Title :
A parametric approach to the design of linear time-varying tracking controllers for nonlinear systems
Author :
Deutscher, Joachim
Author_Institution :
Lehrstuhl fur Regelungstech., Univ. Erlangen-Nurnberg, Erlangen, Germany
Abstract :
In this paper the computation of linear time-varying tracking controllers on the basis of a Jacobian linearization of a nonlinear system about a reference trajectory is considered. An exponentially stabilizing controller is determined by approximately solving a Sylvester matrix differential equation using a Galerkin approach. The solution is obtained in parametric form so that conditions for the free parameters can be derived to assure exponential stability of the tracking error dynamics. The design procedure is demonstrated by computing a tracking controller for the stabilization of the side stepping of the inverted pendulum.
Keywords :
Galerkin method; Jacobian matrices; asymptotic stability; control system synthesis; differential equations; linear systems; linearisation techniques; nonlinear control systems; pendulums; time-varying systems; Galerkin approach; Jacobian linearization; Sylvester matrix differential equation; exponential stability; exponentially stabilizing controller; inverted pendulum; linear time-varying tracking controller design; nonlinear system; reference trajectory; side stepping stabilization; tracking error dynamics; Eigenvalues and eigenfunctions; Equations; Nonlinear systems; State feedback; Time-varying systems; Vectors;
Conference_Titel :
Control Conference (ECC), 2009 European
Conference_Location :
Budapest
Print_ISBN :
978-3-9524173-9-3
