Sinusoidal disturbances compensation for a class of nonlinear non-minimum phase stable systems

It is considered a class of asymptotically stable nonlinear systems which may contain non-minimum phase systems, affected by unknown structured disturbances. It is solved the problem of designing an output feedback compensator which drives the state of the system exponentially to zero if the disturbance consists of a known number of biased sinusoids with unknown bias, magnitudes, phases, and frequencies. If the disturbance, in addition to the sinusoidal terms, includes an unmodelled noise, it is shown that the closed loop error system is input-to-state stable with respect to the unmodelled noise. The control algorithm is designed using adaptive observer techniques and contains convergent estimates of the biased sinusoidal disturbances and of its parameters, including frequencies. Finally, a simulation example has been introduced to show the effectiveness of the proposed algorithm.