Abstract
This paper considers a problem of fractional-order PID controller tuning to optimize it in average over a set of initial states of the plant–controller closed system and over a set of typical input signals. The problem is reduced to a multidimensional optimization problem. We suggest an approach to the solution, implementing it algorithmically. The approach is illustrated by a parametric design of an optimal in average fractional-order PID controller for pitch control of an aircraft.
Similar content being viewed by others
References
Avsievich, A.V. and Avsievich, V.V., Modeling of Systems of Automatic Control with a Fractional PID Controller, Vestn. Samarsk. Gos. Tekhn. Univ., Ser. Tekhn. Nauki, 2010, no. 1(26), pp. 6–59.
Bodner, V.A., Teoriya avtomaticheskogo upravleniya poletom (Automatic Flight Control Theory), Moscow: Nauka, 1961.
Butkovskii, A.G., Postnov, S.S., and Postnova, E.A., Fractional Integro-Differential Calculus and Its Control-Theoretical Applications. II. Fractional Dynamic Systems: Modeling and Hardware Implementation, Autom. Remote Control, 2013, vol. 74, no. 5, pp. 725–749.
Panteleev, A.V. and Letova, T.A., Metody optimizatsii v primerakh i zadachakh (Optimization Methods in Examples and Problems), Moscow: Vysshaya Shkola, 2008.
Panteleev, A.V., Letova, T.A., and Pomazueva, E.A., An Application of Global Optimization Methods to the Parametric Synthesis of Generalized Proportional-Integral-Derivative Controller for Flight Control Problems, Tr. MAI, 2015, no. 79.
Panteleev, A.V., Metlitskaya, D.V., and Aleshina, E.A., Metody global’noi optimizatsii. Metaevristicheskie strategii i algoritmy (Global Optimization Methods. Metaheuristic Strategies and Algorithms), Moscow, Vuzovskaya Kniga, 2013.
Cai, X. and Liu, F., Numerical Simulation of the Fractional-Order Control System, J. Appl. Math. Comp., 2007, vol. 23, no. 1–2, pp. 229–241.
Caponetto, R., Dongola, G., Fortuna, L., et al., Fractional Order Systems. Modelling and Control Applications, Singapore: World Scintific, 2010.
Castillo, F.J., Feliu, V., Rivas, R., et al., Design of a Class of Fractional Controllers from Frequency Specifications with Guaranteed Time Domain Behavior, Comput. Math. Appl., 2010, vol. 50, pp. 1656–1666.
Chen, Y.Q., Petras, I., and Xue, D., Fractional Order Control: A Tutorial, Proc. 2009 Am. Control Conf., St. Louis, 2009, pp. 1397–1411.
Harley, T.T. and Lorenzo, C.F., Dynamics and Control of Initialized Fractional-Order Systems, Nonlin. Dyn., 2002, vol. 29, no. 1–4, pp. 201–233.
Matingnon, D., Stability Properties for Generalized Fractional Differential Systems, Proc. Colloq. Fractional Differential Systems: Models, Methods and Applications, Paris, 1998, vol. 5, pp. 145–158.
Monje, C.A., Chen, Y.Q., Vinagre, B.M., et al., Fractional-Order Systems and Controls: Fundamentals and Applications, London: Springer-Verlag, 2010.
Mophou, G.M., Optimal Control of Fractional Diffusion Equation, Comput. Math. Appl., 2011, vol. 61, pp. 68–78.
Mozyrska, D. and Torres, D.F.M., Modified Optimal Energy and Initial Memory of Fractional Continuous-Time Linear Systems, Signal Proc., 2011, vol. 91, pp. 379–385.
Özdemir, N., Karadeniz, D., and Iskender, B.B., Fractional Optimal Control Problem of a Distributed System in Cylindrical Coordinates, Phys. Lett. A, 2009, vol. 373, pp. 221–226.
Padula, F. and Visioli, A., Tuning Rules for Optimal PID and Fractional-Oder PID Controlles, J. Proc. Contr., 2011, vol. 21, pp. 69–81.
Tavazoei, M.S., Notes on Integral Performance Indices in Fractional-Order Control Systems, J. Proc. Contr., 2010, vol. 20, pp. 285–291.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © A.V. Panteleev, T.A. Letova, E.A. Pomazueva, 2015, published in Upravlenie Bol’shimi Sistemami, 2015, No. 56, pp. 176–200.
Rights and permissions
About this article
Cite this article
Panteleev, A.V., Letova, T.A. & Pomazueva, E.A. Parametric Design of Optimal in Average Fractional-Order PID Controller in Flight Control Problem. Autom Remote Control 79, 153–166 (2018). https://doi.org/10.1134/S0005117918010137
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0005117918010137