TY - JOUR
T1 - Dynamic analysis, circuit realization and accelerated adaptive backstepping control of the FO MEMS gyroscope
AU - Luo, Shaohua
AU - Yang, Guanci
AU - Li, Junyang
AU - Ouakad, Hassen M.
N1 - Funding Information:
This project is supported by National Key Research and Development Program of China (No. 2018YFB1304800 ), National Natural Science Foundation of China (No. 52065008 ), Science and Technology Foundation of Guizhou Province (Nos. QKHZC[2019]2814 , PTRC[2020]6007 , JXCX[2021]001 and [2021]5634 ), Open Research Fund of Key Laboratory of Advanced Manufacturing Technology of the Ministry of Education (No. GZUAMT2021KF[02]) and Science and Technology Research Program of Chongqing Municipal Education Commission (Nos. KJZD-K201903001 and KJQN201803004 ).
Publisher Copyright:
© 2021
PY - 2022/2
Y1 - 2022/2
N2 - In this paper, an accelerated adaptive backstepping control problem is investigated for the fractional-order (FO) Micro-electro-mechanical system (MEMS) gyroscope. Its dynamical behaviors are studied through effective tools such as phase diagrams, time histories, Lyapunov exponent, 0-1 test and bifurcation diagram. And its equivalent analog circuits producing regular behaviors as well as complex ones are constructed to further reveal nonlinear dynamics especially chaotic oscillations. In the controller design, the Fourier series and the interval type-2 fuzzy logic system (IT2FLS) are utilized to reconstruct imprecise reference trajectories, and unknown functions are approximated through the IT2FLS with adaptive laws. The speed function is constructed to improve the transient response performance of the FO MEMS gyroscope, and a tracking differentiator (TD) is introduced to solve the problem of ‘explosion of complexity’. Then, an accelerated adaptive backstepping controller integrating the IT2FLS, speed function and TD into the technical framework of backstepping is proposed here. The stability analysis proves that all signals of the closed-loop FO MEMS gyroscope are asymptotically uniformly bounded. Finally, the effectiveness of the proposed control scheme is verified by abundant results.
AB - In this paper, an accelerated adaptive backstepping control problem is investigated for the fractional-order (FO) Micro-electro-mechanical system (MEMS) gyroscope. Its dynamical behaviors are studied through effective tools such as phase diagrams, time histories, Lyapunov exponent, 0-1 test and bifurcation diagram. And its equivalent analog circuits producing regular behaviors as well as complex ones are constructed to further reveal nonlinear dynamics especially chaotic oscillations. In the controller design, the Fourier series and the interval type-2 fuzzy logic system (IT2FLS) are utilized to reconstruct imprecise reference trajectories, and unknown functions are approximated through the IT2FLS with adaptive laws. The speed function is constructed to improve the transient response performance of the FO MEMS gyroscope, and a tracking differentiator (TD) is introduced to solve the problem of ‘explosion of complexity’. Then, an accelerated adaptive backstepping controller integrating the IT2FLS, speed function and TD into the technical framework of backstepping is proposed here. The stability analysis proves that all signals of the closed-loop FO MEMS gyroscope are asymptotically uniformly bounded. Finally, the effectiveness of the proposed control scheme is verified by abundant results.
KW - Adaptive backstepping control
KW - Analog circuit
KW - FO MEMS gyroscope
KW - IT2FLS
KW - Imprecise reference trajectories
UR - http://www.scopus.com/inward/record.url?scp=85121764534&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85121764534&partnerID=8YFLogxK
U2 - 10.1016/j.chaos.2021.111735
DO - 10.1016/j.chaos.2021.111735
M3 - Article
AN - SCOPUS:85121764534
SN - 0960-0779
VL - 155
JO - Chaos, Solitons and Fractals
JF - Chaos, Solitons and Fractals
M1 - 111735
ER -