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The choice of a mathematical model of eye movement has had a significant impact on scientific research. This research resulted in a controlling robotic arm that could follow the movement of the human eye and thoroughly examine the structure of the human eye. Exploring the previous models, a model equivalent to a robot with two degrees of freedom is presented. Then, by designing and simulating an optimal linear square controller on the desired system, we could model an eye robot. The purpose of tracking is to target the system, which is shown by simulating this controller. This paper describes how to design a fuzzy controller for the system by presenting the simulation results. Finally, the performance of the two control methods in non-zero initial conditions, rapid eye movements, and uncertainty in the model system constructions are compared. The simulation results show that despite the system control provided by both control methods, the fuzzy control method has a better performance for tracking fast eye movements. This method is resistant to modeling uncertainties by using the qualitative behavior of the system instead of its exact mathematical model. Also, the smaller volume of simulation of control inputs in the fuzzy controller will significantly reduce costs by using this controller. [ABSTRACT FROM AUTHOR]