Tuning Guidelines and Experimental Comparisons of Sine Based Auto-Tuning Methods for Fractional Order Controllers

Abstract

Accurate process modeling is occasionally difficult. In such situations, auto-tuning methods enable the design of suitable controllers based on experimental data and predefined mathematical approaches. Fractional order PIDs have recently emerged as a generalization of the standard PID controller, but auto-tuning methods for these controllers are scarce. In this paper, three sine-test based methodologies are presented from a control engineer's perspective consisting of novel Sine-Test, FO-KC and FO-ZN methods, with clear design and implementation guidelines. The approaches are exemplified on a highly nonlinear experimental platform. An in depth comparison is performed based on experimental closed loop system performance for wide operating areas, tuning effort and complexity, with a focus on the suitability for industrial applications. The study aims at providing a solid foundation for practitioners that desire to explore auto-tuning possibilities, presenting tuning workflows and implementation guidelines, while also considering the challenges associated with real-life process.

PID Tuning Using Differential Evolution With Success-Based Particle Adaptations

“…• DEPA and DEP: the proposed algorithm with and without parameter adaptation. Whereas DEPA (section IV) implements the adaptation mechanisms ( 14)- (19), DEP forgoes such adaptation mechanisms and uses fixed parameters F, G for all individuals in the population. • DERAND and DERAND A : DE with DE/rand/1/bin mutation strategy [96], this algorithm is considered highly exploratory, and implements the random-based difference of vectors.…”

“…The key motivation of the above is to enable fair comparisons across adaptive mechanisms in PID tuning. DEPA extends the above-mentioned adaptation principle through ( 14)- (19), whereas heuristic SHADE inherently implements such adaptation scheme, yet using a distinct notion of difference of vectors. As such, for fair comparisons, we implemented the adaptation of both scaling parameters F i and crossover rate CR i for each individual across all the above-mentioned DE-based algorithms [96], [108], [109], [111]- [115].…”

“…In the context of optimization, particle filtering improves the computation complexity [16], constrained optimization enables the inclusion of robustness contraints [17], and the ensembles of Kalman Filters use fewer particles while allowing a slight increase in computational time for complex transfer functions [18]. A comparison of tuning rules for fractional-order PID control is provided by [19]. Furthermore, derivative-based and interior-point algorithms such as [20] approach PID control and parameter tuning by iterative sampling.…”

“…In a second set of experiments, we studied the convergence performance using the adaptive versions of the list of algorithms mentioned in section V-G. As such, in this section we used DEPA, which is the heuristic using the parameter adaptation mechanisms presented in (14)-(19). For fair comparisons across benchmark algorithms, we used the extended heuristics described in section V-G, that is the modified versions with the "A" subscript, as described in section V-G. Also, to complement our evaluations presented in sectionVOLUME 4, 2016 …”