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

• DOI: 10.3390/math13040610
• Publication Date: 2025-02-13T13:01:19Z
• Authors: Haizhen Wang; Huihua Jian; Jianhua Huang; Yonghong Lan
• Keywords: robust; model-free adaptive control; QA1-939; discrete-time system; fractional order; Mathematics

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.