. Experimental validation of a PEM fuel cell reduced order model and a moto‐compressor higher order sliding mode control. IEEE Transactions on Industrial Electronics, 57(6): 1906–1913, 2010.

      18 A. J. van der Schaft. ‐Gain and Passivity Techniques in Nonlinear Control. Springer‐Verlag, Berlin, 3rd edition, 2016.

Acknowledgments

      This book is the result of extensive research collaborations during the last 10 years. Some of the results of these collaborations have been reported in the papers (Bergna‐Díaz et al., 2019; Borja et al., 2016, 2020; Castaños et al., 2009; Chang et al., 2000; Cisneros et al., 2013, 2015, 2016, 2020; Donaire and Junco, 2009; Donaire et al., 2016a, 2017; Escobar et al., 1999; Ferguson et al., 2017a; Ferguson et al., 2017b, 2018, 2020; Gandhi et al., 2016; Hernández‐Gómez et al., 2012; Jaafar et al., 2013; Jayawardhana et al., 2007; Jung et al., 2015; Monshizadeh et al., 2019; Ortega et al., 2020; Pérez et al., 2004; Talj et al., 2009, 2010, 2011; Wu et al., 2020; Zhang et al., 2015, 2018; Zonetti and Ortega, 2015; Zonetti et al., 2015). We are grateful to our co‐authors, S. Aranovskiy, A. Astolfi, A. Allawieh, D. Bazylev, M. Becherif, A. Benchaib, G. Bergna‐Díaz, A. Bobtsov, F. Castaños, G. Chang, R. Cisneros, M. Crespo, G. Duan, D. Efimov, G. Escobar, G. Espinosa‐Pérez, J. Espinoza, J. Ferguson, P. Gandhi, R. Gao, E. García‐Canseco, E. Godoy, M. Hernández‐Gómez, M. Hilairet, D. Hissel, I. Husain, A. Jaafar, B. Jayawardhana, D. Jeltsema, S. Junco, F. Kazi, F. Lamnabhi‐Lagarrigue, Z. Liu, F. Mancilla‐David, R. Mehra, E. Mendes, R. H. Middleton, N. Monshizadeh, P. Monshizadeh, M. Pérez, M. Pirro, A. Pyrkin, S. Sánchez, S. Satpute, J. Scherpen, B. Siciliano, M. Singh, H. Su, R. Talj, E. Tedeschi, A. van der Schaft, D. Wu, M. Zhang, D. Zonetti, for several stimulating discussions and for their hospitality while visiting their institutions.

      Some of the topics of this book have been taught by the first author at the EECI Graduate School on Control in Istanbul, Turkey, in 2016, in the Winter Course of the Mexican Association of Automatic Control in 2016, in the Summer School of the Institute of Control Problems of the Academy of Sciences in Moscow, Russia, in 2017 and in the University of Chile, Santiago, Chile, in 2018. A workshop on this topic was organized in Zhejiang University, Hangzhou, China, in 2017.

A large part of this work would not have been possible without the financial support of several institutions. The first author would like to thank ITMO University in Saint Petersburg, Russia, for having sponsored part of this work and the Instituto Tecnológico Autónomo de México (ITAM) for opening its doors for the continuation of his scientific career in Mexico. The second author wishes to thank the Ecole Doctorale‐Sciences et Technologies de l'Information des Télécommunications et des Systèmes (ED‐STITS) for having funded his doctoral studies and the ITAM for supporting his research activities. The third author wants to thank the National Council of Science and Technology (CONACyT), the Mexican Secretary of Public Education (SEP), and the University of Groningen for all the support received during his academic career. The fourth author wants to thank the University of Newcastle for supporting his research and academic activities.

      Mexico/Groningen/Newcastle