Selection of Decentralised Schemes and Parametrisation of the Decentralised Degenerate Compensators

Abstract

The design of decentralised control schemes has two major aspects. The selection of the decentralised structure and then the design of the decentralised controller that has a given structure and addresses certain design requirements. This paper deals with the parametrisation and selection of the decentralized structure such that problems such as the decentralised pole assignment may have solutions. We use the approach of global linearisation for the asymptotic linearisation of the pole assignment map around a degenerate compensator. Thus, we examine in depth the case of degenerate compensators and investigate the conditions under which certain degenerate structures exist. This leads to a parametrisation of decentralised structures based on the structural properties of the system.

Structure assignment problems in linear systems: Algebraic and geometric methods

“…DAP based criteria may be deployed on existing generic solvability conditions and on the DAP diagnostics (Plücker matrices, decentralized Markov parameters) linked to solvability conditions and avoidance of fixed modes. The parametrisation of degenerate compensations for decentralized schemes (Karcanias et al, 2016b) together with the DAP invariants and their properties also provides a possible route for the classification of decentralization schemes with good control potential. Minimal design problem: Dynamic compensation problems may be reduced to constant DAP problems.…”

“…The DAP framework has been used for the study of constant and dynamic pole assignment, where low complexity solutions have been established (Leventides and Karcanias, 1998b), as well as for problems of zero assignment by squaring down (Karcanias and Giannakopoulos, 1989), (Leventides and Karcanias, 2009). Degenerate feedback gains (Karcanias et al, 2016b) are defined for both constant and dynamic assignment problems. Parametrising the family of degenerate feedbacks gives extra degrees of freedom in computing appropriate controllers that linearise asymptotically DAP and enabling the selection of solutions with reduced sensitivity This parametrisation methodology plays a key role in selecting feasible structures for decentralized control problems.…”