Robust 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 that are described by uncertain linear dynamics and bounded nonlinearities. First, the nonlinear terms are transformed into an equivalent bounded disturbance at the output of a linear system. Then, a disturbance observer (DOB) is added to the closed loop to achieve robust disturbance rejection. The DOB design is formulated as an extended Luenberger observer having internal dynamics with at least an 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. Closed loop response shows that tracking performance is indeed greatly enhanced with the DOB.