Adaptive compensation of unknown disturbances in MIMO linear systems with distinct input delays

   The paper considers the problem of compensation for unknown external disturbances for a class of linear stationary multidimensional systems with distinct input delays. It is assumed that external disturbances are harmonic signals with unknown frequencies, phases, amplitudes, and biases that simultaneously affect both the input and output of the system. To solve the problem, the direct disturbance compensation method based on the internal model principle is used in combination with the classical Falb-Wolovich linear state feedback decoupling method which allows increasing the convergence rate of output signals with a small adaptation parameter. In order to eliminate cross-interactions between control loops, the channel decoupling method based on Falb-Wolovich linear state feedback decoupling approach is applied to the system. Then, an observer is constructed to estimate the state vector of the external disturbance model and, based on the estimations, an adaptive control law with the memory regressor extension is designed to compensate for external disturbances based on the internal model principle. The system is stabilized simultaneously with the decoupling of control channels, which allows one to proceed to the problem of compensating for external unknown disturbances, bypassing the design phase of the stabilizing component of the control signal. There are no restrictions on the observability and stability of the control plant. An adaptive algorithm with the memory regressor extension combined with the Falb-Volovich linear state feedback decoupling method is proposed to compensate for unknown external disturbances for a class of linear stationary multidimensional systems with distinct control delays. The efficiency of the proposed approach is illustrated by an example of numerical simulation in the MATLAB/Simulink environment. The resulting transient response plots demonstrate that the proposed algorithm ensures the boundedness of all closed-loop signals and the asymptotic stability of the output variables in the presence of distinct input delays under external harmonic disturbances. The proposed approach allows obtaining an improved rate of convergence of processes and can be applied in engineering systems and complexes the mathematical description of which is given in the form of linear multidimensional systems with distinct input delays.

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