Control configuration selection for bilinear systems via generalised Hankel interaction index array

Abstract

Decentralised and partially decentralised control strategies are very popular in practice. To come up with a suitable decentralised or partially decentralised control structure, it is important to select the appropriate input and output pairs for control design. This procedure is called control configuration selection. It is well known that a suitable control configuration selection is an important prerequisite for a successful industrial control. In this paper the problem of control configuration selection for multiple-input and multiple-output (MIMO) bilinear processes is addressed. First, the concept of the cross-gramian is developed for bilinear systems. The conditions for the existence of generalised cross-gramian are derived. It is shown that if the cross-gramian exists it is the solution to the generalised Sylvester equation. To obtain the cross-gramian in a more computationally efficient way, an iterative method for solving the generalised Sylvester equation is proposed. The generalised cross-gramian is used to form the generalised Hankel interaction index array. The generalised Hankel interaction index array is used for control configuration selection of MIMO bilinear processes. Most of the results on control configuration selection, which have been proposed so far, can only support linear systems. The proposed method supports bilinear processes, takes the effects of dynamics of the process into account and can be used to propose a richer (sparse or block diagonal) controller structure. More importantly, since for each element of generalised Hankel interaction index array just one generalised Sylvester equation is needed to be solved, the proposed control configuration selection method is computationally more efficient than its gramian-based counterparts.

Keywords:

• control configuration selection
• bilinear systems
• cross-gramian
• interaction measure
• Sylvester equation