Unfalsified control based on the H∞ controller parameterisation

Abstract

This paper presents an implementation of the unfalsified control (UC) method using the Riccati-based parameterisation of ${\mathcal{H}}_{\infty }$ controllers. The method provides an infinite controller set to (un)falsify the real-time data streams seeking for the best performance. Different sets may be designed to increase the degrees of freedom of the set of controller candidates to perform UC. In general, a set of m central controllers could be designed, each one seeking different objectives and all with their own parameterisation as a function of a stable and bounded transfer matrix. For example, one controller parameterisation could be designed to solve the robust stability of a model set which covers the physical system, therefore guaranteeing feasibility. The implementation requires the online optimisation of either quadratic fractional or quadratic problems, depending on the selection of the cost function. A multi-input, multi-output (MIMO) time-varying model of a permanent magnet synchronous generator illustrates the use of this technique.

Keywords:

• unfalsified control
• ${\mathcal{H}}_{\infty }$ controller parameterisation
• linear fractional transformation (LFT)

Acknowledgements

The research of F.D. Bianchi was supported by the European Regional Development Funds (ERDF, ‘FEDER Programa Competitivitat de Catalunya 2007-2013’). R.S. Sánchez Peña and P. Colmegna were supported by the program PRH No. 71 (PICT 290 and PFDT) of the Ministry of Science, Technology and Innovation of Argentina.

Notes

1. The UC problem is feasible if there exists at least one stabilising controller in the candidate set, see Stefanovic and Safonov (2011).

2. There are no bounds on the time it takes for V to detect an unstable closed-loop system (Dehghani, Anderson, & Lanzon, 2007).

3. Note that in the context of ${\mathcal{H}}_{\infty }$ control theory, performance is based on an infinite amount of data, whereas in UC it refers to a finite amount of data points $\mathcal{Z}$, as defined in Section 2.1.

Additional information

Notes on contributors

R.S. Sánchez-Peña

Ricardo S. Sánchez-Peña is an electronic engineer from the University of Buenos Aires (UBA, 1978), MS and PhD from the California Institute of Technology (1986 and 1988, respectively). In Argentina he worked in CITEFA, CNEA and the space agencies CNIE and CONAE. He collaborated with NASA in aeronautical and satellite projects and with the German (DLR) and Brazilian (CTA/INPE) space agencies. He was a full professor at UBA (1989–2004), ICREA Senior Researcher at the Universitat Politècnica de Catalunya (2005–2009, Barcelona) and visiting professor/researcher at the California Institute of Technology, Pennsylvania State University, Virginia Polytechnic Institute & State University, Purdue University and Universidad Politécnica de Valencia. He has consulted for ZonaTech (USA), STI and VENG (Argentina) in aerospace applications and with Alstom-Ecotecnia (Spain) in wind turbine applications. He has published three books in Edit. Control (1992 and 1999), Wiley (1998) and Springer (2007), and more than 120 articles in journals and proceedings. Since 2009 he has been heading the PhD Department in Engineering at the Buenos Aires Institute of Technology (ITBA) and is a CONICET Principal Investigator. He is interested in identification and control and has applied them to acoustics, mechanics, aeronautics and astronautics engineering and in the last years to Diabetes type I.

P. Colmegna

Patricio Colmegna was born in Buenos Aires, Argentina, on 4 April 1987. He received his BS degree in automation and industrial control engineering from the Universidad Nacional de Quilmes (UNQ), Buenos Aires, Argentina, in 2010. He is currently pursuing his PhD degree in automatic control at the Instituto Tecnológico de Buenos Aires (ITBA), Buenos Aires, Argentina, being supported by a research scholarship from the Agencia Nacional de Promoción Científica y Tecnológica, Ministerio de Ciencia y Tecnología e Innovación Productiva, Argentina. He is also working as a teaching assistant in control systems courses at UNQ. His research interests include modelling, identification and robust control for type 1 diabetes mellitus and mechatronics.

F. Bianchi

Fernando D. Bianchi received his BS and PhD degrees in electronic engineering from the National University of La Plata (UNLP), Argentina, in 1999 and in 2005, respectively. From 1999 to 2006, he was a PhD student and a postdoctoral fellow at the Laboratory of Industrial Electronic, Control and Instrumentation (LEICI, UNLP, La Plata, Argentina). From 2006 to 2010, he was a postdoctoral researcher at the Technical University of Catalonia, Barcelona, Spain. In 2010, he joined the Power Electronics and Electric Power Grids Group, Catalonia Institute for Energy Research (IREC), Barcelona, as a scientific researcher. His main research interests include robust control and linear parameter-varying systems and their applications to the control of renewable energy conversion systems.