Suppression of effects of nonlinearities in a class of nonlinear systems by disturbance observers

In this paper, a class of single-input single-output (SISO) nonlinear systems is considered. A nonlinear system in this class has the property that its output is equal to the summation of the output of a stable SISO linear time-invariant system and a bounded function of time. A disturbance observer is designed to estimate the effects of nonlinearities in the system and cancel them subsequently. The disturbance observer is thus able to make the nonlinear system behave linearly and, for instance, be free of limit cycle behavior. An example is given to show that limit cycles in a Van der Pol type system caused by a nonlinearity can be effectively suppressed by a disturbance observer. Furthermore, a methodology for designing controllers for a class of nonlinear feedback systems is presented. The designed controllers consist of two parts: a disturbance observer by which the effects of nonlinearities are suppressed and a linear controller to have the system achieve desired goals.