Fast Adaptive Compensation of Multi-Sinusoidal Disturbance in Linear MIMO Systems with Multiple Input Delays

The paper addresses the problem of adaptive compensation of multi-sinusoidal disturbances in linear timeinvariant multi-input multi-output (MIMO) plants with multiple input delays.The disturbance is considered as the vector output of a dynamical autonomous model with known order, but unmeasurable state and unknown parameters. The model parameters are related to a priori unknown frequencies, phases and amplitudes of the disturbance harmonics. Two solutions to the problem with different adaptation algorithms are derived. The first solution uses standard gradient adaptation algorithm with relatively slow convergence dependent on disturbance persistent excitation (PE). At the same time, the algorithm is simple and demonstrates the asymptotical stability property despite the inputs delays. The second solution is based on adaptation algorithm driven by disturbance dependent regressors (measurable functions) filtered by a linear operator with memory. Despite the inputs delays the rate of parametric convergence of the algorithm can be arbitrary increased by simultaneous use of linear operator with memory and increase of adaptation gain. Proposed solutions are verified via Matlab/Simulink environment.