Open AccessDesign of switching hyperplanes for multi‐inputs multi‐outputs discrete‐time linear systems
Author(s) -
Darío LuisDelgado José,
Mohammed AlHadithi Basil,
Jiménez Agustín
Publication year - 2016
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2015.0684
Subject(s) - control theory (sociology) , eigenvalues and eigenvectors , hyperplane , transformation (genetics) , representation (politics) , computer science , surface (topology) , range (aeronautics) , linear system , mimo , mathematics , simple (philosophy) , mathematical optimization , control (management) , engineering , artificial intelligence , channel (broadcasting) , law , aerospace engineering , mathematical analysis , computer network , chemistry , biochemistry , geometry , quantum mechanics , political science , physics , politics , gene , philosophy , epistemology
The design of sliding switching surfaces consist in finding a manifold where the controlled system dynamics are asymptotically stable. This problem has been studied for a long time, during which a wide range of designing approaches has been proposed, which can be classified into two research methodologies; the first one corresponding to eigenvalues designing approaches and the second one is based on optimal approaches. In addition, some research approaches only can be applied to specific type of systems, e.g. single‐input single‐output systems or continuous time systems. Finally, the performance or the level of the achieved accuracy among the different approaches varies significantly. The proposed approach facilitates the task of designing sliding surfaces applied to multi‐input multi‐output (MIMO) linear systems. The presented methodology introduces a switching surface for MIMO linear systems through a simple equation that allows both eigenvalues placement design or optimal methods without any coordinate system representation transformation. In addition, a design parameter is also included for the adjustment of the non‐ideal dynamics. Moreover, this approach guarantees high accuracy of the system dynamics, either for arbitrary eigenvalues assignment or for optimal switching surface definitions. In addition, these benefits are attained using a single switching surface equation. An illustrative example is included to show the advantages of the proposed design methodology.