Skip to main content
SpringerLink
Log in

Adaptive output recurrent cerebellar model articulation controller for nonlinear system control

  • Original Paper
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

In this study, an adaptive output recurrent cerebellar model articulation controller (AORCMAC) is investigated for a nonlinear system. The proposed AORCMAC has superior capability to the conventional cerebellar model articulation controller in efficient learning mechanism and dynamic response. The dynamic gradient descent method is adopted to online adjust the AORCMAC parameters. Moreover, the analytical method based on a Lyapunov function is proposed to determine the learning-rates of AORCMAC so that the stability of the system can be guaranteed. Furthermore, the variable optimal learning-rates are derived to achieve the best convergence of tracking error. Finally, the effectiveness of the proposed control system is verified by the several simulation and experimental results. Those results show that the favorable performance can be obtained by using the proposed AORCMAC.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  • Agarwal A (1997) A systematic classification of neural-network-based control. IEEE Control Syst Mag 17:75–93

    Article  Google Scholar 

  • Chen JY, Tsai PS, Wong CC (2005) Adaptive design of a fuzzy cerebellar model arithmetic controller neural network. IEE Proc Control Theory Appl 152(2):133–137

    Article  Google Scholar 

  • Chiang CT, Lin CS (1996) CMAC with general basis functions. Neural Netw 9(7):1199–1211

    Article  Google Scholar 

  • Chow TWS, Fang Y (1998) A recurrent neural-network-based real-time learning control strategy applying to nonlinear systems with unknown dynamics. IEEE Trans Ind Electron 45(1):151–161

    Article  MathSciNet  Google Scholar 

  • Gonzalez-Serrano FJ, Figueiras-Vidal AR, Artes-Rodriguez A (1998) Generalizing CMAC architecture and training. IEEE Trans Neural Netw 9(6):1509–1514

    Article  Google Scholar 

  • Hwang KS, Lin CS (1998) Smooth trajectory tracking of three-link robot: a self-organizing CMAC approach. IEEE Trans Syst Man Cybern B 28(5):680–692

    Article  Google Scholar 

  • Hwang CL, Jan C, Chen YH (2001) Piezomechanics using intelligent variable-structure control. IEEE Trans Ind Electron 48(1):47–59

    Article  Google Scholar 

  • Jagannathan S (1999) Discrete-time CMAC NN control of feedback linearizable nonlinear systems under a persistence of excitation. IEEE Trans Neural Netw 10(1):128–137

    Article  Google Scholar 

  • Jan JC, Hung SL (2001) High-order MS_CMAC neural network. IEEE Trans Neural Netw 12(3):598–603

    Article  Google Scholar 

  • Kim YH, Lewis FL (2000) Optimal design of CMAC neural-network controller for robot manipulators. IEEE Trans Syst Man Cybern C 30(1):22–31

    Article  Google Scholar 

  • Kuschewski JG, Hui S, Zak SH (1993) Application of feed-forward neural networks to dynamical system identification and control. IEEE Trans Control Syst Technol 1(1):37–49

    Article  Google Scholar 

  • Lane SH, Handelman DA, Gelfand JJ (1992) Theory and development of higher-order CMAC neural networks. IEEE Control Syst Mag 12(2):23–30

    Article  Google Scholar 

  • Li YM, Leong SH (2004) Kinematics control of redundant manipulators using a CMAC neural network combined with a genetic algorithm. Robotica 22:611–621

    Google Scholar 

  • Lin CM, Hsu CF (2002a) Neural-network-based adaptive control for induction servomotor drive system. IEEE Trans Ind Electron 49(1):115–123

    Article  Google Scholar 

  • Lin CM, Hsu CF (2002b) Recurrent neural network adaptive control of wing-rock motion. J Guidance Control Dyn 25(6):1163–1165

    Article  Google Scholar 

  • Lin FJ, Lin CM, Hong CM (2000) Robust control of linear synchronous motor servodrive using disturbance observer and recurrent neural network compensator. IEE Proc Electr Power Appl 147(4):263–272

    Article  Google Scholar 

  • Lo JC, Kuo YH (1998) Decoupled fuzzy sliding-mode control. IEEE Trans Fuzzy Syst 6:426–435

    Article  Google Scholar 

  • Peng YF, Chiu CH (2008) The implementation of wheeled robot using adaptive output recurrent CMAC. 2008 IEEE international joint conference on neural networks, pp 2942–2947

  • Peng YF, Hsu CF, Lin CM and Chiu CH (2005) Intelligent adaptive control scheme for uncertain nonlinear systems using H control technique. 2005 IEEE international conference on mechatronics and automation, pp 2216–2221

  • Su SF, Lee ZJ, Wang YP (2006) Robust and fast learning for fuzzy cerebellar model articulation controllers. IEEE Trans Syst Man Cybern B 36(1):203–208

    Article  Google Scholar 

  • Wu TF, Tsai PS, Chang FR, Wang LS (2006) Adaptive fuzzy CMAC control for a class of nonlinear systems with smooth compensation. IEE Proc Control Theory Appl 153(6):647–657

    Article  Google Scholar 

  • Zheng Y, Luo S, Lv Z (2006) Control Double inverted pendulum by reinforcement learning with double CMAC network. In: Proceedings of the 18th international conference on pattern recognition, pp 639–642

Download references

Acknowledgment

This work was supported by the National Science Council of Taiwan, ROC under the Grant NSC95-2221-E-033-098

Author information

Authors and Affiliations

  1. Department of Electrical Engineering, Yuan-Ze University, 135 Yuan-Tung Rd., Chung-Li, Tao-Yuan, 320, Taiwan, ROC

    Chih-Hui Chiu

Authors
  1. Chih-Hui Chiu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chih-Hui Chiu.

Appendix

Appendix

The system parameters of double inverted pendulum:

$$ f_{1} = \frac{{A_{21} }}{{l_{1} m_{1} }}\sin \left( {\theta_{2} - \theta_{1} } \right) + \frac{1}{{l_{1} }}g\sin \theta_{1} - \frac{{A_{11} }}{{l_{1} m_{c} }}\cos \theta_{1} \sin \theta_{1} $$
$$ b_{1} = \frac{{A_{22} }}{{l_{1} m_{1} }}\sin \left( {\theta_{2} - \theta_{1} } \right) + \frac{{\cos \theta_{1} }}{{l_{1} m_{c} }} - \frac{{A_{12} }}{{l_{1} m_{c} }}\cos \theta_{1} \sin \theta_{1} $$
$$ f_{2} = \frac{{A_{22} }}{{l_{2} m_{1} }}\sin \left( {\theta_{2} - \theta_{1} } \right) $$
$$ b_{2} = \frac{{A_{12} }}{{l_{2} m_{1} }}\sin \left( {\theta_{2} - \theta_{1} } \right) $$
$$ a_{11} = \frac{1}{{m_{1} }} + \frac{{\sin^{2} \theta_{1} }}{{m_{c} }} $$
$$ a_{12} = - \frac{{\cos \left( {\theta_{2} - \theta_{1} } \right)}}{{m_{1} }} $$
$$ a_{22} = \frac{1}{{m_{1} }} + \frac{1}{{m_{2} }} $$
$$ \Updelta = a_{11} a_{22} - a_{12}^{2} $$
$$ A_{11} = \frac{{a_{22} \left( {l_{1} \dot{\theta }_{1}^{2} - g\cos \theta_{1} } \right) - a_{12} l_{2} \dot{\theta }_{2}^{2} }}{\Updelta } $$
$$ A_{12} = - \frac{{a_{22} \sin \theta_{1} }}{{\Updelta \cdot m_{c} }} $$
$$ A_{21} = \frac{{ - a_{12} \left( {l_{1} \dot{\theta }_{1}^{2} - g\cos \theta_{1} } \right) + a_{11} l_{2} \dot{\theta }_{2}^{2} }}{\Updelta } $$
$$ A_{22} = \frac{{a_{12} \sin \theta_{1} }}{{\Updelta \cdot m_{c} }} $$

where l 1 is the length of pole 1; l 2 length of pole 2; u apply force to move the cart; g acceleration of gravity; m c mass of the cart; m 1 mass of the ball at the top of pole 1; m 2 mass of the ball at the top of pole 2.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chiu, CH. Adaptive output recurrent cerebellar model articulation controller for nonlinear system control. Soft Comput 14, 627–638 (2010). https://doi.org/10.1007/s00500-009-0431-3

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-009-0431-3

Keywords

Search

Navigation