Pole assignment and distributed output feedback control via graph-based decomposition

ABSTRACT

A new distributed observer-based output feedback control design with an arbitrary control structure is proposed. Assuming that the linear time-invariant (LTI) system does not have any fixed-modes with respect to the control structure, the pole placement at the desired locations becomes theoretically feasible. In this paper, the structural output feedback controller design is transformed into equivalent problems based on a graph-theoretic approach. Two augmented structures are established and formulated as the solution of a set of binary linear programs (BLP). The first one facilitates the incorporation of the maximum number of edges in the principal bipartite graph and the second one results in the least order of dynamic control for the principal block. Next, the distributed design problem is segmented into two stages: (i) design of a set of static control loops based on convex optimisation, to maximise the controllability/observability radius and (ii) design of the control loops corresponding to the principal bipartite graph based on the reduced-order observer-based control. The performance of the proposed approach is investigated in terms of the pole-placement accuracy, control effort, robustness to perturbations in system dynamics, and effect of controller order reduction.

KEYWORDS:

• Convex optimisation
• fixed-modes
• controllability/observability radius
• pole assignment
• control structure
• bipartite graph

Disclosure statement

No potential conflict of interest was reported by the author(s).