Frequency frame approach on loop shaping of first order plus time delay systems using fractional order PI controller

• Published in: ISA transactions 2019-03, Vol.86, p.192-200
• Main Authors: Şenol, Bilal, Demiroğlu, Uğur
• Format: Article
• Language: English
• Subjects: Auto-tuning; First order plus time delay; Fractional order; Frequency frame; Iso-damping; Loop shaping; Proportional integral controller; Robustness
• ISSN: 0019-0578; 1879-2022
• DOI: 10.1016/j.isatra.2018.10.021

This study proposes an analytical design method of fractional order proportional integral (FOPI) controllers for first order plus time delay (FOPTD) systems. Suggested technique obtains the general computation equations of controllers for such systems. These equations are used to tune controller parameters to meet specified frequency and phase properties to satisfy the stability of whole system. It is found that the designed controllers not only make the system stable, but also have positive effect on the performance and robustness of the system. Main contribution of the paper lays on this thought. There proposed a concept, “frequency frame” which encloses the curves between phase and gain crossover frequencies in Bode plot. Robustness of the control system can be improved by expanding or constricting the edges of this frame and flattening the curves inside the frame. Thus, any case that leads the system to instability can be avoided. Analytically derived equations are tested with proper examples and the results are shown illustratively. Advantages and disadvantages of the method are comparatively given. •The “frequency frame” concept is proposed in this paper.•Main aim of the study is to flatten the curves inside the frame to ensure system stability and robustness equalization.•A controller is designed for FOPTD plants.•Generalized equations to obtain the FOPI controller are given.•Proposed controller is tested with two plants under unexpected load disturbance.