Dynamical analysis of the fractional-order centrifugal flywheel governor system and its accelerated adaptive stabilization with the optimality

Abstract This paper investigates the issues of dynamical analysis and accelerated adaptive stabilization of the fractional-order (FO) centrifugal flywheel governor system with optimality. The dynamic behavior of the centrifugal flywheel governor system is revealed and its local stability is discussed in the fractional calculus (FC). A speed function is introduced to accelerate convergence rate within a pre-given time and a hierarchical type-2 fuzzy neural network (HT2FNN) is employed to play an approximating role for unknown nonlinear items. An extended state tracking differentiator which overcomes repetitive differentiation problem is used to approximate the derivative of virtual control input. Then, a stabilization controller is designed by integrating with the speed function, neural network and tracking differentiator in the framework of backstepping. It is proved that the proposed scheme guarantees the boundedness of all signals of the closed-loop system by using the frequency distributed model and makes the predefined cost function smallest. Finally, simulation results verify the effectiveness of the presented scheme.

[1]  Zheng-Ming Ge,et al.  Control, anticontrol and synchronization of chaos for an autonomous rotational machine system with time-delay , 2005 .

[2]  Xiaolin Tang,et al.  Nonlinear Fractional-Order Estimator With Guaranteed Robustness and Stability for Lithium-Ion Batteries , 2018, IEEE Transactions on Industrial Electronics.

[3]  Baotong Cui,et al.  Observer‐based output feedback control for a boundary controlled fractional reaction diffusion system with spatially‐varying diffusivity , 2018, IET Control Theory & Applications.

[4]  Guilin Wen,et al.  Anti-controlling Hopf bifurcation in a type of centrifugal governor system , 2015 .

[5]  Samir Ladaci,et al.  Fractional order adaptive controller for stabilised systems via high-gain feedback , 2013 .

[6]  P. Tse,et al.  Adaptive backstepping output feedback control for a class of nonlinear fractional order systems , 2016 .

[7]  Donglian Qi,et al.  Asymptotic pseudo-state stabilization of commensurate fractional-order nonlinear systems with additive disturbance , 2015 .

[8]  Changchun Hua,et al.  Tracking differentiator and extended state observer-based nonsingular fast terminal sliding mode attitude control for a quadrotor , 2018, Nonlinear Dynamics.

[9]  Sehraneh Ghaemi,et al.  Synchronization of chaotic systems and identification of nonlinear systems by using recurrent hierarchical type-2 fuzzy neural networks. , 2015, ISA transactions.

[10]  Frank L. Lewis,et al.  Online actor-critic algorithm to solve the continuous-time infinite horizon optimal control problem , 2010, Autom..

[11]  Shaocheng Tong,et al.  Fuzzy Adaptive Fault-Tolerant Control of Fractional-Order Nonlinear Systems , 2021, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[12]  Yongduan Song,et al.  Prescribed Performance Control of Uncertain Euler–Lagrange Systems Subject to Full-State Constraints , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[13]  Mohammad Pourmahmood Aghababa,et al.  Chaos suppression of rotational machine systems via finite-time control method , 2012 .

[14]  M. P. Aghababa.  Finite-time chaos control and synchronization of fractional-order nonautonomous chaotic (hyperchaotic) systems using fractional nonsingular terminal sliding mode technique , 2012 .

[15]  Sehraneh Ghaemi,et al.  A modified sliding mode approach for synchronization of fractional-order chaotic/hyperchaotic systems by using new self-structuring hierarchical type-2 fuzzy neural network , 2016, Neurocomputing.

[16]  S. S. Ezz-Eldien,et al.  A new Legendre operational technique for delay fractional optimal control problems , 2016 .

[17]  Zheng-Ming Ge,et al.  Regular and chaotic dynamics of a rotational machine with a centrifugal governor , 1999 .

[18]  Frank L. Lewis,et al.  $ {H}_{ {\infty }}$ Tracking Control of Completely Unknown Continuous-Time Systems via Off-Policy Reinforcement Learning , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[19]  Hua-Cheng Zhou,et al.  New integral inequalities and asymptotic stability of fractional-order systems with unbounded time delay , 2018, Nonlinear Dynamics.

[20]  Okyay Kaynak,et al.  Robust predictive synchronization of uncertain fractional-order time-delayed chaotic systems , 2018, Soft Comput..

[21]  Elsayed Ahmed,et al.  On chaos control and synchronization of the commensurate fractional order Liu system , 2013, Commun. Nonlinear Sci. Numer. Simul..

[22]  Honglun Wang,et al.  Robust back-stepping output feedback trajectory tracking for quadrotors via extended state observer and sigmoid tracking differentiator , 2018 .

[23]  Zhen Wang.  Synchronization of an Uncertain Fractional-Order Chaotic System via Backstepping Sliding Mode Control , 2013 .

[24]  Yong Zhou,et al.  LMI-based robust control of fractional-order uncertain linear systems , 2011, Comput. Math. Appl..

[25]  Charalampos P. Bechlioulis,et al.  Robust Adaptive Control of Feedback Linearizable MIMO Nonlinear Systems With Prescribed Performance , 2008, IEEE Transactions on Automatic Control.

[26]  Huai-Ning Wu,et al.  Adaptive synchronization control based on QPSO algorithm with interval estimation for fractional-order chaotic systems and its application in secret communication , 2018, Nonlinear Dynamics.

[27]  Yongduan Song,et al.  Neuro-Adaptive Control With Given Performance Specifications for Strict Feedback Systems Under Full-State Constraints , 2019, IEEE Transactions on Neural Networks and Learning Systems.

[28]  Xiang Li,et al.  Exponential synchronization and phase locking of a multilayer Kuramoto-oscillator system with a pacemaker , 2018, Neurocomputing.

[29]  Denis de Carvalho Braga,et al.  Stability and Hopf Bifurcation in an Hexagonal Governor System With a Spring , 2006 .

[30]  Peng Shi,et al.  Neural-Network-Based Adaptive Backstepping Control With Application to Spacecraft Attitude Regulation , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[31]  Jiangang Zhang,et al.  Bifurcation and chaos of a non-autonomous rotational machine systems , 2008, Simul. Model. Pract. Theory.

[32]  Di Cao,et al.  Adaptive Fuzzy-Neural Fractional-Order Current Control of Active Power Filter with Finite-Time Sliding Controller , 2019, Int. J. Fuzzy Syst..

[33]  Y. Chu,et al.  Chaos and chaos synchronization for a non-autonomous rotational machine systems , 2008 .

[34]  Shuai Ling,et al.  Stabilization and synchronization for a mechanical system via adaptive sliding mode control. , 2017, ISA transactions.

[35]  Lu Xu,et al.  Fractal structures in centrifugal flywheel governor system , 2017, Commun. Nonlinear Sci. Numer. Simul..

[36]  Zhuangde Jiang,et al.  Nonlinear dynamic analysis of fractional order rub-impact rotor system , 2011 .

[37]  S. Sumathi,et al.  Artificial Neural Network for coordinated control of STATCOM, generator excitation and tap changing transformer , 2015 .

[38]  Devendra K. Chaturvedi,et al.  Short term load forecast using fuzzy logic and wavelet transform integrated generalized neural network , 2015 .

[39]  Reza Eslamloueyan,et al.  Designing a hierarchical neural network based on fuzzy clustering for fault diagnosis of the Tennessee-Eastman process , 2011, Appl. Soft Comput..

[40]  Shaocheng Tong,et al.  Adaptive Neural Networks Prescribed Performance Control Design for Switched Interconnected Uncertain Nonlinear Systems , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[41]  Juntao Fei,et al.  Adaptive Backstepping Design of a Microgyroscope , 2018, Micromachines.

[42]  Yong Zhou,et al.  A class of fractional evolution equations and optimal controls , 2011 .

[43]  Long Wang,et al.  Linear matrix inequality approach to quadratic stabilisation of switched systems , 2004 .

[44]  Vijay K. Yadav,et al.  Chaos control and function projective synchronization of fractional-order systems through the backstepping method , 2015 .

[45]  Jianjun Hu,et al.  Anti-oscillation and chaos control of the fractional-order brushless DC motor system via adaptive echo state networks , 2018, J. Frankl. Inst..

[46]  Jun Yang,et al.  Exponential synchronization for stochastic neural networks with multi-delayed and Markovian switching via adaptive feedback control , 2015, Commun. Nonlinear Sci. Numer. Simul..

[47]  Jiangang Zhang,et al.  The invariant measure and stationary probability density computing model based analysis of the governor system , 2017, Cluster Computing.

[48]  Yongduan Song,et al.  Accelerated adaptive control of nonlinear uncertain systems , 2017, 2017 American Control Conference (ACC).

[49]  Yongping Pan,et al.  Adaptive Fuzzy Backstepping Control of Fractional-Order Nonlinear Systems , 2017, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[50]  Z. Ge,et al.  Chaos, control and synchronization of a fractional order rotational mechanical system with a centrifugal governor , 2007 .

[51]  Peng Shi,et al.  Exponential Stability of Markovian Jumping Systems via Adaptive Sliding Mode Control , 2019, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[52]  Juntao Fei,et al.  Adaptive Fuzzy Super-Twisting Sliding Mode Control for Microgyroscope , 2019, Complex..

[53]  Sehraneh Ghaemi,et al.  Optimal synchronization of fractional-order chaotic systems subject to unknown fractional order, input nonlinearities and uncertain dynamic using type-2 fuzzy CMAC , 2017, Nonlinear Dynamics.