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. 2023 Nov 21;18(11):e0294726.
doi: 10.1371/journal.pone.0294726. eCollection 2023.

Controlled synchronization of a vibrating screen driven by two motors based on improved sliding mode controlling method

Lei Jia  1 , Guohui Wang  1 , Cheng Pan  1 , Ziliang Liu  1 , Xin Zhang  1
Affiliations

Controlled synchronization of a vibrating screen driven by two motors based on improved sliding mode controlling method

Lei Jia et al. PLoS One. .

Abstract

With a requirement of miniaturization in modern vibrating screens, the vibration synchronization method can no longer meet the process demand, so the controlled synchronization method is introduced in the vibrating screen to achieve zero phase error state and realize the purpose of increasing the amplitude. In this article, the controlled synchronization of a vibrating screen driven by two motors based on improved sliding mode controlling method is investigated. Firstly, according to the theory of mechanical dynamics, the motion state of the vibrating screen is simplified as the electromechanical coupling dynamical model of a vibrating system driven by two inductor motors. And then the synchronization conditions and stability criterion of the vibrating system are derived and numerically analyzed. Based on a master-slave controlling strategy, the controllers of two motors are respectively designed with Super-Twisting sliding mode control (ST-SMC) and backstepping second-order complementary sliding mode control (BSOCSMC), while the uncertainty is estimated by an adaptive radial basis function neural network (ARBFNN). In addition, Lyapunov stability analysis is performed on the two controllers to prove their stability theoretically. Finally, simulation analysis is conducted based on the dynamics model in this paper.

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Conflict of interest statement

The authors have declared that no competing interests exist.

Figures

Fig 1
Fig 1. Mechanical model of a vibrating screen driven by two motors.
Fig 2
Fig 2. Structure of the control system.
Fig 3
Fig 3. Model predictive torque control (MPTC).
Fig 4
Fig 4. Characterization of synchronization conditions and stability conditions.
(a) Synchronization conditions at different speeds. (b) Effect of θ on synchronization conditions. (c) Effect of r1 on synchronization conditions. (d) Stabilized areas at different speeds. (e) Effect of η on stabilized areas. (f) Effect of θ on stabilized areas.
Fig 5
Fig 5. Effect of rl on parameters aij(i,j = 1,2), bij(i,j = 1,2) and stability conditions for zero phase error.
(a) Stability conditions at (θ1,θ2) = (0°,180°). (b) Stability conditions at (θ1,θ2) = (30°,150°). (c) Stability conditions at (θ1,θ2) = (45°,135°). (d) Stability conditions at (θ1,θ2) = (60°,120°). (e) Effect of rl on parameters aij(i,j = 1,2). (f) Effect of rl on parameters bij(i,j = 1,2).
Fig 6
Fig 6. Results of self-synchronous simulation.
(a) Speed of two motors. (b) Phase tracking error. (c) Response in x, y directions. (d) Response in ψ direction. (e) The trajectory of the body.
Fig 7
Fig 7. Results of controlled synchronization simulation.
(a) Speed of two motors. (b) Speed tracking error. (c) Phase tracking error. (d) Response in x, y directions. (e) Response in ψ direction. (f) Load of motor 1 and motor 2. (g) Electromagnetic torque of two motors. (h) The trajectory of the body.
Fig 8
Fig 8. Comparison and analysis of multiple control methods.
(a) Speed of motor 1. (b) Speed tracking error. (c) Electromagnetic torque of motor 1of motor 1. (d) Phase tracking error. (e) Speed of motor 2. (f) Speed tracking error of motor 2. (g) Speed of motor 2 under perturbation. (h) Phase tracking error under perturbation.
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References

    1. Zhang XL, Wen BC, Zhao CY. Synchronization of three homodromy coupled exciters in a non-resonant vibrating system of plane motion[J]. Acta Mechanica Sinica, 2012, 28(5): 1424–1435.
    1. Wen BC, Fan J, Zhao CY, Xiong WL. Vibratory synchronization and controlled synchronization in engineering[M]. Beijing: Science Press, 2009.
    1. Blekhman II. Synchronization in science and technology[M], New York: ASME Press,1988.
    1. Blekhman II. Synchronization of dynamical systems[M], Moscow: Nauka,1971.
    1. Wen BC, Zhang H, Liu SY, He Q, Zhao CY. Theory and techniques of vibrating machinery and their applications[M], Beijing: Science Press, 2010.