The act of changing the eye’s crystalline lens to focus the retinal picture is known as ocular accommodation. Therefore, the primary input for accommodation is retinal defocus, and the main function of accommodative control is to instruct the ciliary muscle to reduce the amount of defocus. Although, for a study, researchers sought to help vision scientists without foundation in control theory, they first offered a tutorial introduction to it in the article. 

Then, they proposed a comprehensive theory of accommodative regulation that describes the characteristics of the accommodative response to various accommodating stimuli. In light of prior research, they concluded that dual integral control, with a “fast” or “phasic” integrator enabling response to rapid changes in demand, transfers control to a “slow” or “tonic” integrator, which maintains the response to steady demand, is a good explanation for the majority of accommodation-related phenomena. Sensorimotor latencies of the system, delay both information concerning defocus and the accommodation modifications performed in response, and the slow reaction of the motor plant makes control difficult. A Smith predictor, which enabled the system to foretell the delayed sensory effects of its own motor movements, can be used to get around these problems. The gain and phase for sinusoidal oscillations in demand were both accounted for via critically-damped dual integral control with a Smith predictor for the first time. 

Additionally, they suggested a brand-new proportional-control signal to explain the nonlinear resonance seen for low-amplitude, high-frequency input, as well as the power spectrum of accommodative microfluctuations during stable fixation, which may be significant in the quest for optimal focus.

Reference: jov.arvojournals.org/article.aspx?articleid=2783542