Problems of constructing an adaptive optical system intended for correcting the wavefront of laser radiation that has passed through a turbulent atmosphere are considered. To ensure high-quality wavefront correction, the frequency of the discrete system should be at least 1 kHz or more. This performance can be achieved by using FPGA as the main control element of the system. The results of a laboratory experiments of the laser beam phase fluctuations caused by turbulence, produced by the airflow of a fan heater, correction by means of the FPGA-based adaptive optical system are presented. The system efficiency was evaluated at various correction frequencies up to 1875 Hz.