Fractional-order sliding-mode controller for semi-active vehicle MRD suspensions
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ORIGINAL PAPER
Fractional-order sliding-mode controller for semi-active vehicle MRD suspensions Sy Dzung Nguyen . Bao Danh Lam . Van Hoa Ngo
Received: 19 June 2019 / Accepted: 8 July 2020 Ó Springer Nature B.V. 2020
Abstract Due to the complexly natural attributes of technical systems, reality has been shown that many systems could be modeled more precisely if they are modeled by using fractional calculus and fractionalorder differential equations. Inspired by this advantage, in this work a fractional-order derivative-based sliding mode controller (FD-SMC) for magnetorheological damper based on semi-active vehicle suspensions (MRD-SAVSs) is proposed to make the states of the given system asymptotically stable in the finite time. To show this assertion, a new estimate result for fractional differential inequality is presented S. D. Nguyen B. D. Lam Division of Computational Mechatronics, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam e-mail: [email protected] B. D. Lam e-mail: [email protected] S. D. Nguyen B. D. Lam Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam V. H. Ngo (&) Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam e-mail: [email protected] V. H. Ngo Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam
to derive an FD-SMC law for the systems of MRDSAVS. Then, this corresponding fractional-order sliding mode controller is designed to provide robustness, high performance control, finite time convergence in the presence of uncertainties and external disturbances. Finally, numerical simulation results are presented to demonstrate the effectiveness of the proposed control method. Keywords Fractional-oder sliding mode control Fractional-oder control Fractional-order Lyapunov direct method Semi-active MRD suspension
1 Introduction Owning potential advantages, MRD-based semi-active suspensions (MRD-SASs) have been used for many fields including road and railway transport vehicles [1–4]. For these applications, the fact that the negative impact of external disturbance and uncertainty UAD always exists as an inevitable status. UAD derives from many sources such as the lack of accuracy of the measurement devices, the model errors, and the unknown influence of the surrounding environment. In the MRD-based suspension field, the model errors relate to the change in the physical properties of magnetorheological fluids because of the temperature variability, or the difference between the dynamic response of the mathematical models
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employed to describe the dampers, springs, etc., and the real dynamic response of the corresponding equipment [5–7]. How to enhance the control effectiveness in the presence of UAD is a challenge. Many approach ways have been considered such as exploiting SMC, fuzzy
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