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.
Adaptive Tracking Control of Linear Uncertain Mechanical Systems Subjected to Unknown Sinusoidal Disturbances
Contributed by the Dynamic Systems and Control Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received by the ASME Dynamics Systems and Control Division, Oct. 2001; final revision, Aug. 2002. Associate Editor: Y. Chait.
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Xian, B., Jalili, N., Dawson and , D. M., and Fang, Y. (March 10, 2003). "Adaptive Tracking Control of Linear Uncertain Mechanical Systems Subjected to Unknown Sinusoidal Disturbances." ASME. J. Dyn. Sys., Meas., Control. March 2003; 125(1): 129–134. https://doi.org/10.1115/1.1538624
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