Design of optimal sliding-mode control using partial eigenstructure assignment

ABSTRACT

This paper describes a new framework for the design of a sliding surface for a given system while multi-channel ${\mathcal{H}}_2$ performances of the closed-loop system are under control. In contrast to most of the current sliding surface design schemes, in this new method, the level of control effort required to maintain sliding is penalised. The proposed method for the design of optimal sliding mode control is implemented in two stages. In the first stage, a state feedback gain is derived using a linear matrix inequality (LMI)-based scheme that can assign a number of the closed-loop eigenvalues to a known value whilst satisfying performance specifications. The sliding function matrix related to the particular state feedback derived in the first stage is obtained in the second stage by using one of the two different methods developed for this goal. The proposed theory is evaluated by using numerical examples including the problem of steady-state output tracking via a state-feedback SMC for flight control.

KEYWORDS:

• Multi-channel ${\mathcal{H}}_2$ synthesis
• partial eigenstructure assignment
• regional pole placement LMI characterisation
• sliding surface selection

Disclosure statement

No potential conflict of interest was reported by the authors.