The objective of this research is to analyze and develop controller to minimize vibrations of the drill string in rotary drilling rigs. The rotary drilling process is affected by many vibrations which adversely affect the drilling efficiency. The vibrations are mainly classified into three: lateral, tosional and axial. Among the vibrations, lateral vibrations are the most destructive. The research conducted a detailed analysis on lateral vibrations. Bent drill string and unbalanced drill bit was found to be its major causes; and the resultant phenomenon was known as drill bit whirl. Practical demonstration and analysis of the bit whirl phenomenon was done by conducting experiments using an unbalanced drill bit model. Their controllability issues were also discussed and practical solutions suggested. Black box identification methods were applied to develop mathematical models for the system. Box Jenkins structure model was identified and validated by a twofold procedure. Accurate simulations results were obtained with a mere 0.05% residual. Studies revealed that the vibrations in rotary drilling were aggravated by two major causes: borehole friction and critical operation speeds. This research developed a self tuning adaptive controller which could effectively mitigate the vibration aggravating causes and improve overall drilling efficiency. On practical implementation, the controller automatically detected vibrations, mitigated the vibration aggravating causes, and resumed normal drilling operation in less than 10 seconds. The controller action was proven experimentally in two cases: (1) when affected by borehole friction and (2) in presence of an unbalanced drill bit. All the experiments and control techniques applied in this research are validated by experimental data. The prototype used in this research is also distinguished from the rest due to a universal joint, providing an additional two degrees of freedom. Thus, the laboratory set-up provided better dynamic analysis.