  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.
