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This work analyzes the method of synthesis of the controller is investigated assuming the plant dynamics uncertainty. The controller is designed using model predictive control methodology, including discrete time-regression predictive model of the forward dynamics of the plant based on linear neural network structure. The model is parameterized via offline learning on the experimental data, obtained from the plant. The method of determining the tolerant prediction horizon value is proposed for tuning the controller. The control system structure for single-link flexible manipulator is considered using two predictive controllers via hub angular velocity control loop and flexible link angular tip position control loop. The control system is tested with both the computer simulation with MATLAB and controlling the laboratory model of the planar single-link flexible manipulator. The test has proved the effective vibration suppression and tip force disturbance rejection of the flexible link.