Abstract
Nuclear fusion is one of the newest and most promising clean and safe energies hence, it imposes a new research area of control. In this paper, the design of a multivariable adaptive proportional-integral-derivative (PID) controller for the control of the plasma current, shape and position to ensure the safe operation of the fusion reactor is successfully developed. The recursive least square algorithm is used in an alternative way as an adaptation mechanism for tuning PID controller gains. Since stability is a vital issue in the evaluation of control systems, therefore stability analysis of the proposed controller is developed using the Lyapunov stability theory. The main objective of plasma current, shape and position controller in fusion reactors is to improve the stability and the performance of tokamak magnetic systems without contravening the limits imposed by the actuating coils voltages physical limitations. The proposed APID (adaptive PID) controller tunes online its parameters to cope with the presence of the disturbance or any parameters changes occur during the operation. The results of the proposed APID on a simulation code of a tokamak show a noteworthy improvement with respect to those obtained with other control techniques in the cases of changing the initial controller gains, adding disturbance signal and variation in the reactor model parameters.
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References
P. Vyas, Plasma Vertical Position Control on COMPASS-D. Ph.D. dissertation, Department of Engineering Science, Oxford University, Oxford (1996)
M. Ariola, G. Ambrosino, A. Pironti, J.B. Lister, P. Vyas, Design and experimental testing of a robust multivariable controller on a tokamak. IEEE Trans. Control Syst. Technol. 10(5), 646–653 (2002)
P. Vyas, F. Villone, J.B. Lister, R. Albanese, The separatrix response of diverted TCV plasmas compared with the predictions of the CREATE-L model. Nucl. Fusion 38(7), 1043–1053 (1998)
M. Ariola, G. Ambrosino, J. Lister, A. Pironti, F. Villone, P. Vyas, A modern plasma controller tested on the TCV tokamak. Fusion Technol. 36, 126–138 (1999)
M.L. Walker, D.A. Humphreys, J.R. Ferron, Control of plasma poloidal shape and position in the DIII-D tokamak. In Proceedings of the 36th IEEE Conference on Decision and Control, 1997, San Diego, CA, vol. 4, pp. 3703–3708 (1997)
G. Ambrosino, M. Ariola, Y. Mitrishkin, A. Pironti, A. Portone, Plasma current and shape control in tokamaks using H∞ and μ-synthesis. In Proceedings of the 36th IEEE Conference on Decision and Control, 1997, vol. 4, pp. 3697–3702 (1997)
H. El-Zobaidi, I. Jaimoukha, D. Limebeer, Normalized H controller reduction with a priori bounds. IEEE Trans. Autom. Control 46(9), 1477–1483 (2001)
A.S. Sharma, D.J.N. Limebeer, I.M. Jaimoukha, J.B. Lister, Modeling and control of TCV. IEEE Trans. Control Syst. Technol. 13(3), 356–369 (2005)
N. Cruz, J.M. Moret, S. Coda, B.P. Duval, H.B. Le, A.P. Rodrigues, C.A.F. Varandas, C.M.B.A. Correia, B. Gonçalves, An optimal real-time controller for vertical plasma stabilization. IEEE Trans. Nucl. Sci. 62(6), 3126–3133 (2015)
N. Cruz, Digital Control System for Vertical Stability of the TCV Plasma. Ph.D. dissertation, Universidade de Lisboa (2014)
G. Ambrosino, M. Ariola, A. Pironti, A. Portone, M. Walker, A control scheme to deal with coil current saturation in a tokamak. IEEE Trans. Control Syst. Technol. 9(6), 831–838 (2001)
J.Y. Favez, J.B. Lister, D. Bonvin, Enhancing the Control of Tokamaks via a Continuous Nonlinear Control Law. PhD, No. 3034, École Polytechnique Fédérale de Lausanne, Switzerland (2004)
J. Young Mo, Design of Optimal Position and Shape Controller Based on Perturbed Equilibrium Response Model for Tokamak Plasmas. College of Engineering, Department of Nuclear Engineering, Theses (Ph.D.) (2006)
Technical Data. Technical data|SPC. http://spc.epfl.ch/TCV-technical-data (2016)
R.A. Fahmy, R.I. Badr, F.A. Rahman, Model reference adaptive PID controller for unstable SISO systems. Mediterr J Meas Control 11(3), 438–443 (2015)
K.J. Aström, B. Wittenmark, Adaptive Control, 2nd edn. (Addison-Wesley, Reading, 1995)
S. Haykin, Adaptive Filter Theory, 4th edn. (Prentice-Hall, New Jersey, 2002)
Y. Wakasa, K. Tanaka, Y. Nishimura, Online controller tuning via FRIT and recursive least-squares. In IFAC Conference on Advances in PID Control PID’12 (2012)
T. Shiota, H. Ohmori, Design of adaptive I-PD control system using argument error method. In IFAC Conference on Advances in PID Control PID’12, Brescia, Italy (2012)
“atisharma/rzip” GitHub. https://github.com/atisharma/rzip (2016)
A. Coutlis, I. Bandyopadhyay, J.B. Lister, P. Vyas, R. Albanese, D.J.N. Limebeer, F. Villone, J.P. Wainwright, Measurement of the open loop plasma equilibrium response in TCV. Nucl. Fusion 39, 663 (1999)
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Fahmy, R.A., Badr, R.I. & Rahman, F.A. Multivariable Online Adaptive PID Controller for Plasma Current, Shape, and Position in Tokamaks. J Fusion Energ 35, 831–840 (2016). https://doi.org/10.1007/s10894-016-0110-1
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DOI: https://doi.org/10.1007/s10894-016-0110-1