A novel framework to design and compare limit cycle minimizing controllers: demonstration with integer and fractional-order controllers

作者：Kesarkar Ameya Anil; Selvaganesan N^*; Priyadarshan H

来源：Nonlinear Dynamics, 2014, 78(4): 2871-2882.

DOI：10.1007/s11071-014-1632-6

• Nonlinearity
• Limit cycle
• Describing function
• Fractional-order controller
• Static backlash
• Oustaloup approximation

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 ; PID and ) 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.

• 出版日期2014-12