第五章、 結論與未來研究方向
5.2 未來展望
舉出一些未來能夠繼續研究的方向與相關的主題:
1. 將本論文的方法擴充到其他系統的應用,如時間延遲系統。
2. 使用其他參數調整方法替換 Ziegler–Nichols 參數調整方法使其在用 Matlab 求 解參數能有更好的效果,或者是使用其他方法取代Matlab 的函數 ’fsolve’ 來 尋找控制器參數。
3. 尋找其他更有效的方法將本篇使用兩個階段做設計這點改善至可以直接設計 出達到期望效能的控制器。
參考文獻
[1] G. W. Leibniz, Letter from Hanover, Germany, September 30, 1695 to G. A.
L'Hospital. Leibnizen Mathematische Schrifien, Vol. 2, pp. 301-302, Olms Verlag, Hildesheim, Germany, 1962, First published in 1849.
[2] J. Liouville, " Memoire sur quelques Questions de Geometrie et de Mecanique, et sur un nouveau genre de Calcul pour resoudre ces Questions," J. Ecole Polytech, Section 21, pp. 1-69, 1832.
[3] B. Riemann, "Versuch einer allgemeinen Auffasung der Integration und Differen-Differentiation," The Collected Works of Bernhard Riemann (H.
Weber, ed.), 2nd ed. Dover, New York, 1953.
[4] H. J. Holmgren, "Om differentialkalkylen med indices of hvad nature sam heist,"
Kongliga Svenska Vetenskaps-Akademiens Handlinger 11, pp. 1-83, 1864.
[5] L. Euler, "De Progressionibus Transcentibus, sev Quarum Termini Algebraice Dari Nequeunt," Comment. Acad. Sci. Imperialis Petropolitanae 5, pp. 38-57, 1738.
[6] J. L. Lagrange, " Sur une nouvelle espece de calcul relatif a la differentiation et a l'integration des quantites variables," Oeuvres de Lagrange, Vol. 3, pp. 441-476.
Gauthier-Villars, Paris, 1849, First appeared in Nouv. Mem. Acad. Roy. Sci.
Belles- Lett. Berlin 3, pp. 185-206, 1772.
[7] A. K. Griinwald, " Ueber ‘begrenzte’ Derivationen und deren Anwendung," Z.
Math. Phys. 12, pp. 441-480, 1867.
[8] A. Krug, "Theorie der Derivationen," Akad. Wiss. Wien Denkenschriften, Math.
Naturwiss. Kl. 57, pp. 151-228, 1890.
[9] H. Weyl, "Bemerkungen zum Begriff des Differentialquotienten gebrochener Ordnung," Vierteljschr. Naturforsch. Gesellsch. Zurich 62, pp. 296-302, 1971.
[10] G. H. Hardy, "On Some Properties of Integrals of Fractional Order," Messenger Math. 41, pp. 145-150, 1917.
[11] G. H. Hardy and J. E. Littlewood, "Some Properties of Fractional Integrals,"
Proc. London Math. Soc. [2], 24, pp. 37-41, 1925.
[12] G. H. Hardy and J. E. Littlewood, "Some Properties of Fractional Integrals, I,"
Math. Z. 27, pp. 565-606, 1928.
[13] G. H. Hardy and J. E. Littlewood, "Some Properties of Fractional Integrals, II,"
Math. Z. 34, pp. 403-439, 1932.
[14] H. Kober, " On Fractional Integrals and Derivatives," Quart. J. Math. Oxford Ser. 11, pp. 193-211, 1940.
[15] B. Kuttner, "Some Theorems on Fractional Derivatives," Proc. London Math.
Soc. [3] 3, pp. 480-497, 1953.
[16] A. Erdélyi, "Transformation of Hypergeometric Integrals by Means of Fractional Integration by Parts," Quart. J. Math. Oxford Ser. 10, pp. 176-189, 1939.
[17] A. Erdélyi, "On fractional integration and its applications to the theory of Hankel transforms," Quart. J. Math. Oxford Ser. 11, pp. 293, 1940.
[18] A. Erdélyi and staff of the Bateman Manuscript Project, "Tables of Integral Trans- Transforms," Vol. 2, pp. 181-214. McGraw-Hill, New York, 1954.
[19] T. J. Osler, "Leibniz Rule for Fractional Derivatives Generalized and an Application to Infinite Series," SIAM J. Appl. Math. 16, pp. 658-674, 1970.
[20] E. L. Post, "Generalized Differentiation," Trans. Amer. Math. Soc. 32, pp. 723-781, 1930.
[23] A. Erdelyi, "Axially Symmetric Potentials and Fractional Integration," SIAM J.
Appl. Math. 13, pp. 216-228, 1965.
[24] T. P. Higgins, "The Use of Fractional Integral Operators for Solving Nonhomo-geneous Differential Equations," Document DI-82-0677, Boeing Sci. Res. Lab., Seattle, Washington, 1967.
[25] G. W. Scott Blair, "The role of psychophysics in rheology," J. Colloid Sci. 2, pp.
21, 1947.
[26] T. D. Shermergor, "On the use of fractional differentiation operators for describing the hereditary properties of materials," Z. Prikl. Mech. i Tekhn. Fiz.
6, pp. 118, 1966.
[27] G. W. Scott Blair, "The role of psychophysics in rheology," J. Colloid Sci. 2, pp.
21, 1947.
[28] G. W. Scott Blair, "Measurements of Mind and Matter," Dennis Dobson, London, 1950.
[29] G. W. Scott Blair, " Some aspects of the search for invariants," British J. Philos.
Sci. 1, pp. 230, 1950.
[30] G. W. Scott Blair, and J. E. Caffyn, "An application of the theory of quasi-properties to the treatment of anomalous stress-strain relations," Philos. Mag. 40, pp. 80, 1949.
[31] A. Graham, G. W. Scott Blair, and R. F. J. Withers, "A methodological problem in rheology," British J. Philos. Sci. 11, pp. 265, 1961.
[32] V. A. Belavin, R. Sh. Nigmatullin, A. I. Miroshnikov, and N. K. Lutskaya,
"Fractional differentiation of oscillographic polarograms by means of an
[34] K. B. Oldham, and J. Spanier, "The replacement of Fick's laws by a formulation involving semidifferentiation," J. Electroanal. Chem. Interfacial Electrochem.
26, pp. 331, 1970.
[35] M. Grenness, and K. B. Oldham, " Semiintegral electroanalysis: theory and verification," Anal. Chem. 44, pp. 1121, 1972.
[36] R. L. Somorjai, and D. M. Bishop, "Integral-transformation trial functions of the fractional-integral class." Phys. Rev. A 1, pp. 1013, 1970.
[37] K. B. Oldham, "Diffusive transport to planar, cylindrical, and spherical electrodes," J. Electroanal. Chem. Interfacial Electrochem. 41, pp. 351, 1973.
[38] K. B. Oldham, and J. Spanier, "A general solution of the diffusion equation for semiinfinite geometries," J. Math. Anal. Appl. 39, pp. 655, 1972.
[39] I. Podlubny, "Fractional-order systems and PI D controllers," IEEE Transactions on Automatic Control, volume. 44, issue 1, pp 208-214, 1999.
[40] M. Dorigo, "Optimization, Learning and Natural Algorithms," PhD Dissertation, Politecnico di Milano, 1992.
[41] J. Kennedy, and R. Eberhart, "Particle Swarm Optimization," Proc. of the IEEE International Conference on Neural Networks, N. J. IEEE Press, pp. 1942-1948, 1995.
[42] Y. Shi, and R. Eberhart, "A Modified Particle Swarm Optimizer," Procedings of the 1998 IEEE International Conference on Evolutionary Computation, pp. 69-73, 1998.
[43] Y. Shi, and R. Eberhart, "Empirical Study of Particle Swarm Optimization,"
Proceedings of the 1999 Congress on Evolutionary Computation, Vol.3, pp.
[45] A. Ratnaweera, S. K. Halgamuge, and H. C. Watson, "Self-Organizing Hierarchical Particle Swarm Optimizer With Time-Varying Acceleration Coefficients," IEEE Transactions on Evolutionary Computation, Vol. 8(3), pp.240-255, 2004.
[46] A. Chatterjee, and P. Siarry, "Nonlinear inertia weight variation for dynamic adaptation in particle swarm optimization," Computers and Operations Research, Vol. 33, pp. 859-871, 2006.
[47] C. N. Ko, Y. P. Chang, and C. J. Wu, "An orthogonal-array-based particle swarm optimizer with nonlinear time-varying evolution," Applied Mathematics and Computation, Vol. 191, pp. 272-279, 2007.
[48] K. Oldham, and J. Spanier, "The Fractional Calculus," Hardcover: 234 pages.
Publisher: Academic Press, pp. 45-60. 1974.
[49] M. D. Ortigueira, and F. Coito, "From Differences to Derivatives," Fractional Calculus and Applied Analysis. 7(4), pp. 459-471, 2004.
[50] M. Riesz, "L'intégrale de Riemann-Liouville et le problème de Cauchy," Acta Mathematica 81 (1), pp. 1-223, 1949.
[51] E. Hille and R. S. Phillips, "Functional analysis and semi-groups," Revised Edition, Amer. Math. Soc. 1957.
[52] K. S. Miller, and B. Ross, "An Introduction to the Fractional Calculus and Fractional Differential Equations," John Wiley & Sons, 1993.
[53] P.I. Lizorkin, "Fractional integration and differentiation in M. Hazewinkel,
"Encyclopedia of Mathematics," Springer Verlag, Berlin, Heidelberg, New York, 2001.
[56] J. G. Ziegler and N. B. Nichols, "Optimum settings for automatic controllers,"
Trans. Amer. Soc. Mech. Eng., vol. 64, pp. 759–768, 1942.
[57] A. S. McCormack, and K. R. Godfrey, "Rule-Based Autotuning Based on Frequency Domain Identification," IEEE Transactions on Control Systems Technology, Vol. 6, No. 1, pp. 43-60, 1998.
[58] D. W. Pessen, "A new look at PID-controller tuning," Trans. Amer. Soc. Mech.
Eng., J. Dynamic Syst., Meas., Contr., vol. 116, pp. 553–557, 1994.
[59] D. E. Seborg, T. F. Edgar, and D. A. Mellichamp, "Process Dynamics and Control." New York, Wiley, 1989.
[60] C. Y. Wang, J. F. Li, Y. D. Liu and M. Q. Li, "Research on UAV Attitude Control Based on Fractional Order Proportional Integral Controllers," IEEE Proceedings of the 33rd Chinese Control Conference, Nanjing, China, pp. 3552-3557, 2014.
[61] J. H. Chou, "Optimization approaches," Lecture Notes and Handouts at the Institute of Electrical Engineering (National Kaohsiung University of Applied Sciences), Taiwan, part 3, pp. 1-42, 2013.
[62] D. V. Deepak, and S. U. Kumari, "Modified method of tuning for fractional PID controllers," Power Signals Control and Computations (EPSCICON), 2014 International Conference on IEEE, pp. 1-6, 2014.
[63] C. Yeroglu, and N. Tan, "Note on fractional-order proportional integral-differential controller design," IET Control Theory Application, Vol. 5, issue 17, pp. 1978-1989, 2011.
[64] C. A. monje, Y. Q. Chen, D. Xue, B. M. Vinagre and V. Feliu, "Fractional-order Systems and Control : Fundamentals and Applications," Advances in Industrial Control, Springer, 2010.
[65] D. Xue, Y. Q. Chen and D. P. Atherton, "Linear Feedback Control Analysis and Design with MATLAB, " Advances in Design and Control, Siam, 2007.
[66] B. Kada, and Y. Ghazzawi, "Robust PID Controller Design for an UAV Flight
Computer Science. Vol. 2, pp. 1-6, 2011.