Application of Gain and Phase Margins for Designing Robust Controllers within Quantitative Feedback Theory

Document Type : Research Article

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Faculty of Mechanical Engineering, Guilan University, Rasht, Iran

Abstract

Modeling uncertainty in the form of additional gain and phase and calculating robustness margins based on them is one of the standard methods in designing robust control systems and comparing their robustness. On the other hand, one of the prevalent methods of robust control in the frequency domain is Quantitative Feedback Theory (QFT), which, due to modeling uncertainty in the form of parametric uncertainty with a specified range, faces challenges such as the inability to compare controllers and non-automated design. Additionally, the system's conditions for parametric uncertainty values outside the design range are unknown. This research addresses these issues using uncertainty modeling in the form of gain and phase within the QFT method. To this end, a combined margin consisting of gain and phase is introduced and calculated using a modified Nichols chart and inequalities related to design criteria in the QFT method. The position control of a DC motor is selected as a case study, and an optimal and robust proportional-derivative (PD) controller is designed for it. The results are examined both numerically and experimentally which show that the proposed method effectively overcomes the shortcomings of the QFT method. The controller designed in this manner gains more favorable results than the controller designed using the conventional QFT method, and even maintains its performance better for parametric uncertainty values higher than the design range.

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Amirkabir Journal of Mechanical Engineering
Volume 56, Issue 7
October 2024
Pages 2-2

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