Robust adaptive compensation of unknown multi-harmonic disturbances in multivariable linear systems

This paper proposes a new direct adaptive disturbance compensation method for multivariable linear systems, which is robust with respect to external disturbances. The external disturbances are assumed to be multi-harmonic signals (regular component) with additional random noise (irregular component), where the bias, phase, amplitude, and frequency are all unknown. The objective is to design a state-feedback control law capable of regulating the system output to zero in the absence of random noise. The robustness of the closed-loop system with respect to additive unmodeled disturbances is reflected in the fact that the proposed control law guarantees boundedness of all closed-loop signals. To solve this problem, first, the system inputs and outputs are decoupled using Falb–Wolovich approach. Then, the direct disturbance compensation method based on the internal model principle is applied to the resulting decoupled system. As a result, the adaptive algorithm can be constructed robustly and independently for each control channel. The adaptive algorithm with memory regressor extension is employed to improve the convergence rate of signals in the closed-loop system.