Abstract
The backstepping technique is greatly effective for the integral-order triangular nonlinear systems. Nevertheless, it is dramatically challenging to implement backstepping technique in the manipulation of fractional-order permanent magnet synchronous motors (FOPMSMs), since the fractional derivatives of the composite functions are deeply complex. In this paper, a fuzzy adaptive backstepping-based control scheme for FOPMSMs on the basis of fractional Lyapunov stability criterion is established. First, we propose a novel adaptive synchronous controller for FOPMSMs by coupling with fuzzy logic systems and backstepping technique. Then, we present a detailed stability analysis in terms of FOPMSMs via the proposed controllers. Finally, a simulation example is given to reveal that the proposed controller can effectively eliminate or restrain the chaos of FOPMSMs, and keep the tracking signals synchronous with the reference signals.
Highlights
In late decades, fractional-order non-linear systems (FONSs) [1] have been widely studied, owing to their accurate performance in modeling physical phenomena, and owing to their successful applications in a variety of fields, such as chemistry, medicine, biology, electronics, robotics, fuel cells, and so on [6,7,8,9,10,11]
Based on the above discussion, this paper proposes an adaptive neural network control method of chaotic fractional-order permanent magnet synchronous motors using backstepping technique, which can improve the control performance of non-linear systems
To deal with the synchronization issue of fractionalorder permanent magnet synchronous motor (FOPMSM) with triangular structure, we expect to construct an adaptive neural network (NN) controller combined with backstepping technique
Summary
Fractional-order non-linear systems (FONSs) [1] have been widely studied, owing to their accurate performance in modeling physical phenomena (e.g., chaos, oscillations, impulses, diffusions, see [2,3,4,5]), and owing to their successful applications in a variety of fields, such as chemistry, medicine, biology, electronics, robotics, fuel cells, and so on [6,7,8,9,10,11]. Based on the above discussion, this paper proposes an adaptive neural network control method of chaotic fractional-order permanent magnet synchronous motors using backstepping technique, which can improve the control performance of non-linear systems. To deal with the synchronization issue of fractionalorder permanent magnet synchronous motor (FOPMSM) with triangular structure, we expect to construct an adaptive NN controller combined with backstepping technique This enables every uncertain complex non-linear functions being approximated by a radial basis function neural network (RBFNN) during each control step. In order to analyze the stability of the controlled systems, firstly, some basic results related to fractional calculus and RBFNN are recalled, including a fractional differential inequality, which lays the foundation for the application of the fractional Lyapunov function method It lays a foundation for the stability analysis of other types of FONSs. Secondly, an adaptive NN backstepping recursive control method is proposed for a class of uncertain FOPMSMs. The stability of FOPMSMs is analyzed based on fractional Lyapunov criterion.
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