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Research Papers

Application of V-Belt Continuously Variable Transmission System Using Hybrid Recurrent Laguerre Orthogonal Polynomials Neural Network Control System and Modified Particle Swarm Optimization

[+] Author and Article Information
Chih-Hong Lin

Department of Electrical Engineering,
National United University,
No. 1, Lienda, Kung-Jing Li,
Maioli City 36003,
Miaoli County, Taiwan
e-mail: jhlin@nuu.edu.tw

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received September 9, 2014; final manuscript received February 24, 2015; published online June 10, 2015. Assoc. Editor: Paramsothy Jayakumar.

J. Comput. Nonlinear Dynam 10(5), 051019 (Sep 01, 2015) (16 pages) Paper No: CND-14-1206; doi: 10.1115/1.4030061 History: Received September 09, 2014; Revised February 24, 2015; Online June 10, 2015

Because the V-belt continuously variable transmission (CVT) system spurred by permanent magnet synchronous motor (PMSM) has unknown nonlinear and time-varying properties, the better control performance design for the linear control design is a time consuming procedure. In order to conquer difficulties for design of the linear controllers, the hybrid recurrent Laguerre orthogonal polynomials neural network (NN) control system, which has online learning ability to react to unknown nonlinear and time-varying characteristics, is developed for controlling PMSM servo-driven V-belt CVT system with the lumped nonlinear load disturbances. The hybrid recurrent Laguerre orthogonal polynomials NN control system consists of an inspector control, a recurrent Laguerre orthogonal polynomials NN control with adaptation law, and a recouped control with estimation law. Moreover, the adaptation law of online parameters in the recurrent Laguerre orthogonal polynomials NN is originated from Lyapunov stability theorem. Additionally, two varied learning rates of the parameters by means of modified particle swarm optimization (PSO) are posed in order to achieve better convergence. At last, comparative studies shown by experimental results are illustrated in order to verify the effectiveness of the proposed control scheme.

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References

Figures

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Fig. 1

Structure of the V-belt CVT system: (a) appearance of the primary pulley side and the secondary pulley side and (b) cross-sectional view of the secondary shaft

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Fig. 2

Schematic diagram of the PMSM-wheel connection through the V-belt CVT system

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Fig. 3

Block diagram of the V-belt CVT system spurred by PMSM

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Fig. 4

Block diagram of the hybrid recurrent Laguerre orthogonal polynomials NN control system

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Fig. 5

Structure of the three-layer recurrent Laguerre orthogonal polynomials NN

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Fig. 6

Experimental results of the V-belt CVT system spurred by PMSM using the well-known PI controller at 188.4 rad/s (1800 rpm) case under the lumped nonlinear external disturbances with parameter variation Tl = ΔTp+Tun: (a) tracking response of command rotor speed ωr*, desired command rotor speed ω* and measured rotor speed ωr; (b) response of tracking error e; and (c) response of tracking error e amplification

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Fig. 7

Experimental results of the V-belt CVT system spurred by PMSM using the well-known PI controller at 376.8 rad/s (3600 rpm) case under the lumped nonlinear external disturbances with twice parameter variations Tl = 2ΔTp+Tun: (a) tracking response of command rotor speed ωr*, desired command rotor speed ω* and measured rotor speed ωr; (b) response of tracking error e; and (c) response of tracking error e amplification

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Fig. 8

Experimental results of the V-belt CVT system spurred by PMSM using the well-known PI controller: (a) response of electromagnetic torque Te at 188.4 rad/s (1800 rpm) case under the lumped nonlinear external disturbances with parameter variation Tl = ΔTp+Tun; (b) response of electromagnetic torque Te at 376.8 rad/s (3600 rpm) case under the lumped nonlinear external disturbances with twice parameter variations Tl= 2ΔTp+Tun

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Fig. 9

Experimental results of the V-belt CVT system spurred by PMSM using the hybrid recurrent Laguerre orthogonal polynomials NN control system with two fixed learning rates at 188.4 rad/s (1800 rpm) case under the lumped nonlinear external disturbances with parameter variations Tl = ΔTp+Tun: (a) tracking response of command rotor speed ωr*, desired command rotor speed ω* and measured rotor speed ωr; (b) response of tracking error e; and (c) response of tracking error e amplification

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Fig. 10

Experimental results of the V-belt CVT system spurred by PMSM using the hybrid recurrent Laguerre orthogonal polynomials NN control system with two fixed learning rates at 376.8 rad/s (3600 rpm) under the lumped nonlinear external disturbances with twice parameter variations Tl = 2ΔTp+Tun: (a) tracking response of command rotor speed ωr*, desired command rotor speed ω* and measured rotor speed ωr; (b) response of tracking error e; and (c) response of tracking error e amplification

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Fig. 11

Experimental results of the V-belt CVT system spurred by PMSM using the hybrid recurrent Laguerre orthogonal polynomials NN control system with two fixed learning rates: (a) response of electromagnetic torque Te at 188.4 rad/s (1800 rpm) case under the lumped nonlinear external disturbances with parameter variations Tl = ΔTp+Tun; and (b) response of electromagnetic torque Te at 376.8 rad/s (3600 rpm) case under the lumped nonlinear external disturbances with twice parameter variations Tl = 2ΔTp+Tun

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Fig. 12

Experimental results of the V-belt CVT system spurred by PMSM using the hybrid recurrent Laguerre orthogonal polynomials NN control system with two varied learning rates by means of modified PSO at 188.4 rad/s (1800 rpm) case under the lumped nonlinear external disturbances with parameter variations Tl = ΔTp+Tun: (a) tracking response of command rotor speed ωr*, desired command rotor speed ω* and measured rotor speed ωr; (b) response of tracking error e; and (c) response of tracking error e amplification

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Fig. 13

Experimental results of the V-belt CVT system spurred by PMSM using the hybrid recurrent Laguerre orthogonal polynomials NN control system with two varied learning rates by means of modified PSO at 376.8 rad/s (3600 rpm) under the lumped nonlinear external disturbances with twice parameter variations Tl = 2ΔTp+Tun: (a) tracking response of command rotor speed ωr*, desired command rotor speed ω* and measured rotor speed ωr; (b) response of tracking error e; and (c) response of tracking error e amplification

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Fig. 14

Experimental results of the V-belt CVT system spurred by PMSM using the hybrid recurrent Laguerre orthogonal polynomials NN control system with two varied learning rates by means of modified PSO: (a) response of electromagnetic torque Te at 188.4 rad/s (1800 rpm) case under the lumped nonlinear external disturbances with parameter variations Tl = ΔTp+Tun; and (b) response of electromagnetic torque Te at 376.8 rad/s (3600 rpm) case under the lumped nonlinear external disturbances with twice parameter variations Tl = 2ΔTp+Tun

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Fig. 15

Experimental results of the recurrent Laguerre orthogonal polynomials NN by using modified PSO at 188.4 rad/s (1800 rpm) case under the lumped nonlinear external disturbances with parameter variations Tl = ΔTp+Tun: (a) the convergence response of learning rates μ1; and (b) the convergence response of learning rates μ2

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Fig. 16

Experimental results of the recurrent Laguerre orthogonal polynomials NN by using modified PSO at 376.8 rad/s (3600 rpm) case under the lumped nonlinear external disturbances with twice parameter variations Tl = 2ΔTp+Tun: (a) the convergence response of learning rates μ1; and (b) the convergence response of learning rates μ2

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Fig. 17

Numerical results of the iteration performance for two learning rates in the Laguerre orthogonal polynomials NN by means of modified PSO from 0 s to 0.6 s with 240 iterations (runs) at 188.4 rad/s (1800 rpm) case under the lumped nonlinear external disturbances with parameter variations Tl = ΔTp+ Tun: (a) response of learning rates μ1; and (b) response of learning rates μ2

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Fig. 18

Numerical results of the iteration performance for two learning rates in the Laguerre orthogonal polynomials NN by means of modified PSO from 0 s to 0.6 s with 240 iterations (runs) at 376.8 rad/s (3600 rpm) case under the lumped nonlinear external disturbances with twice parameter variations Tl = 2ΔTp+Tun: (a) response of learning rates μ1; and (b) response of learning rates μ2

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Fig. 19

Experimental results under Tl = 2Nm(Ta)+Tun load disturbances with adding load at 376.8 rad/s (3600 rpm) case: (a) speed adjusted response of command rotor speed ωr*, measured rotor speed ωr using the well-known PI controller; and (b) response of measured current ia in phase a using the well-known PI controller

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Fig. 20

Experimental results under Tl = 2Nm(Ta)+Tun load disturbances with adding load at 376.8 rad/s (3600 rpm) case: (a) speed adjusted response of command rotor speed ωr*, measured rotor speed ωr using the hybrid recurrent Laguerre orthogonal polynomials NN control system with two fixed learning rates; and (b) response of measured current ia in phase a using the hybrid recurrent Laguerre orthogonal polynomials NN control system with two fixed learning rates

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Fig. 21

Experimental results under Tl = 2Nm(Ta)+Tun load disturbances with adding load at 376.8 rad/s (3600 rpm) case: (a) speed adjusted response of command rotor speed ωr*, measured rotor speed ωr using the hybrid recurrent Laguerre orthogonal polynomials NN control system with two varied learning rates by means of modified PSO; and (b) response of measured current ia in phase a using the hybrid recurrent Laguerre orthogonal polynomials NN control system with two varied learning rates by means of modified PSO

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