Nonlinear H∞ state feedback control of an electromagnetic suspension system

For the linear systems, the performance of unstable plants is limited by the unstable poles. Though the nonlinear H
_∞
design inherits the design idea of H
_∞
in linear system and can solve a series of design problems about a class of nonlinear systems, but there is not a perfect result, especially that of HJI inequality. The paper deduces HJI inequality which is suitable for nonlinear H
_∞
state feedback control by starting with the analysis of dissipation of system and gets the nonlinear control laws by putting forward analytical method of series expansion. Combined with magnetic levitation gap control design, the function of proposed nonlinear control law is to expand its best performance near the balance point to the working range of the whole system.