Adaptive rejection of unknown sinusoidal disturbances in linear SISO uncertain systems

This paper describes the design and implementation of an adaptive disturbance rejection approach for single-input-single-output (SISO) linear-time-invariant (LTI) uncertain systems subject to sinusoidal disturbances with unknown amplitude and frequency. The technique is based on the construction of a set of stabilizing tuning functions utilizing a state estimate observer in a backstepping fashion to achieve asymptotic disturbance rejection. Utilizing only the system output, a virtual control input is used in place of non-measurable and unknown signals. The performance of the adaptation algorithm is demonstrated through simulations for both regulation and tracking of a single-degree-of-freedom system with unknown parameters and subject to an unknown sinusoidal disturbance.