The residual error of adaptive optical system based on stochastic parallel gradient descent control algorithm is analyzed. The relation between steps of iteration and control numbers is specified by numerical simulation of correcting static aberrations. Simplified control model for adaptive optical system based on stochastic parallel gradient descent algorithm is introduced. Analytical expression for the relation between residual error and convergence time is deduced. The residual error is analyzed by using the temporal power spectral density of the atmospheric turbulence. It is revealed that if dynamic atmospheric turbulence with a Greenwood frequency fG is to be corrected using a N-element adaptive optical system,the iteration rate should be greater than 86 NfG to ensure the residual error corrected is less than λ/10. It is also pointed out the limited range of adaptive optical system based on stochastic parallel gradient descent control algorithm from a typical computing result.