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Control of systems with sector-bounded nonlinearities: robust stability and command effort minimization by disturbance rejection

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Abstract

The paper shows that a control strategy with disturbance rejection is able to reduce the control effort to a minimum, ensuring at the same time a desired performance level. The disturbance to be rejected is completely unknown, except for a sectorial bound. The control unit is endowed with an extended state observer which includes a disturbance dynamics, whose state tracks the unknown disturbance to be rejected. In summary, the novel contributions of the paper are the following. First, we derive a robust stability condition for the proposed control scheme, holding for all the nonlinearities that are bounded by a known (or estimated) maximum slope. Second, we propose a novel approach for designing the observer and state feedback gains, which guarantee robust closed-loop stability. Third, we show that the designed control system yields, with a minimum control effort, the same control performance as a robust state feedback control, which on the contrary may require a larger command activity. Two simulated case studies are presented to show the effectiveness of the proposed approach.

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Authors and Affiliations

  1. Politecnico di Torino, Torino, Italy

    Carlo Novara, Enrico Canuto & Donato Carlucci

Authors
  1. Carlo Novara
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  2. Enrico Canuto
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  3. Donato Carlucci
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Corresponding author

Correspondence to Carlo Novara.

Additional information

Carlo NOVARA received the Laurea degree in Physics from Universitádi Torino in 1996 and the Ph.D. degree in Computer and System Engineering from Politecnico di Torinoin 2002. He held a post-doc position at the University of California at Berkeleyin 2001 and 2004. He is currently an associate professor at Politecnico di Torino, Turin, Italy. He is the author or co-author of about 100 scientific publications in international journals and conferences. He has been involved in several national and international projects and in several research contracts in collaboration with Italian and European companies. He is the co-author of several patents in the automotive field. He is a member of the IEEE Transactions on System Identification and Adaptive Control, of the IFAC Transactions on Modelling, Identification and Signal Processing, and a founding member of the IEEE-CSS Transactions on Medical and Health-care Systems. His research interests include nonlinear and LPV system identification, filtering/ estimation, time series prediction, nonlinear control, data-driven methods, Set Membership methods, disturbance rejection techniques, sparse methods, and automotive, aerospace, biomedical and sustainable energy applications. E-mail: carlo.novara@polito.it.

Enrico CANUTO was born in Varallo (Piemonte), Italy. He received a degree in Electrical Engineering from Politecnico di Torino, Turin, Italy, where he joined the staff as Professor of Automatic Control in 1983, after ten years as a research staff of the National Electrical Metrology Institute G. Ferraris, Turin, Italy. From 1982 to 1997, he contributed to conception and implementationimplementation of the data reduction of the European astrometric mission Hipparcos. Technological studies in view of scientific and drag-free space missions, like Gaia and GOCE provided the opportunity of applying Embedded Model Control to drag-free satellites and to electrooptics. He contributed to the conception, design and implementation of the Nanobalance interferometric thrust-stand, capable of submicronewton accuracy. Recently, he has been involved in the design of the orbit, formation and attitude control of the Next Generation Gravity Mission of the European Space Agency. He has a longstanding cooperation with Thales Alenia Space Italia, Turin, Italy and other Italian companies in the field of electro-hydraulics. He contributed to the innovative Manufacturing Algebra. Currently, he is cooperating with the Centre for Gravity Experiments of the Huazhong University of Science and Technology, Wuhan, China, in the field of space gravity missions. In the summer 2015, he was a visiting researcher at the Northern China Electrical Power University, Beijing, China, applying Embedded Model Control to hydraulic case studies. His research interests cover all the entire field of control problems that are challenging because of complexity, uncertainty and precision. E-mail: enrico.canuto@polito.it.

Donato CARLUCCI was born in Lavello (Basilicata), Italy. He received a degree in Electrical Engineering from Politecnico di Torino, Turin, Italy, where he joined the staff as Professor of Automatic Control in 1983, after ten years as a research staff of the National Electrical Metrology Institute G. Ferraris, Turin, Italy. In the National Electrical Metrology Institute, he was responsible of the research staff working in the automatic control field. From 1982 to 1997, he contributed to the conception of the data reduction of the European astrometric mission Hipparcos and to instrument design. He has a longstanding cooperation with Italian companies. His research interests cover all the entire field of control problems and more specifically of manufacturing control systems. Email: donato. carlucci@polito.it.

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Novara, C., Canuto, E. & Carlucci, D. Control of systems with sector-bounded nonlinearities: robust stability and command effort minimization by disturbance rejection. Control Theory Technol. 14, 209–223 (2016). https://doi.org/10.1007/s11768-016-6017-6

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  • DOI: https://doi.org/10.1007/s11768-016-6017-6

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