Adaptive auxiliary loop for output-based compensation of perturbations in linear systems

The problem of output-feedback compensation of bounded additive perturbations affecting a minimum-phase linear system with unknown parameters is considered. An adaptive auxiliary loop is developed, which does not require to know the perturbation model and allows one to: (a) separate the processes of estimation of parametric and additive perturbations, (b) estimate and compensate for the additive perturbation with any given accuracy if the conditions of the parametric identifiability are met. The above-mentioned separated estimation of two disturbances of different nature is achieved by augmentation of the A.M. Tsykunov auxiliary loop method with the law to identify the unknown parameters, which is based on the instrumental variables approach and the procedure of dynamic regressor extension and mixing (DREM). The obtained system of the additive perturbations compensation has a certain potential to be used together with the conventional industrial PI-, PID-controllers. The theoretical results of this study are validated via mathematical modelling.