Robust orbital stabilization : A Floquet theory-based approach

• The design of robust orbitally stabilizing feedback is considered. From a known orbitally stabilizing controller for a nominal, disturbance-free system, a robustifying feedback extension is designed utilizing the sliding-mode control (SMC) methodology. The main contribution of the article is to provide a constructive procedure for designing the time-invariant switching function used in the SMC synthesis. More specifically, its zero-level set (the sliding manifold) is designed using a real Floquet–Lyapunov transformation to locally correspond to an invariant subspace of the Monodromy matrix of a transverse linearization. This ensures asymptotic stability of the periodic orbit when the system is confined to the sliding manifold, despite any system uncertainties and external disturbances satisfying a matching condition. The challenging task of oscillation control of the underactuated cart–pendulum system subject to both matched- and unmatched disturbances/uncertainties demonstrates the efficacy of the proposed scheme.

Subject headings

TEKNIK OCH TEKNOLOGIER  -- Elektroteknik och elektronik -- Reglerteknik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Electrical Engineering, Electronic Engineering, Information Engineering -- Control Engineering (hsv//eng)

Keyword

orbital stabilization

robust nonlinear control

sliding mode control

underactuated mechanical systems

Publication and Content Type

ref (subject category)

art (subject category)