Estimating Response of Fractional Order Systems and Control: An Orthogonal HF-BasedApproach

In an attempt to simplify the mathematical solution of real-world systems, further presumptions such as an integer order system and zero initial condition lead to imprecise and incorrect system modeling. By modeling real-world systems with fractional orders these problems can be solved with more accuracy. However, analyzing those systems and determining time-based responses are quite difficult challenges. Several techniques for fractional order system approximation were developed earlier and are accessible in the literature to reduce the mathematical complexity. However, the proposed method for solving the issue is more efficient and provides far more accurate results with a simpler algorithm than existing methods. Based on the orthogonal hybrid functions (HF), the suggested method is found. When working with function samples, the orthogonal HF set can efficiently provide piecewise linear solutions for a variety of control systems. A few examples are included with pertinent figures and tables, and the findings are compared using current methodologies to verify the accuracy of the solution and the efficacy of the method being discussed.