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For almost a decade, Control and Automation engineers have been exploring the control over robotic mechanisms that deals flexibility, which plays an important role in space structure applications. Flexibility is an unwanted feature in robot manipulators which causes vibrations and static deflection control problems. The demand for high-speed robotic manipulators with slight or no vibrations has been a challenging research problem. These requirements and limitations give rise to many interesting issues from a control perspective. The objective of studying the manipulator here is to design and test different control schemes for a single-link flexible manipulator. The dynamic model of the system is derived by using the Lagrangian method. The system has two degrees of freedom (DOF) which corresponds to the motor shaft rotation angle with respect to a coordinate frame fixed to the base and the rotation of the flexible joint to which link is attached with respect to the motor.