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An algebraic approach is presented for the fast feed-forward adaptation of the angular velocity trajectory tracking task in a Boost-converter driven dc-motor system. For the adaptation, the load torque perturbations are assumed piecewise constant and are, nonasymptotically, online estimated using the available noisy measurements of the state variables. The controller is a linear controller based on the exact tracking error dynamics passive output feedback (ETEDPOF) controller design methodology including suitable adaptive feed-forward precompensation depending explicitly on the precisely estimated torque. The performance of the adaptation, which is achieved by means of the algebraic online-estimation of the current unknown load torque, is successfully validated in an experimental laboratory setup.