Off-equilibrium linearisation and design of gain-scheduled control with application to vehicle speed control

Abstract

In conventional gain-scheduled control design, linearisation of a time-invariant nonlinear system and local control design for the resulting set of linear time-invariant systems is performed at a set of equilibrium points. Due to its validity only near equilibrium, such a design may result in poor transient performance. To resolve this problem, one can base the control design on a dynamic linearisation about some nominal trajectory. However, a drawback with this approach is that control design for the resulting linear time-varying system is in general a difficult problem. In this paper it is suggested that linearisation and local controller design should be carried out not only at equilibrium states, but also in transient operating regimes. It is shown that this results in a set of time-invariant linearisations which, when they are interpolated, form a close approximation to the time-varying system resulting from dynamic linearisation. Consequently, the transient performance can be improved by increasing the number of linear time-invariant controllers. The feasibility of this approach, and possible improvements in transient performance, are illustrated with results from an experimental vehicle speed-control application.