Analytical approach on the design of fractional order proportional-integral controller for second order plus time delay models

Abstract

This paper focuses on step by step design of fractional order proportional-integral controller for the stability and robust performance of second order plus time delay plant. Analytically obtained equations are generalized and can be used for mentioned plants. Main aim of the method is to flatten the phase curve of the Bode plot between phase and gain crossover frequencies. Thus, robustness to gain variations is provided. Besides, stability of the whole system is ensured. In contrast to existing studies in the literature, not only the gain crossover frequency, both gain and phase crossover frequencies are considered in the design procedure. Also, the phase flattening is not achieved by equalizing the phase derivative to zero. The paper brings a different point of view to the problem. Two different controllers are calculated. The first one achieves desired gain crossover frequency and phase margin properties. Second one ensures the phase crossover frequency and the gain margin. Then, these controllers are connected and there obtained an only controller satisfying both conditions. Proposed equations are applied on two different models from the literature and the results are given graphically.