A Geometric Algebra Approach to Invariance Control in Sliding Regimes for Switched Systems

• Published in: Advances in applied Clifford algebras 2023-07, Vol.33 (3), Article 35
• Main Authors: Sira-Ramírez, H., Gómez-León, B. C., Aguilar-Orduña, M. A.
• Format: Article
• Language: English
• Subjects: Algorithms; Applications of Mathematics; Control methods; Control systems design; Feedback control; Invariance; Mathematical and Computational Physics; Mathematical Methods in Physics; Nonlinear systems; Physics; Physics and Astronomy; Power converters; SISO (control systems); Sliding mode control; State feedback; Theoretical
• ISSN: 0188-7009; 1661-4909
• DOI: 10.1007/s00006-023-01281-z

Within a Geometric Algebra (GA) framework, this article presents a general method for synthesis of sliding mode (SM) controllers in Single Input Single Output (SISO) switched nonlinear systems. The method, addressed as the invariance control method , rests on a reinterpretation of the necessary and sufficient conditions for the local existence of a sliding regime on a given smooth manifold. This consideration leads to a natural decomposition of the SM control scheme resulting in an invariance state feedback controller feeding a Delta–Sigma modulator that, ultimately, provides the required binary-valued switched input to the plant. As application examples, the obtained results are used to illustrate the design of an invariance controller for a switched power converter system. Using the invariance control design procedure, it is shown how well-known second order sliding regime algorithms can be obtained, via a limiting process, from traditional sliding regimes induced on linear sliding manifolds for certain nonlinear switched systems.