A global optimization approach for sliding mode tuning and existence maps generation
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A global optimization approach for sliding mode tuning and existence maps generation Juan Luis Rosendo1 Fabricio Garelli1
· Dominique Monnet2 · Hernán De Battista1 · Jordan Ninin3 · Benoit Clement3,4 ·
Received: 23 March 2020 / Revised: 19 September 2020 / Accepted: 27 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this work, global optimization techniques based on interval arithmetic are proposed to analyze and synthesize sliding mode (SM) controllers. The proposed methodology allows generating a series of maps, called subpavings, which put in evidence the required relationships among tuning parameters, disturbances and control amplitude to fulfill the sufficient condition of SM in a guaranteed way. The a priori knowledge of the control power necessary to guarantee SM behavior of nonlinear systems despite parameter uncertainties and external disturbances is an advantage of this proposal compared to traditional tuning methods, which usually fall into over-sizing solutions. Although the methodology is developed in the context of conventional first-order SM controllers, it could be extended to any other SM design approach. Keywords Nonlinear control systems · Sliding modes · Robust control design · Global optimization · Interval analysis
1 Introduction The design of controllers based on sliding modes (SM) is characterized by its applicability to nonlinear systems and by its robustness. Extensive studies have been carried out
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Juan Luis Rosendo [email protected] Dominique Monnet [email protected] Hernán De Battista [email protected] Jordan Ninin [email protected] Benoit Clement [email protected] Fabricio Garelli [email protected]
1
Group of Control Applications, LEICI, FI, CONICET, Universidad Nacional de La Plata (UNLP), La Plata, Buenos Aires, Argentina
2
University of British Columbia Okanagan, Kelowna, BC, Canada
3
Lab-STICC, ENSTA Bretagne, Brest, Bretagne, France
4
College of System Engineering, Flinders University, Bedford Park, SA, Australia
in this area based on classical methods like state-feedback sliding surface design, optimization-based designs or even SM methods that combine adaptive control features [1–3]. Conventional designs are performed in two stages. The first stage is devoted to find a sliding manifold on which the desired closed-loop dynamics is achieved. The second stage consists in designing a discontinuous action and a switching logic that enforce the system to reach the prescribed manifold and to slide on it from then on [4–6]. The challenge in this type of design is to find a manifold and a control action that satisfy the necessary and sufficient condition for SM existence, at least in the desired operating range of the system. The traditional design consists in delimiting the parameters of the system by its extreme values, and then to obtain the constant control action necessary for SM operation which is finally tested through simulation [1,7,8]. However, this non
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