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Journal of Applied Mathematics and Computing

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01.10.2015 | Original Research

Newton iterative algorithm based modeling and proportional derivative controller design for second-order systems

verfasst von: Kai Ji, Ling Xu, Weili Xiong, Lei Chen

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1-2/2015

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Abstract

This paper proposes an identification method for estimating the parameters of a stable second-order system based on the impulse response experiment. From the impulse response experiment, the measured data are collected for implementing parameter estimation. By defining and minimizing a cost function, a Newton iterative algorithm is derived for estimating the parameters of the system. The multi-point identification method is used to show the effectiveness of the proposed Newton iterative algorithm. The results show that the estimated model by the proposed Newton iterative estimation method has higher accuracy. Based on the estimated model, a design method of the proportional derivative controller is presented according to the system dynamical performance. The simulation test shows that the proposed controller design method can meet the desired dynamic specifications.

Vorheriger Artikel Convergence analysis of Legendre spectral projection methods for Hammerstein integral equations of mixed type

Nächster Artikel Asymptotic behavior of a non-autonomous predator-prey model with Hassell–Varley type functional response and random perturbation

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Rosa, P.V., Josep, M.F.L., Urbano, L., Javier, C.: Parameter identification method for a three-dimensional footCground contact model. Mech. Mach. Theory 75(5), 107–116 (2014)

Liu, C.H.: Modelling and parameter identification for a nonlinear time-delay system in microbial batch fermentation. Appl. Math. Model. 37(10–11), 6899–6908 (2013)MathSciNetCrossRef

Upadhyay, R.K., Agrawal, R.: Modeling the effect of mutual interference in a delay-induced predator-prey system. J. Appl. Math. Comput. 1–27 (2014). doi:10.1007/s12190-014-0822-1

Li, C.H., Feng, E.M.: Existence of optimal solution and optimality condition for parameter identification of an ecological species system. J. Appl. Math. Comput. 18(1–2), 273–286 (2005)MATHMathSciNetCrossRef

Ding, F.: System Identification-Performances Analysis for Identification Methods. Science Press, Beijing (2014)

Shi, Y., Fang, H.: Kalman filter based identification for systems with randomly missing measurements in a network environment. Int. J. Control 83(3), 538–551 (2010)MATHMathSciNetCrossRef

Zhang, Y.: Unbiased identification of a class of multi-input single-optput systems with correlated disturbances using bias compensation methods. Math. Comput. Model. 53(9–10), 1810–1819 (2011)MATHCrossRef

Liu, Y.J., Ding, F., Shi, Y.: An efficient hierarchical identification method for general dual-rate sampled-data systems. Automatica 50(3), 962–970 (2014)MATHMathSciNetCrossRef

Samanta, G.P., Manna, D., Maiti, A.: Bioeconomic modelling of a three-species fishery with switching effect. J. Appl. Math. Comput. 12(1–2), 219–231 (2003)MATHMathSciNetCrossRef

10.

Boutayeb, A., Chetouani, A., Achouyab, A., Twizell, E.H.: A non-linear population model of diabetes mellitus. J. Appl. Math. Comput. 21(1–2), 127–139 (2006)MATHMathSciNetCrossRef

11.

Liu, T., Wang, Q.G., Huang, H.P.: A tutorial review on process identification from step or relay feedback test. J. Proc. Control 23(10), 1597–1623 (2013)MathSciNetCrossRef

12.

Ahmed, S., Huang, B., Shah, S.L.: Novel identification method from step response. Control Eng. Pract. 15(5), 545–556 (2007)CrossRef

13.

Mei, H., Li, S.Y., Cai, W.J., Xiong, Q.: Decentralized closed-loop parameter identification for multivariable processes from step responses. Math. Comput. Simul. 68(2), 171–192 (2005)MATHMathSciNetCrossRef

14.

Huang, H.P., Lee, M.W., Chen, C.L.: A system of procedures for identification of simple models using transient step response. Ind. Eng. Chem. Res. 40(8), 1903–1915 (2001)CrossRef

15.

Ahemd, S., Huang, B., Shah, S.L.: Identification from step responses with transient initial conditions. J. Process Control 18(2), 121–130 (2008)CrossRef

16.

Chen, L., Li, J.H., Ding, R.F.: Identification for the second-order systems based on the step response. Math. Comput. Model. 53(5–6), 1074–1083 (2011)MATHMathSciNetCrossRef

17.

Shi, Y., Yu, B.: Output feedback stabilization of networked control systems with random delays modeled by Markov chains. IEEE Trans. Autom. Control 54(7), 1668–1674 (2009)MathSciNetCrossRef

18.

Hidayat, E., Medvedev, A.: Laguerre domain identification of continuous linear time-delay systems from impulse response data. Automatica 48(11), 2902–2907 (2012)MATHMathSciNetCrossRef

19.

Deb, A., Sarkar, G., Mandal, P., Biswas, A., Ganguly, A., Biswas, D.: Transfer function identification from impulse response via a new set of orthogonal hybrid functions (HF). Appl. Math. Comput. 218(9), 4760–4787 (2012)MATHMathSciNetCrossRef

20.

Liu, T., Gao, F.R.: A frequency domain step response identification method for continuous-time processes with time delay. J. Process Control 20(7), 800–809 (2010)CrossRef

21.

Mei, H., Li, S.Y.: Decentralized identification for multivariable integrating processes with time delays from closed-loop step tests. ISA Trans. 46(2), 189–198 (2007)CrossRef

22.

Panda, R.C., Vijayan, V., Sujatha, V., Deepa, P., Manamali, D., Mandal, A.B.: Parameter estimation of integrating and time delay processes using single relay feedback test. ISA Trans. 50(4), 529–537 (2011)CrossRef

23.

Xu, L.: A proportional differential control nethod for a time delay system using the Taylor approximation. Appl. Math. Comput. 236(6), 391–399 (2014)MathSciNetCrossRef

24.

Malek, H., Luo, Y., Chen, Y.Q.: Identification and tuning fractional order proportional integral controllers for time delayed systems with a fractional pole. Mechatronics 23(7), 746–754 (2013)CrossRef

25.

Baran, N., Wozny, G., Arellano-Garcia, H.: Model-based system identification and PI controller tuning using closed-loop set-point response. Comput. Aided Chem. Eng. 31, 755–759 (2012)CrossRef

26.

Mohideen, K.A., Saravanakumar, G., Valarmathi, K., Devaraj, D., Radhakrishnan, T.K.: Real-coded genetic algorithm for system identification and tuning of a modified model reference adaptive controller for a hybrid tank system. Appl. Math. Model. 37(6), 3829–3847 (2013)MathSciNetCrossRef

27.

Vörös, J.: Iterative algorithm for parameter identification of Hammerstein systems with two-segment nonlinearities. IEEE Trans. Autom. Control 44(11), 2145–2149 (1999)MATHCrossRef

28.

Liu, M.M., Xiao, Y.S., Ding, R.F.: Iterative identification algorithm for Wiener nonlinear systems using the Newton method Appl. Math. Model. 37(9), 6584–6591 (2013)MathSciNetCrossRef

29.

Ramadan, M.A., Naby, M.A.A., Bayoumi, A.M.E.: Iterative algorithm for solving a class of general sylvester-conjugate matrix equation \(\sum _{i = 1}^{s} A_{i}V + \sum _{j = 1}^{t} B_{j}W = \sum _{l = 1}^{m} E_{l}\overline{V}F_{l} + C\). J. Appl. Math. Comput. 44, 99–118 (2014)MATHMathSciNetCrossRef

30.

Ding, F., Liu, X.G., Chu, J.: Gradient-based and least-squares-based iterative algorithms for Hammerstein systems using the hierarchical identification principle. IET Control Theory Appl. 7(2), 176–184 (2013)MathSciNetCrossRef

31.

Ding, F.: Two-stage least squares based iterative estimation algorithm for CARARMA system modeling. Appl. Math. Model. 37(7), 4798–4808 (2013)MathSciNetCrossRef

32.

Yun, B.I.: Iterative methods for solving nonlinear equations with finitely many roots in an interval. J. Comput. Appl. Math. 236(13), 3308–3318 (2013)CrossRef

33.

Chidume, C.E., Djitté, N.: An iterative method for solving nonlinear integral equations of Hammerstein type. Appl. Math. Comput. 219(10), 5613–5621 (2013)MATHMathSciNetCrossRef

34.

Noor, M.A., Khan, W.A.: New iterative methods for solving nonlinear equation by using homotopy perturbation method. Appl. Math. Comput. 219(8), 3565–3574 (2012)MathSciNetCrossRef

35.

Wu, A.G., Lv, L.L., Duan, G.R.: Iterative algorithms for solving a class of complex conjugate and transpose matrix equations. Appl. Math. Comput. 217(21), 8343–8353 (2011)MATHMathSciNetCrossRef

36.

Sharma, J.R., Arora, H.: On efficient weighted-Newton methods for solving systems of nonlinear equations. Appl. Math. Comput. 222(1), 497–506 (2013)MathSciNetCrossRef

37.

Li, J.H.: Parameter estimation for Hammerstein CARARMA systems based on the Newton iteration. Appl. Math. Lett. 26(1), 91–96 (2013)MATHMathSciNetCrossRef

38.

Bruschetta, M., Picci, G., Saccon, A.: A variational integrators approach to second order modeling and identification of linear mechanical systems. Automatica 50(3), 727–736 (2014)MATHMathSciNetCrossRef

39.

Delis, A.I., Nikolos, I.K., Papageorgiou, M.: High-resolution numerical relaxation approximations to second-order macroscopic traffic flow models. Transp. Res. Part C Emerg. Technol. 44(7), 318–349 (2014)CrossRef

40.

Yuan, K., Li, H.X., Cao, J.D.: Robust stabilization of the distributed parameter system with time delay via fuzzy control. IEEE Trans. Fuzzy Syst. 16(3), 567–584 (2008)CrossRef

41.

Yuan, K., Cao, J.D., Deng, M.: Exponential stability and periodic solutions of fuzzy cellular neural networks with time-varying delays. Nerocomputing 69(13–15), 1619–1627 (2006)CrossRef

42.

Sondhi, S., Hote, Y.V.: Fractional order PID controller for load frequency control. Energy Conserv. Manage. 85(9), 343–353 (2014)CrossRef

43.

Sommer, S., Nguyen, H.N., Kienle, A.: Auto-tuning of multivariable PI/PID controllers using iterative feedback tuning: design examples. Comput. Aided Chem. Eng. 33, 721–726 (2014)CrossRef

44.

Zhang, R., Wu, S., lu, R., Gao, F.R.: Predictive control optimization based PID control for temperature in an industrial surfactant reactor. Chemometr. Intell. Lab. Syst. 135(15), 48–62 (2014)CrossRef

45.

Wu, S., Zhang, R., Lu, R.Q., Gao, F.R.: Design of dynamic matrix control based PID for residual oil outlet temperature in a coke furnace. Chemometr. Intell. Lab. Syst. 134(15), 110–117 (2014)CrossRef

46.

Jeng, J.C., Tseng, W.L., Chiu, M.S.: A one-step tuning method for PID controllers with robustness specification using plant step-response data. Chem. Eng. Res. Des. 92(3), 545–558 (2014)CrossRef

47.

Tran, H.D., Guan, Z.H., Dang, X.K., Cheng, X.M., Yuan, F.S.: A normalized PID controller in networked control systems with varying time delays. ISA Trans. 52(5), 592–599 (2013)CrossRef

48.

Vijayan, V., Panda, R.C.: Design of PID controllers in double feedback loops for SISO systems with set-point filters. ISA Trans. 51(4), 514–521 (2012)CrossRef

49.

Ramasamy, M., Sundaramoorthy, S.: PID controller tuning for desired closed-loop responses for SISO systems using impulse response. Comput. Chem. Eng. 32(8), 1773–1788 (2008)CrossRef

50.

Chen, Z.H., Yuan, X.H., Ji, B., Wang, P.T., Tian, H.: Design of a fractional order PID controller for hydraulic turbine regulating system using chaotic non-dominated sorting genetic algorithm II. Energy Conserv. Manage. 84(8), 390–404 (2014)CrossRef

51.

Yuan, K., Alofi, A., Cao J.D., Al-Mazrooei A., Elaiw a.: Synchronization of the coupled distributed parameter system with time delay via proportional spatial derivative control. Discret. Dyn. Nat. Soc. Article ID 418258 2014, DOI:10.1155/2014/418258

52.

Chen, L.: Identification for transfer function models of continuous-time systems, Jiangnan University Master Degree Thesis (2011)

Titel: Newton iterative algorithm based modeling and proportional derivative controller design for second-order systems
verfasst von: Kai Ji
Ling Xu
Weili Xiong
Lei Chen
Publikationsdatum: 01.10.2015
Verlag: Springer Berlin Heidelberg
Erschienen in: Journal of Applied Mathematics and Computing / Ausgabe 1-2/2015
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-014-0853-7

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