Generalized robust stability regions for fractional PID controllers

Čech, Martin; Schlegel, M.

doi:10.1109/icit.2013.6505651

Cited by 9 publications

(7 citation statements)

References 12 publications

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“…Such a controller has more tuning freedom and thus a wider region of parameters that stabilize the plant under control and offer improvements in control loop robustness. Corresponding studies have been carried out to confirm this fact (see, e.g., [9], [11]- [16]), and we will glance at some milestone works of literature, addressing fractal robustness, in the following sections. Even though FOPID controllers offer advantages over IOPID controllers, the adoption of the former in industry has been slow [17].…”

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confidence: 83%

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Towards Industrialization of FOPID Controllers: A Survey on Milestones of Fractional-Order Control and Pathways for Future Developments

et al. 2021

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The interest in fractional-order (FO) control can be traced back to the late nineteenth century. The growing tendency towards using fractional-order proportional-integral-derivative (FOPID) control has been fueled mainly by the fact that these controllers have additional "tuning knobs" that allow coherent adjustment of the dynamics of control systems. For instance, in certain cases, the capacity for additional frequency response shaping gives rise to the generation of control laws that lead to superior performance of control loops. These fractional-order control laws may allow fulfilling intricate control performance requirements that are otherwise not in the span of conventional integer-order control systems. However, there are underpinning points that are rarely addressed in the literature: (1) What are the particular advantages (in concrete figures) of FOPID controllers versus conventional, integer-order (IO) PID controllers in light of the complexities arising in the implementation of the former? (2) For real-time implementation of FOPID controllers, approximations are used that are indeed equivalent to high-order linear controllers. What, then, is the benefit of using FOPID controllers? Finally, (3) What advantages are to be had from having a near-ideal fractional-order behavior in control practice? In the present paper, we attempt to address these issues by reviewing a large portion of relevant publications in the fastgrowing FO control literature, outline the milestones and drawbacks, and present future perspectives for industrialization of fractional-order control. Furthermore, we comment on FOPID controller tuning methods from the perspective of seeking globally optimal tuning parameter sets and how this approach can benefit designers of industrial FOPID control. We also review some CACSD (computer-aided control system design) software toolboxes used for the design and implementation of FOPID controllers. Finally, we draw conclusions and formulate suggestions for future research.

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confidence: 83%

“…Thus, fractional-order dynamic models and controllers have been introduced. In the industrial context, the apparent benefit of fractional calculus was initially justified at the process model side (see, e.g., [4]- [9]). It has proved more difficult to convey the advantages of fractional calculus on the controller side because of implementation issues.…”

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confidence: 99%

Towards Industrialization of FOPID Controllers: A Survey on Milestones of Fractional-Order Control and Pathways for Future Developments

et al. 2021

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“…(1) Using robustness regions method described earlier inČech and Schlegel (2013), the set of all pairs of controller parameters K, T i ensuring condition 7for any P (s) ∈ S ∞,1 E (σ 2 ) was determined. The set can be drawn as a compact region R in K − K i plane.…”

Section: Controller Design Proceduresmentioning

confidence: 99%

Bode-like control loop performance index evaluated for a class of fractional-order processes

Skarda

Čech

Schlegel

2014

IFAC Proceedings Volumes

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“…In this Section, let us describe the results of optimization procedure which is based on generalized robustness regions method [21], [19], [1] and the claims of Theorem 1 and Lemma 2. The optimization problem can be solved effectively for arbitrary n ≥ 2 and even for n → ∞.…”

Section: Numeric Solution Of Robust Pid Controller Designmentioning

confidence: 99%

Innovated PID pulse autotuner for fractional-order model set: The method of moments

Schlegel

Čech

2014

11th IEEE International Conference on Control &Amp; Automation (ICCA)

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Recently, a successful PID pulse autotuner based on model set approach was developed. Despite high reliability, several requirements for significant improvement have appeared after a decade of its industrial usage. Two of them are handled in this paper. Firstly, the set of a priori admissible processes was extended to fractional-order all-pole models to cover wider range of real plants. Secondly, a new parameter affecting the model set span was introduced. It helps markedly the practitioners to reach the proper robustness/performance ratio especially in the case when the initial controller tuning is too conservative. The authors believe that the new theory will be soon transferred to industrial practice.

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Generalized robust stability regions for fractional PID controllers

Cited by 9 publications

References 12 publications

Towards Industrialization of FOPID Controllers: A Survey on Milestones of Fractional-Order Control and Pathways for Future Developments

Towards Industrialization of FOPID Controllers: A Survey on Milestones of Fractional-Order Control and Pathways for Future Developments

Bode-like control loop performance index evaluated for a class of fractional-order processes

Innovated PID pulse autotuner for fractional-order model set: The method of moments

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