Abstract
This paper discusses synchronization and antisynchronization of N-coupled complex permanent magnet synchronous motors systems with ring connection. Based on the direct design method and antisymmetric structure, the appropriate controllers are designed to ensure the occurrence of synchronization and antisynchronization in an array of N-coupled general complex chaotic systems described by a unified mathematical expression with ring connection. The proposed method is flexible and is suitable both for design and for implementation in practice. Numerical results are plotted to show the rapid convergence of errors to zero and further verify the effectiveness and feasibility of the theoretical scheme.
Highlights
Since Fowler et al [1] were the first to investigate the complex Lorenz equations, complex systems have played an important role in a variety of industrial fields
We find that selecting the coefficient matrix plays an important role in achieving synchronization and antisynchronization of N-coupled complex chaotic systems with ring connection
We investigate synchronization and antisynchronization of N-coupled complex permanent magnet synchronous motor (PMSM) systems with ring connection
Summary
Since Fowler et al [1] were the first to investigate the complex Lorenz equations, complex systems have played an important role in a variety of industrial fields. Complex systems can provide an excellent instrument for the description of various physical phenomena, such as detuned laser systems, amplitudes of electromagnetic fields, and thermal convection of liquid flows [2–4]. Another example is when synchronization of complex chaotic systems is used to transmit information in the secure communications, where complex variables (doubling number of real variables) increase the message contents and enhance security of the transmitted information. Some synchronization schemes of real chaotic systems were extended in the complex field, such as complete synchronization [10], antisynchronization [11, 12], projective synchronization [13], and lag synchronization [14]. There exist many synchronization schemes of complex chaotic systems, including complex complete synchronization [15], complex projective synchronization [16], complex modified projective synchronization [17, 18], and complex function projective synchronization [7], just to enumerate a few examples
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