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

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 α , [PI] α ; PID and PI α D β ) 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.

Fractional-order controller design in frequency domain using an improved nonlinear adaptive seeker optimization algorithm

“…The appropriateness of the proposed variants of the SOA in designing the FOPI controller is also compared with other global optimization techniques (DE [11] and CMAES [12]) and popular classical local search techniques (Nelder-Mead simplex search (NM-SS) [9] and interior point method (IPM) [10]) in Table 3. It can be observed that the CSOA outperforms the other algorithms under consideration, while the ESOA is better than the other algorithms except for the CSOA and is comparable to DE.…”

“…Optimization techniques have been widely adopted for designing FO controllers. In [6,7,9,10], local searchbased techniques were applied for fast tuning of FO controllers. However, their performance was sensitive to the selection of the initial feed point and the solutions obtained were prone to getting trapped into local optima.…”

Input dependent Nyquist plot for limit cycle prediction and its suppression using fractional order controllers

“…In Oliveira et al (2003, 2006, 2012), effective use of DF for the synthesis of controllers to meet the desired limit cycle details is studied. This theory is extended to tune the fractional order controllers (FOCs) and integer order controllers (IOCs) to suppress the limit cycle magnitude by proposed optimization problem (Kesarkar et al, 2014, 2015) in addition to meet the desired specifications for system with single nonlinearity. Lanusse and Oustaloup (2004, 2005) also suggested a FOCs with an anti-windup feature for plants with input saturation nonlinearity.…”