In this paper, a two-degree-of-freedom dynamic model of the human eye is presented. Two separate controllers, a linear square-optimized controller and a fuzzy square-optimized controller, are designed for the system. The performance of these controllers is compared under several conditions, including non-zero initial error, fast trajectory tracking, system uncertainty, and external disturbances. Under the initial error condition, the main advantage of the fuzzy controller is its smaller control input. However, the linear square-optimized controller achieves better overall performance due to its reliance on the accurate system model. Although a fuzzy controller can be tuned through extensive trial and error to match the performance of the linear square-optimal controller, the design process becomes significantly more complex.