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Developing nonlinear adaptive and robust controllers for a two-link flexible robot arm is the main objective of this research. Two different modelling techniques are used to overcome model accuracy problems and these two are evaluated comparatively. These are FEM(Finite Element Method) as a reduced order-approximate model and PDE(Partial Differential Equations)approach as an exact model. The main results of the study are robust regulation of the rigid modes and suppression of elastic vibrations of the flexible robot arm. The dynamic state feedback controller is used to achieve this goal in FEM approach.In the first part of this research the adaptive internal model approach, in parallel with a robust stabilizer, has been modified to manage totally unknown disturbances as well as large parameter uncertainties. The stabilizer part of the controller is optimized successfully with a new efficient evolutionary algorithm. In the second approach (PDE) of this research, the control of a two-link flexible arm with nonuniform cross-section by design is improved. The proposed controller design should be especially useful to professionals who work in interdisciplinary research projects.