عنوان مقاله [English]
A small switching DC-DC power supply which provides different output level is a good alternative in navigation systems. Single inductor multi output (SIMO) converters can be good for existing parallel output configurations in these applications. In this paper, a multivariable control based on signal flow graph modelling is used to reduce the cross regulation problem of a step down single inductor multi output converter. The multi-stages operation of SIMO converters cause, to achieve the model which predicts their all behaviors, be more difficult than typical converters. By SFG method, all small-signal transfer functions can be derived. In the other hand, designing a controller to control each output independently needs an accurate model to predict all behavior of the converter. In this paper a buck/buck SIMO converter is modeled by SFG. An effort has been made to compare modelling results between SFG and state-space averaging method in a buck/buck structure. Then, a multivariable controller scheme based on SFG model is designed to eliminating the cross regulation of the outputs. Simulation results are included to show the validity of the obtained model and designed controller.
 G. E. Rodriguez, Voltage Conversion and Regulation Techniques Employed in the Prime Converter for the Anchored Interplanetary Monitoring Platform (AIMP) Spacecraft, IEEE Transactions on Aerospace and Electronic Systems, no. 6, pp. 466-476, 1966.
 S. Feng, W. Sander, T. Wilson, Small-capacitance nondissipative ripple filters for DC supplies, IEEE Transactions on Magnetics, vol. 6, no. 1, pp. 137-142, 1970.
 S. H. Marx, R. W. Bounds, A kilowatt rotary power transformer, IEEE Transactions on Aerospace and Electronic Systems, no. 6, pp. 1157-1163, 1971.
 F. Grassi, S. A. Pignari, J. Wolf, Channel characterization and EMC assessment of a PLC system for spacecraft DC differential power buses, IEEE Transactions on Electromagnetic Compatibility, vol. 53, no. 3, pp. 664-675, 2011.
 J. Zhang, H. Wu, X. Qin et al., PWM plus secondary-side phase-shift controlled soft-switching full-bridge three-port converter for renewable power systems, IEEE Transactions on Industrial Electronics, vol. 62, no. 11, pp. 7061-7072, 2015.
 P. Patra, A. Patra, N. Misra, A Single-Inductor Multiple-Output Switcher With Simultaneous Buck, Boost, and Inverted Outputs, IEEE Trans. Power Electronics, vol. 27, 2012.
 Dual-output (positive and negative), DC–DC converter for CCD and LCD, 1988.
 L. Hanh-Phuc, C. Chang-Seok, L. Kwang-Chan etal., A single inductor switching DC–DC converter with five outputs and ordered power-distributive control, IEEE J. Solid-State Circuits, vol. 42, pp. 2706–2714, 2007.
 M. Brown, Practical Switching Power Supply Design: San Diego, CA Academic, 1990.
 R. W. Erickson, Fundamentals of Power Electronics, Boston: MA Kluwe, 1999.
 M. Dongsheng, K. Wing-Hung, T. Chi-ying etal., Single-inductor multiple-output switching converters with time-multiplexing control in discontinuous conduction mode, IEEE J. Solid-State Circuits, vol. 38, pp. 89-100, 2003.
 J. Kim, D. S. Kim, C. Kim, A Single-Inductor Eight-Channel Output DC-DC Converter With Time-Limited Power Distribution Control and Single Shared Hysteresis Comparator, IEEE Trans. Circuits and Systems, vol. 60, 2013.
 K. S. Seol, K. J. Woo, A Synchronous Multioutput Step-Up/Down DC–DC Converter with Return Current Control, IEEE Trans. Circuits and Systems, pp. 56-62, 2009.
 Choi, Woo-Young, High-Efficiency DC–DC Converter with Fast Dynamic Response for Low-Voltage Photovoltaic Sources, IEEE Trans. Power Electronics, vol. 28, pp. 706 - 716, 2013.
 M. C. Lee, J. B. Lio, D. Y. Chen etal., Small-signal modeling of multiple-output flyback converters in continuous conduction mode with weighted feedback, IEEE Trans. Ind. Electron, vol. 45, pp. 236–248, 1998.
 G. Ma, W. Qu, G. Yu et al., A zero-voltage switching bidirectional DC–DC converter with state analysis and soft switching- oriented design consideration, IEEE Trans. Ind. Electron, vol. 56, pp. 2174–2184, 2009.
 Y. S. Lee, A systematic and unified approach to modeling switches in switch-mode power supplies, IEEE Trans. Ind. Electron, vol. 32, pp. 445–448, 1985.
 P. Patra, J. Ghosh, A. Patra, Control Scheme for Reduced Cross-Regulation in Single-Inductor Multiple-Output DC–DC Converters, IEEE Trans. Power Electronics, vol. 60, pp. 5095-5104, 2013.
 R. Trinchero, P. Manfredi, I. S. Stievano etal., Steady-state analysis of switching converters via frequency-domain circuit equivalents, IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 63, no. 8, pp. 748-752, 2016.
 H. Behjati, L. Niu, A. Davoudi etal., Alternative time-invariant multi-frequency modeling of PWM dc-dc converters, IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 60, no. 11, pp. 3069-3079, 2013.
 M. Veerachary, General rules for signal flow graph modeling and analysis of DC-DC converters, Aerospace and Electronic Systems, IEEE Transactions, pp. 259-271, 2004.
 M. Abbasi, A. Afifi, M. R. A. Pahlavani, Signal flow graph modeling and disturbance observer based output voltage regulation of an interleaved boost converter, Power Electronics and Drive Systems Technologies Conference (PEDSTC), 2016, pp. 464-469, 2016.
 R. Loera-Palomo, J. A. Morales-Saldana, J. Leyva-Ramos, Signal flow graphs for modelling of switching converters with reduced redundant power processing, IET Power Electronics, vol. 5, no. 7, pp. 1008-1016, 2012.
 A. Abramovitz, J. Yao, K. Smedley, Unified Modeling of PWM Converters with Regular or Tapped Inductors Using TIS-SFG Approach, IEEE Transactions on Power Electronics, vol. 31, no. 2, pp. 1702-1716, 2016.
 H. Chen, Y. Zhang, D. Ma, A SIMO parallel-string driver IC for dimmable led backlighting with local bus voltage optimization and single time-shared regulation loop, IEEE Trans. Power Electronics, vol. 27, pp. 452–462, 2012.
 D. Ma, W. H. Ki, C. Y. Tusi etal., Single-inductor multiple output switching converters with time-multiplexing control in discontinuous mode, IEEE J. Solid-State Circuits, vol. 38, pp. 89–100, 2003.
 T. Li, Single inductor multiple output boost regulator, 2000.
 A. Ghosh, F. Boora, A. Zare, Multi-output buck–boost converter with enhanced dynamic response to load and input voltage changes, IET Power Electronics, vol. 4, pp. 194–208, 2011.
 A. Nami, F. Zarei, A. Ghoshi etal., Multi-output DC–DC converters based on diode-clamped converters configuration: topology and control strategy, IET Power Electronics, vol. 3, pp. 197–208, 2010.
 K. Wing-Hung, M. Dongsheng, Single-inductor multiple-output switching converters, in PESC. 2001 IEEE 32nd Annual in Power Electronics Specialists Conference, 2001, pp. 226-231.
 B. C. Kuo, F. Golnaraghi, Automatic control systems, John Wiley, 2002.
 A. Khaki-Sedigh, B. Moaveni, Control configuration selection for multivariable plants, Springer, vol. 391, 2009.
 J. M. Maciejowski, Multivariable feedback Design: Addison-Wesley, 1989.