Adaptive tracking control of linear uncertain mechanical systems subjected to unknown sinusoidal disturbances

The design and implementation of an adaptive disturbance rejection approach is presented for single-input-single-output linear-time-invariant uncertain mechanical systems subject to sinusoidal disturbances with unknown amplitudes and frequencies. The proposed technique suggests construction of a set of stabilizing tuning functions via a state estimate observer in a backstepping fashion to achieve asymptotic disturbance rejection. The tuning functions design is based on a single Lyapunov function incorporating both the error states and update law, and hence, global stability and improved transient performance are readily achieved. 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 both simulations and experiments for a single-degree-of-freedom system with unknown parameters and subject to an unknown sinusoidal disturbance. Significant matching between the simulation and experimental results is observed.