Adaptive Regulation in Unstable MIMO LTI Plants Using Falb-Wolovich Decoupling Method

Existing algorithms for the direct compensation of unknown disturbances in multivariable systems typically employ a single adaptive controller for the entire system. As a result, only one adaptive gain is available to adjust the overall convergence rate of all control channels. This paper presents a novel adaptive control algorithm for a class of unstable linear time-invariant (LTI) multi-input multi-output (MIMO) systems subjected to unknown disturbances, allowing the adaptive gain of each control channel to be selected independently in order to adjust the convergence rate of the processes. Knowledge of the exact number of harmonic external disturbances is not required. It is assumed that a priori information regarding the upper bound on the number of disturbance harmonics is available. The canonical form of the disturbance description is used, which allows also to consider the case of harmonic components of the same frequency. The control problem is solved by combining a state-feedback decoupling approach with a direct disturbance compensation method based on the internal model principle. As a result, the adaptive algorithm can be designed independently for each control channel. Consequently, the proposed method eliminates the adverse effects caused by the interactions of the control inputs on the system outputs. Furthermore, it reduces the number of parameters that must be tuned in the adaptive algorithm, thereby decreasing the overall complexity of the adaptive control scheme.