Robustness issues associated with the provision of integral action in nonlinear systems

Abstract

A key motivation for feedback control is that of disturbance compensation. In the case of linear systems, this is a very well understood problem. It is known, for example, that the straight forward inclusion of integral action gives compensation for constant disturbances and off-sets. Moreover, in the linear case, no interactions occur between disturbances and the underlying dynamics since the principle of superposition holds. However, in nonlinear systems, superposition does not hold, and this implies, inter-alia, that non trivial interactions can arise between disturbances and plant dynamics. As a result, a disturbance that is incorrectly interpreted can destabilise an otherwise stable system. Thus, disturbance compensation and, in particular, the provision of integral action, presents non-trivial challenges for nonlinear systems. The aim of this paper is to raise awareness to these issues and suggest possible strategies for attacking the problem.