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**:** 107
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**:** 2024
**:** .., .. // . 107. .: , 2024. .43-65. DOI: https://doi.org/10.25728/ubs.2024.107.3

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** (.):** single-link manipulator with flexible joint, tracking, external disturbances, uncertain input, combined control, mixed variable observer

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** (.):** As a control plant, we consider a single-link manipulator with a flexible joint that functions under parametric uncertainty and external uncontrollable disturbances. The dynamic of the current loop is not introduced. The armature current of the DC motor is considered as the control, which can be converted into torque applied to the gearbox shaft. We pose the problem of synthesizing dynamic feedback that provides specified changes in the angular position of the manipulator under the following atypical assumptions: 1) only the current deviation of the manipulator position from the reference signal (tracking error) is available for measurements; 2)the multiplier before the control (input matrix) is not known exactly. The first factor motivates the use the transformation to the block form of input-output with respect to the tracking error for solving the problem of observation and synthesis of dynamic feedback based on mixed variables (combinations of state variables, external influences and their derivatives). The main contributions include, firstly, amethod for designing a mixed variable observer of minimum possible order with piecewise linear corrective actions. This observer recovers mixed variables from tracking error measurements. To simplify its tuning, both the principles of construction of the state observer and the differentiator of external signals are simultaneously used in one algorithm. The second main contribution is a method for the formation of combined control with compensation of matched disturbances under conditions of uncertain multiplier before control. The numerical simulation results are presented. They demonstrate the robustness of the closed-loop system and guaranteed stabilization of the tracking error with a given accuracy when external disturbances, reference actions, and uncertain parameters change within acceptable ranges.

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