Sensorless Adaptive Vibration Suppression in Two-Mass Systems via Joint Estimation of Controller Parameters and System States

The scope of this study is to develop a novel sensorless adaptive vibration suppression controller for two-mass systems with joint estimation of states and controller parameters. Unlike existing solutions, we simultaneously: (i) propose an analytically proved, unified and singularity-issue-free scheme of parameters adjustment of a control law with additional feedbacks that ensures convergence of such parameters to their true values under extremely weak regressor finite excitation (FE) requirement, (ii) derive an adaptive observer of a two-mass electromechanical system physical states with guarantee of their convergence to the ground truth values under clear FE condition, (iii) rigorously prove the exponential stability of the obtained closed-loop system of adaptive vibration suppression for two-mass systems that includes the above-mentioned adaptive observer and adaptive controller. These approaches are grounded on the recently proposed method of parameters identification for one class of nonlinearly parameterized regression equation and thoroughly investigated dynamic regression extension and mixing procedure (DREM). The obtained theoretical results are confirmed via numerical experiments.