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In this project, we aim to design a feedback linearization controller for a non-linear system, as well as simulate it using MATLAB. By using feedback linearization, we can transform our non-linear system into a linear one, thus allowing us to utilize classical linear control techniques. This method involves the use of a nonlinear feedback transformation that maps the original system into a linear system. Additionally, we can use MATLAB to simulate the resulting linear system and analyze its behavior under different conditions. Through this project, we hope to gain a better understanding of feedback linearization and its applications in control theory.