This paper proposes an optimal tuning approach for designing robust generalized-order proportional integral (PI) controllers based on the multi-objective optimization problem for multivariable processes. Generalized-order means that the order of the integral term could be an integer order or a fractional one. Due to the sophistication of an MIMO process, the decentralized structure based on the simplified decoupling is addressed to reduce the full matrix controller (n2 controllers) to the diagonal form (n controllers). Multi-objective particle swarm optimization (MOPSO) is adopted to design a generalized-order PI controller for each diagonal element of the decoupled matrix. The objective functions are to minimize the integrated absolute error (IAE) for both servomechanism and regulator problems which are normally conflicting in terms of system performance. In the first stage, a Pareto front (PF) including the optimal solutions is obtained, then in the second stage, the most appropriate control parameters are chosen from the PF based on the maximum peak of the sensitivity function (Ms). The robustness stability of the whole system (the MIMO one) is finally evaluated to guarantee the applicability of the control structure. Some simulation examples in comparison with other well-known methods are presented to demonstrate the effectiveness of the proposed method.

Fraction-order PI Controller MOPSO Algorithm Robust Performance Simplified Decoupling Pareto Front Optimization

Truong NLV, Lee M, J. Chem. Eng. Jpn., 43, 196 (2010)
Truong NLV, Lee M, J. Chem. Eng. Jpn., 46, 279 (2013)
Chuong VL, Vu TNL, Truong NTN, Jung JH, Appl. Sci., 9, 2487 (2019)
Bialkowski WL, Pulp Pap., 11, 19 (1994)
Chen YQ, Petras I, Xue D, Fractional order control - a tutorial, American Control Conference (2009).
Astrom KJ, Panagopoulos H, Hagglund T, Automatica, 34(5), 585 (1998)
Kim TH, Maruta I, Sugie T, Automatica, 44, 1104 (2008)
Vilanova R, Arrieta O, Ponsa P, ISA Trans., 81, 177 (2018)
Dastjerdi AA, Vinagre BM, Chen YQ, HosseinNia H, Annu. Rev. Control, 47, 51 (2019)
Padula F, Visioli A, J. Process Control, 21, 69 (2011)
Vu TNL, Lee M, ISA Trans., 52, 583 (2013)
Keyser RD, Muresan CI, Ionescu CM, ISA Trans., 62, 268 (2016)
Yumuk E, Guzelkaya M, Eksin I, ISA Trans., 91, 196 (2019)
Beschi M, Padula F, Visioli A, Control Eng. Practice, 60, 190 (2016)
Moradi M, J. Process Control, 24, 336 (2014)
Sánchez HS, Padula F, Visioli A, Vilanova R, ISA Trans., 66, 344 (2017)
Hajiloo A, Nariman-zadeh N, Moeini A, Mechatronics, 22, 788 (2012)
Pan I, Das S, Int. J. Electr. Power Energy Syst., 43, 393 (2012)
Morari M, Zafiriou E, Robust process control, Englewood Cliffs, Prentice Hall (1989).
Skogestad S, Postlethwaithe I, Multivariable feedback control analysis and design, John Wiley & Sons (1996).
Coello CAC, Lechuga MS, CEC'02 (Cat. No. 02TH8600), USA, 2, 1051 (2002)
Coello CAC, Pulido GT, Lechuga MS, IEEE Trans. Evo. Comp., 8(3), 256 (2004)
Monje CA, Chen YQ, Vinagre BM, Xue DY, Feliu V, Fractional-order systems and controls, fundamentals and applications, Springer-Verlag, London (2010).
Chuong VL, Vu TNL, Truong NTN, Jung JH, Appl. Sci., 9(23), 5262 (2019)
Ogunnaike BA, Lemaire JP, Morari M, Ray WH, AIChE J., 29, 632 (1983)
Ghosh S, Pan S, ISA Trans., 110, 117 (2021)
Shen Y, Cai WJ, Li S, Control Eng. Practice, 18(6), 652 (2010)
Khandelwal S, Detroja KP, J. Process Control, 96, 23 (2020)