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Indirect Adaptive Inverse Control Synthesis via Fractional Least Mean Square Algorithm

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Modeling, Simulation and Optimization

Part of the book series: Smart Innovation, Systems and Technologies ((SIST,volume 292))

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Abstract

This work has as main objective to perform the performance analysis of the fractional least mean square (FLMS) algorithm, with respect to convergence speed and steady-state mean square error (MSE), in the indirect adaptive inverse control (IAIC) design. Since the main goal of IAIC, through inverse identification of the plant model, is to obtain a controller that tracks the plant inverse dynamics at each update of the controller weight vector, then performance analysis of the estimation algorithm is of fundamental importance. As a complexity scenario and aiming to obtain nonconservative results, the performance analysis was performed in the IAIC design for a non-minimum phase plant in the presence of sinusoidal reference signal and sinusoidal disturbance signal.

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References

  1. Widrow, B., Walach, E.: Adaptive signal processing for adaptive control. IFAC Proc. Vol. 16(9), 7–12. Elsevier (1983)

    Google Scholar 

  2. Widrow, B., Walach, E.: Adaptive Inverse Control: A Signal Processing Approach, Reissue ed. Wiley, Inc (2008)

    Google Scholar 

  3. Shafiq, M., Lawati, A. M., Yousef, H.: A simple direct adaptive inverse control structure. In: Canadian Conference on Electrical and Computer Engineering (CCECE), pp. 1–4. IEEE (2016)

    Google Scholar 

  4. Rigney, B., Pao, L., Lawrence, D.: Adaptive inverse control for settling performance improvements. In: American Control Conference, pp. 190–197. IEEE (2009)

    Google Scholar 

  5. Rigney, B.P., Pao, L.Y., Lawrence, D.A.: Nonminimum phase adaptive inverse control for settle performance applications. Mechatronics 20(1), 35–44. Elsevier (2010)

    Google Scholar 

  6. Noronha, R.P.: Adaptive inverse control synthesis subject to sinusoidal disturbance for non-minimum phase plant via FVSS-NLMS algorithm. In: 2021 Australian & New Zealand Control Conference, pp. 179–184. IEEE (2021)

    Google Scholar 

  7. Noronha, R.P.: Indirect adaptive inverse control design based on the FASS-NLMS algorithm. IFAC-PapersOnLine 54(20), 354–359. Elsevier (2021)

    Google Scholar 

  8. Shafiq, M., Shiaf, M.A., Yousef, H.A.: Stability and convergence analysis of direct adaptive inverse control. Complexity. Hindawi (2017)

    Google Scholar 

  9. Liu, Z., Lu, K., Lai, G., Chen, C.L.P., Zhang, Y.: Indirect fuzzy control of nonlinear systems with unknown input and state hysteresis using an alternative adaptive inverse. IEEE Trans. Fuzzy Syst. 29, 500–514. IEEE (2019)

    Google Scholar 

  10. Karatzinis, G., Boutalis, Y.S., Kottas, T.L.: System identification and indirect inverse control using fuzzy cognitive networks with functional weights. In: European Control Conference (ECC), pp. 2069–2074. IEEE (2018)

    Google Scholar 

  11. Diniz, P.S.R.: Adaptive filtering, vol. 4. Springer (1997)

    Google Scholar 

  12. Wang, X.Y., Wang, Y., Li, Z.S.: Research of the 3-DOF helicopter system based on adaptive inverse control. Appl. Mech. Mat. 389, 623–631. Trans Tech Publ (2013)

    Google Scholar 

  13. Zahoor, R.M.A., Qureshi, I.M.: A modified least mean square algorithm using fractional derivative and its application to system identification. Eur. J. Sci. Res. 35(1), 14–21 (2009)

    Google Scholar 

  14. Shoaib, B., Qureshi, I.M., Shafqatullah, I.: Adaptive step-size modified fractional least mean square algorithm for chaotic time series prediction. Chinese Phys. B 23(5), 050503. IOP Publishing (2014)

    Google Scholar 

  15. Gorenflo, R., Mainardi, F.: Fractional calculus. In: Fractals and Fractional Calculus in Continuum Mechanics, pp. 223–276. Springer (1997)

    Google Scholar 

  16. Taraso, V.E.: Handbook of Fractional Calculus with Applications, vol. 5. Gruyter Berlin (2019)

    Google Scholar 

  17. Hilfer, R.: Applications of fractional calculus in physics. World scientific (2000)

    Google Scholar 

  18. Ren, H.P., Wang, X., Fan, J.T., Kaynak, O.: Fractional order sliding mode control of a pneumatic position servo system. J. Franklin Inst. 356(12), 6160–6174. Elsevier (2019)

    Google Scholar 

  19. Khan, S., Naseem, I., Malik, M.A., Togneir, R., Bennamoun, M.: A fractional gradient descent-based rbf neural network. Circuits Syst. Signal Process. 37(12), 5311–5332. Springer (2018)

    Google Scholar 

  20. Song, W., Li, M., Li, Y., Cattani, C., Chi, C.H.: Fractional Brownian motion: difference iterative forecasting models. Chaos Solitons Fract. 123, 347–355. Elsevier (2019)

    Google Scholar 

  21. Dai, W., Huang, J., Qin, Y., Wang, B.: Regularity and classification of solutions to static Hartree equations involving fractional Laplacians. Discrete Continuous Dyn. Syst. 39(3), 1389. American Institute of Mathematical Sciences (2019)

    Google Scholar 

  22. Ahilan, A., Manogaran, G., Raja, C., Kadry, S., Kumar, S.N., Kumar, C.A., Jarin, T., Sujatha, K., Kumar, P.M., Babu, G.C., Murugan, N.S., Parthasarathy: Segmentation by fractional order darwinian particle swarm optimization based multilevel thresholding and improved lossless prediction based compression algorithm for medical images. IEEE Access 7, 89570–89580. IEEE (2019)

    Google Scholar 

  23. Khan, S., Wahab, A., Naseem, I., Moinuddin, M.: Comments on Design of fractional-order variants of complex LMS and NLMs algorithms for adaptive channel equalization. Nonlinear Dyn. 101(2), 1053–1060. Springer (2020)

    Google Scholar 

  24. Ahmad, J., Usman, M., Khan, S., Naseem, I., Syed, H.J.: Rvp-flms: a robust variable power fractional LMS algorithm. In: 6th IEEE International Conference on Control System, Computing and Engineering (ICCSCE), pp. 494–497. IEEE (2016)

    Google Scholar 

  25. Atangana, A., Gmóes-Aguilar, J.F.: Numerical approximation of Riemann-Liouville definition of fractional derivative: from Riemann-Liouville to Atangana-Baleanu. Numer. Methods Partial Diff. Eq. 34(5), 1502–1523. Wiley Online Library (2018)

    Google Scholar 

  26. Lin, S.Y., Yen, J.Y., Chen, M.S., Chang, S.H., Kao, C.Y.: An adaptive unknown periodic input observer for discrete-time LTI SISO systems. IEEE Trans. Autom. Control 62(8), 4073–4079. IEEE (2016)

    Google Scholar 

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Authors and Affiliations

  1. Federal University of Maranhão, Graduate Program in Electrical Engineering, São Luís, 65080-805, Brazil

    Rodrigo Possidônio Noronha

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  1. Rodrigo Possidônio Noronha
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Correspondence to Rodrigo Possidônio Noronha .

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Editors and Affiliations

  1. Department of Mechanical Engineering, National Institute of Technology Silchar, Silchar, India

    Biplab Das

  2. Department of Computer Science and Engineering, National Institute of Technology Silchar, Silchar, India

    Ripon Patgiri

  3. National Institute of Technology Silchar, Silchar, India

    Sivaji Bandyopadhyay

  4. Department of Automatics and Applied Software, “Aurel Vlaicu” University of Arad, Arad, Romania

    Valentina Emilia Balas

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Noronha, R.P. (2022). Indirect Adaptive Inverse Control Synthesis via Fractional Least Mean Square Algorithm. In: Das, B., Patgiri, R., Bandyopadhyay, S., Balas, V.E. (eds) Modeling, Simulation and Optimization. Smart Innovation, Systems and Technologies, vol 292. Springer, Singapore. https://doi.org/10.1007/978-981-19-0836-1_37

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