Suppression of effects of nonlinearities by disturbance observers

In this paper, the application of disturbance observers to suppress chaotic behavior in a class of single-input single-output (SISO) nonlinear systems is studied. 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 disturbance. The bounded disturbance captures the effects of all nonlinearities in the system. A disturbance observer is designed to estimate the bounded disturbance (equivalently, the effects of nonlinearities in the system) and cancel it subsequently. The disturbance observer is thus able to make the nonlinear system behave linearly and, for instance, be free of chaotic behavior. An example is given to show that chaotic behavior due to a nonlinearity in a Duffing-type system can be effectively suppressed by a disturbance observer.