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

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.

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

Romeo Ortega

José Guadalupe Romero

Pablo Borja

Alejandro Donaire

ACalternate currentAMMassumed modes methodCbIcontrol by interconnectionCLcontrolled LagrangiansDACdigital‐to‐analog converterDCdirect currentDOFdegree(s)‐of‐freedomELEuler–LagrangeFOCfield‐oriented controlGASglobally asymptotically stableGESglobal exponential stabilityHVDChigh‐voltage direct currentIAintegral actionIDAinterconnection and damping assignmentIISSintegral input‐to‐state stabilityISSinput‐to‐state stabilityLMIlinear matrix inequalityLTIlinear time‐invariantMDICSmatched disturbance integral controlled systemPBCpassivity‐based controlPDEpartial differential equationPEMproton exchange membranepHport‐HamiltonianPDproportional‐derivativePIproportional‐integralPIDproportional‐integral‐derivativePMSGpermanent magnet synchronous generatorPMSMpermanent magnet synchronous motorPWMpulse‐width modulationSPRstrictly positive realVSRvoltage source rectifiersVTOLvertical take‐off and landing

Given a vector , the symbol denotes its Euclidean norm, i.e. . We denote the th element of as . The th element of the canonical basis of is represented by . To ease the readability, column vectors are also expressed as .

Consider the matrix , then denotes the th column of , the th row of , and the th element of . Moreover, denotes the transpose of . Given a square matrix , . To simplify the notation, we express diagonal matrices as , where are the diagonal elements of the matrix.