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We discuss development and integration of a coherent fiber array system composed of densely packed fiber collimators with built-in capabilities for adaptive wavefront phase piston and tilt control at each fiber collimator. In this system, multi-channel fiber-integrated phase shifters are used for phase locking of seven fiber collimators and the precompensation of laboratory-generated turbulence-induced phase aberrations. Controllable x and y displacements of the fiber tips in the fiber collimator array provide additional adaptive compensation of the tip and tilt phase aberration components. An additional control system is utilized for equalization of the intensity of each of the fiber collimator beams. All three control systems are based on the stochastic parallel gradient descent optimization technique. The paper presents the first experimental results of adaptive dynamic phase distortion compensation with an adaptive phase-locked fiber collimator array system.