Dynamic gain scheduled control in a multi-variable control framework

A controller designed for linearizations at various trim/operating points of a nonlinear system using linear approaches is not necessarily well-performing or stable once scheduled with a state to retain the scheduled control law design close to the current operating point. Dynamic gain scheduling (DGS) is a technique aimed to resolve this controller scheduling issue for rapidly changing dynamics and states. It entails scheduling the control law gains with a fast varying state variable rather than with a slowly varying state. It has been applied to aircraft system models successfully in a single-input-single-output fashion, allowing also for nested loops. The aim of this paper is to extend dynamic gain scheduling to general multi-variable nonlinear control systems. Given a linear design, suitable transformations are provided which allow fast scheduling of multi-variable controllers. Theoretical results are shown, providing important parallels to nonlinear dynamic inversion control. Several examples are presented in order to emphasize the characteristics of DGS. Comparative results of dynamic gain scheduling in relation to two other gain scheduling approaches show significant advantages when controlling highly nonlinear systems.