Generalized fractional controller for singular systems of differential equations
Ioannis Dassios, Georgios Tzounas, Federico Milano
Abstract
In this article we consider a class of singular linear systems of first order, and introduce a generalized fractional order feedback controller of Caputo type. The closed loop system in question is a singular system of differential equations having both first, and fractional order derivatives. We provide a comprehensive theory for the existence and uniqueness of solutions, as well as for the stability of the system with inclusion of the fractional order controller. An example of a singular system with a fractional order proportional integral controller, as well as an example on a 3-bus power system with inclusion of a fractional order damping controller, is given to illustrate our theory.
Topics & Concepts
MathematicsController (irrigation)UniquenessFractional calculusOrder (exchange)Stability (learning theory)Control theory (sociology)Ordinary differential equationApplied mathematicsMathematical analysisDifferential equationControl (management)Computer scienceMachine learningFinanceEconomicsAgronomyBiologyArtificial intelligenceNumerical methods for differential equationsFractional Differential Equations SolutionsAdvanced Differential Equations and Dynamical Systems