Analytical and robust design of fractional order controllers in the frequency domain and development of an interface software

The performance of models described by first, second, and third order time delay transfer functions is improved in this thesis by employing analytical design approaches for fractional proportional integral and fractional proportional derivative controllers. Non-integer order proportional integral controller design methodology for first order models with time delay was provided in our master's thesis. The approach in issue has been improved upon and, its scope has been widened in this thesis. The main contribution of the work may be summarized as the analytical methods for developing a controller that will provide the values of the phase margin and the gain and phase crossover frequencies required by the researcher for three-order time delay models. The "frequency frame" method used in this thesis differs greatly from similar methods in the literature. Similar investigations on the issue have shown that analytical techniques may be used to determine the gain crossover frequency for time-delay models. For analogous studies, it can be shown that analytical calculations that bring the derivative of the phase curve to zero at the tangent frequency are effective; however, this method makes the computation more challenging and adds additional mathematical complexity. This thesis study enables the presented model to successfully obtain phase margin along with phase crossover frequencies in order to overcome the mentioned difficulties and limitations. The system phase curve may be flattened by modifying these values as needed, which enhances the system's resilience and stability. The effectiveness of the suggested method is visibly demonstrated. Models used from the literature as examples helped to test the technique. The strategy has also been applied in a number of studies that have been written up in international journals with peer review. To make the approach simple for researchers to utilize, a MATLAB-based interface tool has been created. In light of this knowledge, it is anticipated that this thesis study will significantly advance the field of literature. Keywords: Fractional Order, Analytical, Controller Design, Stability, Interface