In this article, a novel sampled-data control method is proposed for direct current to direct current converter. According to its switching property, the direct current to direct current converter is described as a switched affine system. A novel error tracking switching law is designed based on the multi-Lyapunov functions method and sampled-data control strategy with variant sampling intervals. The sufficient condition concerning the state of the constructed switched affine system converging to a finite region is developed, which guarantees the outcome voltage can approach the desired value and achieve the voltage adjustment. Based on it, the condition under uncertain parameters is developed as well, which would be more desirable in applications. The effectiveness of the proposed method is verified by numerical simulations. The proposed method is also applicable to other types of power converters.
ArbetterBEricksonRMaksimovicD. DC-DC converter design for battery-operated systems. In: Proceedings of PESC 95: power electronics specialist conference, vol. 1, Atlanta, GA, 18–22 June 1995, pp.103–109. New York: IEEE.
2.
ZhangGLiZZhangB, et al. Power electronics converters: past, present and future. Renew Sust Energ Rev2018; 81: 2028–2044.
3.
ZhangGIuHHZhangB, et al. An impedance network boost converter with a high-voltage gain. IEEE T Power Electr2017; 32(9): 6661–6665.
4.
LiMChenYXuL, et al. Asynchronous control strategy for semi-Markov switched system and its application. Inf Sci2020; 532: 125–138.
5.
HoCFLingBKLiuYQ, et al. Optimal PWM control of switched-capacitor DC-DC power converters via model transformation and enhancing control techniques. IEEE T Circuits I2008; 55(5): 1382–1391.
6.
BeccutiAGMariethozSCliquennoisS, et al. Explicit model predictive control of DC-DC switched-mode power supplies with extended Kalman filtering. IEEE T Ind Electron2009; 56(6): 1864–1874.
7.
KimSParkCRKimJ, et al. A stabilizing model predictive controller for voltage regulation of a DC/DC boost converter. IEEE T Contr Syst T2014; 22(5): 2016–2023.
8.
FossasEOlmJMZinoberAS, et al. Galerkin-based sliding mode tracking control of non-minimum phase DC-to-DC power converters. Int J Robust Nonlin2010; 17(7): 587–604.
9.
TanSCLaiYMTseCK.A unified approach to the design of PWM-based sliding-mode voltage controllers for basic DC-DC converters in continuous conduction mode. IEEE T Circuits I2006; 53(8): 1816–1827.
10.
TheunisseTAFChaiJSanfeliceRG, et al. Robust global stabilization of the DC-DC boost converter via hybrid control. IEEE T Circuits I2015; 62(4): 1052–1061.
11.
BeneuxGRiedingerPDaafouzJ, et al. Robust stabilization of switched affine systems with unknown parameters and its application to DC/DC Flyback converters. In: Proceedings of the 2017 American control conference (ACC), Seattle, WA, 24–26 May 2017, pp.4528–4533. New York: IEEE.
12.
HauroignePRiedingerPIungC.Switched affine systems using sampled-data controllers: robust and guaranteed stabilization. IEEE T Automat Contr2011; 56(12): 2929–2935.
13.
DeaectoGSGeromelJCGarciaFS, et al. Switched affine systems control design with application to DC-DC converters. IET Control Theory A2010; 4(7): 1201–1210.
14.
AlbeaCGarciaGZaccarianL. Hybrid dynamic modeling and control of switched affine systems: application to DC-DC converters. In: Proceedings of the 54th IEEE conference on decision and control (CDC), Osaka, Japan, 15–18 December 2015, pp.2264–2269. New York: IEEE.
15.
Gavagsaz-GhoachaniRPhattanasakMMartinJ, et al. A Lyapunov function for switching command of a DC-DC Power converter with an LC input filter. IEEE T Ind Appl2017; 53(5): 5041–5050.
16.
YoshimuraVLAssuncaoETeixeiraMCM, et al. Performance enhancement of switched affine systems by switched quadratic Lyapunov functions: applications in DC-DC converters. In: Proceedings of the 2013 Brazilian power electronics conference, Gramado, Brazil, 27–31 October 2013, pp.311–318. New York: IEEE.
17.
NoghreianEKoofigarHR.Robust tracking control of robot manipulators with friction and variable loads without velocity measurement: a switched control strategy. Proc IMechE, Part I: J Systems and Control Engineering2021; 235: 532–539.
18.
WangCShenTJiH.Common quadratic Lyapunov function for two classes of special switched linear systems. IEICE T Inf Syst2014; 97(2): 175–183.
19.
WangFZhangXChenB, et al. Adaptive finite-time tracking control of switched nonlinear systems. Inf Sci2017; 421: 126–135.
20.
LiPLiuYZhangB, et al. Stability analysis problems of periodic piecewise polynomial systems. J Frankl Inst2019; 356(16): 9804–9823.
21.
XiangWXiaoJZhaiG.Dissipativity and dwell time specifications of switched discrete-time systems and its applications in and robust passive control. Inf Sci2015; 320(1): 206–222.
22.
GaoYWenJPengL.New exponential stability criterion for switched linear systems with average dwell time. Proc IMechE, Part I: J Systems and Control Engineering2019; 233(8): 935–944.
23.
LiPLamJLuR, et al. Stability and L2 synthesis of a class of periodic piecewise time-varying systems. IEEE T Automat Contr2019; 64(8): 3378–3384.
24.
LiPLamJKwokKW, et al. Stability and stabilization of periodic piecewise linear systems: a matrix polynomial approach. Automatica2018; 94: 1–8.
25.
YangDZongGZhaoJ.H∞ fault-tolerant control for switched linear parameter-varying systems: a parameter and state-dependent switching method with dwell time. Proc IMechE, Part I: J Systems and Control Engineering2019; 233(1): 18–30.
26.
ZhaoXZhangLShiP, et al. Dynamic output feedback control for a class of switched delay systems under asynchronous switching. IEEE T Automat Contr2012; 57: 1809–1815.
27.
WangSJiWJiangY, et al. Average dwell time approach to H∞ filter for continuous-time switched linear parameter varying systems with time-varying delay. Proc IMechE, Part I: J Systems and Control Engineering2018; 233(1): 80–90.
28.
HetelLFridmanE.Robust sampled-data control of switched affine systems. IEEE T Automat Contr2013; 58(11): 2922–2928.
29.
YanXShuZSharkhSM. Prediction-based sampled-data control for DC-DC buck converters. In: Proceedings of the 2015 first workshop on smart grid and renewable energy (SGRE), Doha, Qatar, 22–23 March 2015, pp.1–6. New York: IEEE.
30.
YanXShuZSharkhSM, et al. Sampled-data control with adjustable switching frequency for DC-DC converters. IEEE T Ind Electron2018; 66(10): 8060–8071.
HetelLFridmanE. Sampled-data control of switched affine systems: a continuous-time approach. In: Proceedings of the 7th IFAC symposium on robust control design, Aalborg, 20–22 June 2012, pp.582–587. Amsterdam: Elsevier.
33.
GeromelJCColaneriP.Stability and stabilization of continuous-time switched linear system. SIAM2006; 45(5): 1915–1930.
34.
FridmanE.New Lyapunov–Krasovskii functionals for stability of linear retarded and neutral type systems. Syst Control Lett2001; 43(4): 309–319.
