Performance enhanced design of chaos controller for the mechanical centrifugal flywheel governor system via adaptive dynamic surface control

Abstract

This paper addresses chaos suppression of the mechanical centrifugal flywheel governor system with output constraint and fully unknown parameters via adaptive dynamic surface control. To have a certain understanding of chaotic nature of the mechanical centrifugal flywheel governor system and subsequently design its controller, the useful tools like the phase diagrams and corresponding time histories are employed. By using tangent barrier Lyapunov function, a dynamic surface control scheme with neural network and tracking differentiator is developed to transform chaos oscillation into regular motion and the output constraint rule is not broken in whole process. Plugging second-order tracking differentiator into chaos controller tackles the “explosion of complexity” of backstepping and improves the accuracy in contrast with the first-order filter. Meanwhile, Chebyshev neural network with adaptive law whose input only depends on a subset of Chebyshev polynomials is derived to learn the behavior of unknown dynamics. The boundedness of all signals of the closed-loop system is verified in stability analysis. Finally, the results of numerical simulations illustrate effectiveness and exhibit the superior performance of the proposed scheme by comparing with the existing ADSC method.

Multistability in a Fractional-Order Centrifugal Flywheel Governor System and Its Adaptive Control

“…where x, y, z, and w are state variables and u 1 , u 2 , u 3 , and u 4 are external active control inputs. en, the adaptive control system can be defined by Substituting (13) into (12), the closed-loop system is obtained as…”

“…In recent years, the research on chaos and control of the centrifugal flywheel governor system has attracted wide attention of scholars [3][4][5][6][7][8][9][10][11][12][13][14]. For example, Zhang et al [3] studied the evolution from Hopf bifurcation to chaos of the centrifugal flywheel governor system subjected to external distance.…”

“…Rao et al [11] investigated the global structure of nonlinear response of mechanical centrifugal governor and found a new type of mixed-mode oscillations in the periodic response. Luo et al [12] addressed chaos suppression of the mechanical centrifugal flywheel governor system with output constraint and fully unknown parameters via adaptive dynamic surface control. Aghababa et al [13] derived an adaptive robust controller to suppress the chaos of nonautonomous centrifugal flywheel governor systems in a given finite time effectively by using the adaptation laws and Lyapunov control theory.…”

Complexity and Multistability in the Centrifugal Flywheel Governor System With Stochastic Noise

“…change of load torque. Dynamics, chaos, Hopf bifurcation and control of the centrifugal flywheel governor system have been studied by many researches [16]- [21]. For instance, Aghababa and Aghababa [18], [19] investigated the robust control and finite-time stabilization of a centrifugal flywheel governor system with nonlinearities in control inputs.…”