According to wide spread applications of piezoelectric actuators in various fields like automation, communications, optics, nanotechnology and semiconductor technology, as well as their effective capability in providing nanometer and subnanometer displacement, specially at high frequencies with high resolution , it is necessary to design a system to control piezoelectric actuators. To control the motion of piezoelectric actuators , it is necessary to model their behavior. The models commonly used to simulate the mechanical and electrical behavior of piezoelectric actuators generally are based o implified assumptions often invalid for practical designs. Although the geometry of practical actuators are often 2-D or 3-D, most usual models, however, are based on one dimensional models or are designed for special purposes and nonphysical description of piezoelectrics. In this thesis we have utilized IEEE constitutive relations to derive a piezoelectric actuator model and we have used finite element method to analyse the partial differential equations. In this way we obtain the equations needed to model the piezoelectric.The above mentioned, provides physical insight into piezo actuator.We have used iterative learning control methods for motion control of these actuators to track desired displacement profile. For a given refrence trajectory, we make use of various iterative learning control methods , to find the coresponding input to the system ,such that the output follows the desired trajectory as acqurate as possible. It is also necessary to optimize the algorithm for computational requirements. We incorporate different 2-D learning control algorithms to a 3-D piezoelectric actuator and by comparing their sum of square errors produced in a determined amount of iterations, we compare them and select the most approprite ones.