Robust tracking performance and disturbance rejection for a class of nonlinear systems using disturbance observers

This paper is concerned with disturbance rejection performance in single-input single-output (SISO) nonlinear systems described by uncertain linear dynamics and bounded nonlinearities. After transforming the nonlinear terms into an equivalent bounded disturbance at the output of a linear system, a disturbance observer (DOB) is added to achieve robust disturbance rejection. The DOB design is formulated as Luenberger observer state estimation for an augmented system which contains at least one eigenvalue at the origin. The synthesis of a (sub)optimal DOB is carried out by solving multi-objective H
_∞
sensitivity optimization. The design approach is applied to an inverted pendulum with actuator backlash.