Despite the fact that the hydrodynamic lubrication is a self-controlled process, the rotor dynamics and energy efficiency in fluid film bearing are often the subject to be improved. We have designed control systems with adaptive PI and DQN-agent based controllers to minimize the rotor oscillations amplitude in a conical fluid film bearing. The design of the bearing allows its axial displacement and thus adjustment of its average clearance. The tests were performed using a simulation model in MATLAB software. The simulation model includes modules of a rigid shaft, a conical bearing, and a control system. The bearing module is based on numerical solution of the generalized Reynolds equation and its nonlinear approximation with fully connected neural networks. The results obtained demonstrate that both the adaptive PI controller and the DQN-based controller reduce the rotor vibrations even when imbalance in the system grows. However, the DQN-based approach provides some additional advantages in the controller designing process as well as in the system performance.