Fractional-Order MFAC with Application to DC Motor Speed Control System

Haizhen Wang, Huihua Jian, Jianhua Huang () and Yonghong Lan ()
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Haizhen Wang: School of Mechanical and Electrical Engineering, Xinyu University, Xinyu 338004, China
Huihua Jian: School of Mechanical and Electrical Engineering, Xinyu University, Xinyu 338004, China
Jianhua Huang: Jiangxi Provincial Key Laboratory of Power Batteries and Energy Storage Materials, Xinyu University, Xinyu 338004, China
Yonghong Lan: School of Automation and Electronic Information, Xiangtan University, Xiangtan 411105, China

Mathematics, 2025, vol. 13, issue 4, 1-13

Abstract: Model-free adaptive control (MFAC) can carry out various tasks using only I/O data, providing advantages such as lower operational costs, higher scalability and easier implementation. However, the robustness of MFAC remains an open problem. In this paper, a robust fractional-order model-free adaptive control (RFOMFAC) scheme is proposed to address the robust tracking control issue for a class of uncertain discrete-time nonlinear systems with bounded measurement disturbance. First, we use a fractional-order dynamic data model relating the relationship between the output signal and the fractional-order input variables based on the compact form dynamic linearization. Then, the pseudo-partial derivative (PPD) is obtained using a higher-order estimation algorithm that includes more information about past input and output data. With the introduction of a reference equation, a fractional-order model-free adaptive control (FOMFAC) law is then proposed. Consequently, using a higher-order PPD-based FOMFAC law can improve the control performance. Furthermore, a modified RFOMFAC algorithm with decreasing gain is constructed. Theoretical analysis indicates that the proposed algorithm can effectively attenuate measurement disturbances. Finally, simulation results demonstrate the effectiveness of the proposed method.

Keywords: model-free adaptive control; fractional order; robust; discrete-time system (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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