A novel framework to design and compare limit cycle minimizing controllers: demonstration with integer and fractional-order controllers |
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Authors: | Ameya Anil Kesarkar N Selvaganesan H Priyadarshan |
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Institution: | 1. Department of Avionics, Indian Institute of Space Science and Technology (IIST), Thiruvananthapuram?, 695547, India
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Abstract: | In this paper, a constrained optimization problem is formulated to tune the limit cycle minimizing controllers meeting additional loop-shaping performances such as phase margin and gain crossover frequency. A graphical approach is proposed so as to determine the superior controller in terms of better limit-cycle suppression. The framework is illustrated with a suitable case of elementary servo plant which has separable static backlash nonlinearity in its model. For this plant, integer-order controllers and their fractional counterparts (PI and \( PI ^\alpha , PI ]^\alpha \) ; PID and \( PI ^\alpha D^\beta \) ) are designed and compared. Interestingly, it is found that the fractional controllers produce better limit-cycle responses than their integer counterparts while both meeting the rest of the specifications. Correspondingly, the better sustained oscillations in the plant output response are obtained with fractional controllers. Such a ‘fractional superiority’ is further verified with the closed-loop nonlinear simulation. |
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