Title :
Design of a class of nonlinear controllers via state dependent Riccati equations
Author :
Erdem, Evrin B. ; Alleyne, Andrew G.
Author_Institution :
Burke E. Porter Machinery Co., Grand Rapids, MI, USA
Abstract :
In this brief, infinite-horizon nonlinear regulation of second-order systems using the State Dependent Riccati Equation (SDRE) method is considered. By a convenient parametrization of the A(x) matrix, the state-dependent algebraic Riccati equation is solved analytically. As a result, the closed-loop system equations are obtained in analytical form. Global stability analysis is performed by a combination of Lyapunov analysis and LaSalle´s Principle. Accordingly, a relatively straightforward condition for global asymptotic stability of the closed-loop system is derived. This is one of the first global results available for this class of systems controlled by SDRE methods. The stability results are demonstrated on an experimental magnetic levitation setup and are found to provide a great deal of flexibility in the control system design.
Keywords :
Lyapunov methods; Riccati equations; closed loop systems; control system synthesis; magnetic levitation; nonlinear control systems; stability; LaSalle principle; Lyapunov analysis; closed loop system equations; control system design; global stability analysis; infinite horizon nonlinear regulation; magnetic levitation; nonlinear controllers; second order systems; state dependent algebraic Ricatti equations; Control systems; Error correction; Magnetic analysis; Nonlinear control systems; Nonlinear equations; Nonlinear systems; Performance analysis; Riccati equations; Sliding mode control; Stability analysis;
Journal_Title :
Control Systems Technology, IEEE Transactions on
DOI :
10.1109/TCST.2003.819588