Fractional order PID and application of its circuit model

Abstract In this paper, the circuit design of a fractional order proportional-integrated derivation (FO-PID) controller for synchronization between different FO chaotic systems has been described. Chaotic synchronization and control are used in different applications in nonlinear physical systems such as performance tests for controllers and chaotic communication systems. FO chaotic systems have been created, and the synchronization control of these two systems has been carried out using an FO-PID controller. The total square error should be minimized in order to determine the parameters and orders of the designed FO controller circuit. The results obtained using the FO controller are better than those obtained using classical control systems. Using an FO-PID controller, the time to reach synchronization decreased significantly.

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