Fractional Order Control Systems and Applications

Fractional-order control extends traditional integer-order frameworks by introducing non-integer differentiation and integration orders, thereby capturing memory and hereditary properties of many physical, biological and economic systems. By offering two extra tuning degrees of freedom, fractional-order proportional–integral–derivative (FOPID) controllers enable refined frequency-response shaping, improved robustness against model uncertainty, enhanced disturbance rejection and more flexible transient performance. These controllers have been successfully applied to temperature regulation in chemical reactors, tension control in manufacturing lines, vibration damping in mechanical structures and voltage regulation in power converters. Advances in numerical approximation methods, such as the recursive Oustaloup filter, and automated parameter assignment techniques have facilitated real-time implementation. Stability and performance analyses in both time and frequency domains have yielded design guidelines for single-loop and multi-loop architectures. Recent efforts focus on integrating fractional control into modular “plug-and-play” hardware suitable for industry 4.0, as well as extending applications to renewable energy systems, robotics and biomedical devices. Despite these successes, challenges remain in ensuring computational efficiency, simplifying tuning procedures and standardising industrial toolchains. Ongoing research aims to bridge gaps between theoretical potential and industrial deployment, paving the way towards more resilient and adaptable control solutions across diverse sectors.

Research from Nature Portfolio

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Research from all publishers

In the past two years, several comprehensive reviews and methodological studies have advanced fractional-order control theory and its practical realisation. A survey on industrialisation milestones maps the evolution of FOPID controllers, highlighting new computer-aided control system design toolboxes and global optimisation strategies for tuning fractional orders and gains, thereby charting pathways towards wider industrial adoption. In power electronics, fractional-order strategies have been reviewed for converters in industrial drives, electric vehicles and smart grids, with emphasis on fractional PI/PID and sliding mode controllers that enable finer trade-offs between efficiency, robustness and dynamic response in renewable energy interfaces. Research on autotuning frameworks has examined automatic configuration of FOPID parameters across diverse plant models, providing comparative analyses of optimisation algorithms and real-world process case studies that demonstrate reduced commissioning time and improved closed-loop performance. These developments reflect a maturing field in which theoretical insights increasingly converge with practical requirements.

Fractional Order Control Systems and Applications publication trend

The graph below shows the total number of articles in fractional order control systems and applications across all publications each year (not limited to Nature Index journals).

Technical terms

Fractional calculus: Mathematical extension of differentiation and integration to non-integer orders, modelling memory and hereditary effects.

Fractional-order differential equation: A differential equation involving derivatives of non-integer order, used to represent complex dynamical behaviour.

FOPID controller: Fractional-order proportional–integral–derivative controller featuring two additional parameters—the non-integer integration and differentiation orders—for enhanced tuning flexibility.

Oustaloup approximation: A recursive numerical method for approximating fractional derivatives and integrals by high-order rational transfer functions.

Autotuning: Automated method for adjusting controller parameters in real time or during commissioning to achieve desired closed-loop performance.

Sliding mode control: A robust control technique that enforces system trajectories to reach and slide along a predefined surface, here extended to fractional orders for enhanced robustness.

References

1. Towards Industrialization of FOPID Controllers: A Survey on Milestones of Fractional-Order Control and Pathways for Future Developments. IEEE Access (2021).
2. Fractional Order Calculus: Basic Concepts and Engineering Applications. Mathematical Problems in Engineering (2010).
3. Fractional-Order PID Controllers for Temperature Control: A Review. Energies (2022).
4. Design of an Optimal Fractional Order PID for Constant Tension Control System. IEEE Access (2020).
5. Improved Decentralized Fractional PD Control of Structure Vibrations. Mathematics (2020).
6. Fractional Order Control of Power Electronic Converters in Industrial Drives and Renewable Energy Systems: A Review. IEEE Access (2021).
7. A Review of Recent Developments in Autotuning Methods for Fractional-Order Controllers. Fractal and Fractional (2022).