Power Electronic Converters Modeling and Control pp 393-441 | Cite as

# Variable-Structure Control of Power Electronic Converters

## Abstract

Interest in variable-structure control is justified by the necessity of robustly controlling systems whose structure switches between several configurations. Power electronic converters are such class of systems because they can be described by differential equations with discontinuous right-hand sides (i.e., discontinuous inputs). Moreover, they exhibit nonlinear behavior which can in some applications render unsuitable standard linear control approaches. Good control performance such as large bandwidth is ensured because the switching solution is obtained directly without any other form of supplementary modulation (PWM, sigma-delta modulation).

### Keywords

Manifold### References

- Buhler H (1986) Sliding mode control (in French: Réglage par mode de glissement). Presses Polytechniques Romandes, LausanneGoogle Scholar
- Carpita M, Marchesoni M (1996) Experimental study of a power conditioning system using sliding mode control. IEEE Trans Power Electron 11(5):731–742CrossRefGoogle Scholar
- Carrasco JM, Quero JM, Ridao FP, Perales MA, Franquelo LG (1997) Sliding mode control of a DC/DC PWM converter with PFC implemented by neural networks. IEEE Trans Circuit Syst I Fundam Theor Appl 44(8):743–749CrossRefMATHGoogle Scholar
- DeBattista H, Mantz RJ, Christiansen CF (2000) Dynamical sliding mode power control of wind driven induction generators. IEEE Trans Energy Convers 15(4):728–734Google Scholar
- DeCarlo RA, Żak SH, Drakunov SV (2011) Variable structure, sliding mode controller design. In: Levine WS (ed) The control handbook—control system advanced methods. CRC Press, Taylor & Francis Group, Boca Raton, pp 50-1–50-22Google Scholar
- Emelyanov SV (1967) Variable structure control systems. Nauka, Moscow (in Russian)Google Scholar
- Filippov AF (1960) Differential equations with discontinuous right hand side. Am Math Soc Transl 62:199–231Google Scholar
- Guffon S (2000) Modelling and variable structure control for active power filters (in French: “Modélisation et commandes à structure variable de filtres actifs de puissance”). Ph.D. thesis, Grenoble Institute of Technology, FranceGoogle Scholar
- Guffon S, Toledo AS, Bacha S, Bornard G (1998) Indirect sliding mode control of a three-phase active power filter. In: Proceedings of the 29th annual IEEE Power Electronics Specialists Conference – PESC 1998. Kyushu Island, Japan, pp 1408–1414Google Scholar
- Hung JY, Gao W, Hung JC (1993) Variable structure control: a survey. IEEE Trans Ind Electron 40(1):2–22CrossRefGoogle Scholar
- Itkis U (1976) Control systems of variable structure. Wiley, New YorkGoogle Scholar
- Levant A (2007) Principles of 2-sliding mode design. Automatica 43(4):576–586MathSciNetCrossRefMATHGoogle Scholar
- Levant A (2010) Chattering analysis. IEEE Trans Autom Control 55(6):1380–1389MathSciNetCrossRefGoogle Scholar
- Malesani L, Rossetto L, Spiazzi G, Tenti P (1995) Performance optimization of Ćuk converters by sliding-mode control. IEEE Trans Power Electron 10(3):302–309CrossRefGoogle Scholar
- Malesani L, Rossetto L, Spiazzi G, Zuccato A (1996) An AC power supply with sliding mode control. IEEE Ind Appl Mag 2(5):32–38CrossRefGoogle Scholar
- Martinez-Salamero L, Calvente J, Giral R, Poveda A, Fossas E (1998) Analysis of a bidirectional coupled-inductor Ćuk converter operating in sliding mode. IEEE Trans Circuit Syst I Fundam Theor Appl 45(4):355–363CrossRefGoogle Scholar
- Mattavelli P, Rossetto L, Spiazzi G (1997) Small-signal analysis of DC–DC converters with sliding mode control. IEEE Trans Power Electron 12(1):96–102CrossRefGoogle Scholar
- Šabanovic A (2011) Variable structure systems with sliding modes in motion control—a survey. IEEE Trans Ind Inform 7(2):212–223CrossRefGoogle Scholar
- Šabanovic A, Fridman L, Spurgeon S (2004) Variable structure systems: from principles to implementation, IEE Control Engineering Series. The Institution of Engineering and Technology, LondonCrossRefGoogle Scholar
- Sira-Ramírez H (1987) Sliding motions in bilinear switched networks. IEEE Trans Circuit Syst 34(8):919–933CrossRefGoogle Scholar
- Sira-Ramírez H (1988) Sliding mode control on slow manifolds of DC to DC power converters. Int J Control 47(5):1323–1340CrossRefMATHGoogle Scholar
- Sira-Ramírez H (1993) On the dynamical sliding mode control of nonlinear systems. Int J Control 57(5):1039–1061CrossRefMATHGoogle Scholar
- Sira-Ramírez H (2003) On the generalized PI sliding mode control of DC-to-DC power converters: a tutorial. Int J Control 76(9/10):1018–1033CrossRefMATHGoogle Scholar
- Sira-Ramírez H, Silva-Ortigoza R (2006) Control design techniques in power electronics devices. Springer, LondonGoogle Scholar
- Slotine JJE, Sastry SS (1983) Tracking control of non-linear systems using sliding surface, with application to robot manipulators. Int J Control 38(2):465–492MathSciNetCrossRefMATHGoogle Scholar
- Spiazzi G, Mattavelli P, Rossetto L, Malesani L (1995) Application of sliding mode control to switch-mode power supplies. J Circuit Syst Comput 5(3):337–354CrossRefGoogle Scholar
- Tan S-C, Lai YM, Cheung KHM, Tse C-K (2005) On the practical design of a sliding mode voltage controlled buck converter. IEEE Trans Power Electron 20(2):425–437CrossRefGoogle Scholar
- Tan S-C, Lai Y-M, Tse C-K (2011) Sliding mode control of switching power converters: techniques and implementation. CRC Press, Taylor & Francis Group, Boca RatonGoogle Scholar
- Utkin VA (1972) Equations of sliding mode in discontinuous systems. Autom Remote Control 2(2):211–219MathSciNetGoogle Scholar
- Utkin VA (1977) Variable structure systems with sliding mode. IEEE Trans Autom Control 22(2):212–222MathSciNetCrossRefMATHGoogle Scholar
- Utkin V (1993) Sliding mode control design principles and applications to electric drives. IEEE Trans Ind Electron 40(1):23–36CrossRefGoogle Scholar
- Venkataramanan R, Šabanovic A, Ćuk S (1985) Sliding mode control of DC-to-DC converters. In: Proceedings of IEEE Industrial Electronics Conference – IECON 1985. San Francisco, California, USA, pp 251–258Google Scholar
- Young KD, Utkin VI, Ozguner U (1999) A control engineer’s guide to sliding mode control. IEEE Trans Control Syst Technol 7(3):328–342CrossRefGoogle Scholar