Because of unknown nonlinearity and time-varying characteristic of electric scooter with V-belt continuously variable transmission system driven by using permanent magnet synchronous motor, its accurate dynamic model is difficult to establish for the design of the linear controller in whole system. In order to conquer this difficulty and raise robustness, an adaptive recurrent Chebyshev neural network control system is proposed to control for permanent magnet synchronous motor servo-drive electric scooter with V-belt continuously variable transmission under lumped nonlinear external disturbances in this study. The adaptive recurrent Chebyshev neural network control system consists of a recurrent Chebyshev neural network control and a compensated control with estimation law. In addition, the online parameter tuning methodology of the recurrent Chebyshev neural network and the estimation law of the compensated controller can be derived by using the Lyapunov stability theorem. Moreover, the two optimal learning rates of the recurrent Chebyshev neural network based on the discrete-type Lyapunov function are proposed to guarantee the convergence of tracking error. Finally, comparative studies are demonstrated by experimental results in order to show the effectiveness of the proposed control scheme.
NovotnyDWLipoTA. Vector control and dynamics of AC drives. New York: Oxford University Press, 1996.
2.
LeonhardW. Control of electrical drives. 2nd ed. Berlin: Springer-Verlag, 1996.
3.
LinFJ. Real-time IP position controller design with torque feedforward control for PM synchronous motor. IEEE Trans Ind Electron1997; 4(3): 398–407.
4.
HaykinS. Neural networks. Ottawa, ON, Canada: Maxwell Macmillan, 1994.
5.
SastryPSSantharamGUnnikrishnanKP. Memory neural networks for identification and control of dynamical systems. IEEE Trans Neural Network1994; 5(2): 306–319.
6.
GrinoRCembranoGTorrasC. Nonlinear system identification using additive dynamic neural networks—two on-line approaches. IEEE Trans Circ Syst Fund Theor Appl2000; 47(2): 150–165.
7.
FeiJDingH. Adaptive vibration control of microelectromechanical systems triaxial gyroscope using radial basis function sliding mode technique. Proc IMechE, Part I: J Systems and Control Engineering2013; 227(2): 264–269.
8.
NarendraKSParthasarathyK. Identification and control of dynamical systems using neural networks. IEEE Trans Neural Network1990; 1(1): 4–26.
9.
NguyenDHWidrowB. Neural networks for self-learning control systems. IEEE Contr Syst Mag1990; 10(3): 18–23.
10.
ShankarPYedavalliRK. Neural-network-based observer for turbine engine parameter estimation. Proc IMechE, Part I: J Systems and Control Engineering2009; 223(6): 821–832.
11.
XieXLHouZGChengL. Adaptive neural network tracking control of robot manipulators with prescribed performance. Proc IMechE, Part I: J Systems and Control Engineering2011; 225(6): 790–797.
12.
NamatameAUedaN. Pattern classification with Chebyshev neural networks. Int J Neural Network1992; 3(1): 23–31.
13.
LeeTTJengJT. The Chebyshev polynomial-based unified model neural networks for functional approximation. IEEE Trans Syst Man Cybern B Cybern1998; 28(6): 925–935.
14.
MollerMF. A scaled conjugate gradient algorithm for fast supervised learning. Neural Network1993; 6(4): 525–533.
15.
BattitiR. First- and second-order methods for learning: between steepest descent and Newton’s method. Neural Comput1992; 4: 141–166.
16.
CharalambousC. Conjugate gradient algorithm for efficient training of artificial neural networks. IEE Proc Circ Dev Syst1992; 139(3): 301–310.
17.
HaganMTMenhajMB. Training feedforward networks with Marquardt algorithm. IEEE Trans Neural Network1994; 5(6): 989–993.
18.
MadyasthaRKAazhangB. An algorithm for training multilayer perceptrons for data classification and function interpolation. IEEE Trans Circ Syst Fund Theor Appl1994; 41(12): 866–875.
19.
KuCCLeeKY. Diagonal recurrent neural networks for dynamical system control. IEEE Trans Neural Network1995; 6: 144–156.
20.
ChowTWSFangY. A recurrent neural-network-based real-time learning control strategy applying to nonlinear systems with unknown dynamics. IEEE Trans Ind Electron1998; 45(1): 151–161.
21.
BrdysMAKulawskiGJ. Dynamic neural controllers for induction motor. IEEE Trans Neural Network1999; 10(2): 340–355.
22.
LiXDHoJKLChowTWS. Approximation of dynamical time-variant systems by continuous-time recurrent neural networks. IEEE Trans Circ Syst Exp Brief2005; 52(10): 656–660.
23.
LuCHTsaiCC. Adaptive predictive control with recurrent neural network for industrial processes: an application to temperature control of a variable-frequency oil-cooling machine. IEEE Trans Ind Electron2008; 55(3): 1366–1375.
24.
LinFJLinCH. On-line gain-tuning IP controller using RFNN. IEEE Trans Aero Electron Syst2001; 37(2): 655–670.
25.
LinCHChiangPHTsengCS. Hybrid recurrent fuzzy neural network control for permanent magnet synchronous motor applied in electric scooter. In: 6th international power electronics conference, Sapporo, Japan, 21–24 June 2010, pp.1371–1376. New York: IEEE.
26.
LinCHLinCP. The hybrid RFNN control for a PMSM drive system using rotor flux estimator. Int J Power Electron2012; 4(1): 33–48.
27.
FodoreanDSzaboL. Control of a permanent magnet synchronous motor for electric scooter application. In: 21st international symposium on power electronics, electrical drives, automation and motion, Sorrento, 20–22 June 2012, pp.1178–1181. New York: IEEE.
28.
TsengCYChenLWLinYT. A hybrid dynamic simulation model for urban scooters with a mechanical-type CVT. In: IEEE international conference on automation and logistics, Qingdao, China, 1–3 September 2008, pp.519–519. New York: IEEE.
29.
TsengCYLueYFLinYT. Dynamic simulation model for hybrid electric scooters. In: IEEE international symposium on industrial electronics, Seoul, South Korea, 5–8 July 2009, pp.1464–1469. New York: IEEE.
30.
OliverLRHornungKGSwensonJE. Design equations for a speed and torque controlled variable-ratio V-belt transmission. SAE Trans1973; 82: 730003.
31.
AstromKJHagglundT. PID controller: theory, design, and tuning. Research Triangle Park, NC: Instrument Society of America, 1995.
32.
HagglundTAstromKJ. Revisiting the Ziegler-Nichols tuning rules for PI control. Asian J Contr2002; 4(4): 364–380.
33.
HagglundTAstromKJ. Revisiting the Ziegler-Nichols tuning rules for PI control—part II: the frequency response method. Asian J Contr2004; 6(4): 469–482.
34.
LinCHChouWDLinFJ. Adaptive hybrid control using a recurrent neural network for a linear synchronous motor servo-drive system. IEE Proc Contr Theor Appl2001; 148(2): 156–168.
