Conformable sliding mode control and analysis of Lorenz chaotic system

Haris Calgan; Metin Demirtas

doi:10.65112/tcmis.10078

Authors

Haris Calgan Department of Electrical and Electronics Engineering, University of Balikesir, Balikesir, Türkiye & Mechatronics Research Group, Faculty of Engineering and Physical Science, University of Southampton, Southampton, SO171BJ, United Kingdom https://orcid.org/0000-0002-9106-8144
Metin Demirtas Department of Electrical and Electronics Engineering, University of Balikesir, Balikesir, Türkiye https://orcid.org/0000-0003-2622-5286

DOI:

https://doi.org/10.65112/tcmis.10078

Keywords:

Conformable, chaotic system, Lorenz, sliding mode, fractional calculus

Abstract

This study comparatively and innovatively examines linear state feedback control (LSFC) of the Conformable Sliding Mode Control (CSMC) methods on the conformable fractional-order Lorenz system. The extreme sensitivity of chaotic systems to initial conditions and their nonlinear nature present significant challenges for classical control methods. In this context, the conformable fractional derivative approach integrates the memory effect and fractional order character of the system into the model by adding a t^q−1 multiplier to the system dynamics, while preserving the classical differential form. Thus, both analytical simplification is achieved and the physical interpretation of fractional dynamics is preserved. One of the original contributions of the study is the investigation of the conformable fractional-order form of the Lorenz system under control and the systematic comparison of two different control strategies under the same performance criteria. Innovatively, the effect of the conformable fractional-order on control performance is parametrically analysed, and the decisive role of the fractional order (q) on system stability and convergence speed is revealed. By activating the control signals after a specific delay, the natural evolution of the system in a chaotic regime was observed, and a realistic suppression scenario was created. This approach offers a more practical engineering perspective compared to instantaneous control applications. The results showed that the LSFC method provides a simple control structure and smooth control action. In contrast, the CSMC method achieves shorter settling time, faster convergence, improved disturbance rejection capability, and higher robustness against external disturbances and parameter uncertainties.

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