Abstract
Generalized predictive controller of nonlinear systems are analyzed, to improve the efficiency, a secant method is employed to estimate the parameters of U-model that considered as an easy and effective modelling method for nonlinear dynamic plants. In this way, the final controller output of the nonlinear systems is transformed into solving a polynomial equation based on the available controller output, which greatly decreases the difficulties in the design of nonlinear control systems. The controller output can be derived from the secant method, which does not need to calculate the derivative, reduces the computational complexity and have faster convergence rate. In order to illustrate the design process and its effectiveness of the algorithm, a simulation is conducted to verify the method.
This work was supported by Hatching Foundation of NJUPT (No. NY217063).
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References
Abdeldjebar, B., Khier, B.: Generalized predictive control: application of the induction motor. In: Proceedings of the International Conference on Smart Manufacturing Application, 9–11 April, Gyeonggi-do, Korea, pp. 526–529 (2008)
Min, X., Shaoyuan, L.: A fast generalized predictive control algorithm for the typical industrial processes. In: Proceedings of the 4th World Congress on Intelligent Control and Automation (Cat. No. 02EX527), pp. 2416–2421 (2002)
Zhu, Q.M., Guo, L.Z.: A pole placement controller for nonlinear dynamic plant. Proc. IMechE, Part I: J. Syst. Control Eng. 216(16), 467–476 (2002)
Zhu, Q.M., Warwocl, K., Douce, J.L.: Adaptive general predictive controller for nonlinear systems. IEEE Proc. Control Theory Appl. 138(1), 33–40 (1991)
Chang, W.C.H., Wang, W.J., Jia, H.R.: Radial basis functions neural network of vary learning rate based stochastic U-model. In: International Conference on Electrical and Control Engineering (ICECE), Yichang, pp. 278–281 (2011)
Muhammad, S., Butt, N.R.: Real-time adaptive tracking of DC motor speed using U-model based IMC. Autom. Control Comput. Sci. 41(1), 31–38 (2007)
Tahir, K., Muhammad, S.: A novel internal model control scheme for adaptive tracking of nonlinear dynamic plants. In: 2006 1st IEEE Conference on Industrial Electronics and Applications, Wuhan, pp. 123–130. IEEE (2006)
Shafiq, M., Haseebuddin, M.: U-model-based internal model control for non-linear dynamic plants. Proc. IMechE, Part 1: J. Syst. Control Eng. 219(6), 449–458 (2005)
Shafiq, M., Butt, N.R.: U-model based adaptive IMC for nonlinear dynamic plants. In: 10th IEEE International Conference on Emerging Technologies and Factory Automation, pp. 955–959 (2005)
Du, W.X., Wu, X.L., Zhu, Q.M.: Direct design of a U-model-based generalized predictive controller for a class of non-linear (polynomial) dynamic plants. Proc. Inst. Mech. Eng. Part I: J. Syst. Control Eng. 226(1), 27–42 (2012)
Zhu, F., Yu, Z.J., Hu, Y.Z.: Proportional-integral generalized predictive control for nonlinear systems based on U-model. In: Proceedings of the 25th Chinese Process Control Conference, Dalian, pp. 958–965 (2014)
Du, W.X., Zhu, Q.M., Wu, X.L.: Support vector machine based U-model generalized predictive controller for nonlinear dynamic plants. In: Proceedings of the 33rd Chinese Control Conference, Nanjing, pp. 2178–2182 (2014)
Pang, Z.H., Cui, H.: System Identification and Adaptive Control MATLAB Simulation. Beijing University of Aeronautics and Astronautics Press, Beijing, vol. 8 (2013)
Ding, B.C.: Theory and Methods of Prediction control. Machinery Industry Press, Beijing, vol. X, p. 3 (2013)
Luo, W.C., Yi, X.B.: Calculate the common normal line’s distance of single arc gear based on secant method. In: The 1st International Conference on Information Science and Engineering (ICISE2009), pp. 158–161 (2009)
Hu, J.: A comparative study on the application of Newton method and Secant method. J. Yangtze Univ. 3(2), 479–480 (2006)
Narendra, K.S., Parthasarathy, K.: Identification and control of dynamical systems using neural networks. IEEE Trans. Neural Netw. 1(1), 4–27 (1990)
Ford, I., Kitsos, C.P., Titterington, D.M.: Recent advances in nonlinear experimental design. Technometrics 31(1), 49–60 (1989)
Acknowledgments
Great thank Professor Quanming Zhu for explanation of U-model estimation with Newton-Raphson iteration.
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Zhou, T., Ding, J., Deng, H. (2017). Secant Method Based U-Model Identification and Generalized Predictive Controller for Nonlinear Dynamic Systems. In: Yue, D., Peng, C., Du, D., Zhang, T., Zheng, M., Han, Q. (eds) Intelligent Computing, Networked Control, and Their Engineering Applications. ICSEE LSMS 2017 2017. Communications in Computer and Information Science, vol 762. Springer, Singapore. https://doi.org/10.1007/978-981-10-6373-2_39
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