Conventional adaptive optics algorithms are studied through calibration or closed-loop control point of view. A Hadamard matrix algorithm was used to calculate the interaction matrix from the wavefront slope to the deformable mirror voltage. A fuzzy proportional integral differential (PID) control algorithm was used to adjust the control parameters to complete the closed-loop control of the adaptive optics. The simulation shows that when the atmospheric turbulence intensities D  /  r₀ are 1, 10, and 20, respectively, the mean wavefront peak to valley (PV) values are are 0.38, 0.93, and 3.53  μm, respectively, after wavefront correction by Hadamard + PID algorithm; the wavefront PV mean values are 0.38, 0.93, and 3.48  μm, after wavefront correction by PushPull + FuzzyPID algorithm; and the wavefront PV mean values are 0.36, 0.92, and 3.30  μm after wavefront correction by Hadamard + FuzzyPID algorithm. The experimental results show that: the wavefront PV mean values are 3.84, 3.56, and 3.36  μm for Hadamard + PID algorithm, PushPull + FuzzyPID algorithm, and Hadamard + FuzzyPID algorithm, respectively. The Hadamard algorithm significantly improves the interaction matrix measurement accuracy, and the FuzzyPID control algorithm improves the adaptive ability under strong turbulence conditions. The wavefront correction using two advanced algorithms is better than that of the combination of advanced and conventional algorithms.