linear-non-linear control (lnlc) for dc-dc buck converters stability and transient response analysis

8/10/2019 Linear-non-linear Control (LnLc) for DC-DC Buck Converters Stability and Transient Response Analysis

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The figure 9a presents the obtained waveforms for the sameZ1 and Z2 used to obtain the plot shown in figure 8b, andtherefore, with a linear control unstable. It is possible to see,that the output voltage ripple has been drastically reduced(more than 20 times), due the Non-Linear control operation.

Vo

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Figure 9. Output voltage ripple, output voltage and output current, with

fixed load current. a) BLnL with Unstable Linear control. b) BLnL withoutcompensator in Linear control.

To validate the important influence of the Non-Linearcontrol, the Z1impedance has been removed. If Z1is removed,then the error amplifier in the linear control works like acomparator. The obtained waveforms are shown in figure 9b.Even with these conditions, the output voltage ripple fulfillsspecifications (30mV). In this case, the LnLc control operateslike a hysteretic control.

Therefore, these figures show that if the Non-linear controlis added to the linear control, creating the LnLc control, theconverter is stabilized, keeping the output voltage ripple insidethe 2%, even in the most unfavorable case, Fig. 9b, withoutcompensator.

In figures 10 and 11, the BL and BLnL converters arecompared when load current steps are applied in the outputs.

Firstly, we can notice in figure 10, that if the linearcompensator (Z1, Z2) has been selected to obtain a slow controlwith a small bandwidth, the BL converter presents high spikeswhen the load current change, figure 10a. However, with thesame compensator, the BLnL converter reacts quickly, due theNon-Linear Control, reaching an important reduction of boththe peak voltage and the time of the spikes.

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load current steps. a) Slow control in BL. b) Slow control in BLnL.

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load current steps. a) Fast control in BL. b) Fast control in BLnL.


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In this figure the stabilizer effect of the LnLc can benoticed. From an unstable system, plot 1, with Eo/Use1, plots 2 to 6, coinciding with the obtainedtheoretical and measured results, figure 14.

VI.CONCLUSIONS

In this paper, the main features of the Linear-Non-Linearcontrol have been presented. The LnLc control tries to combinethe best performances of the slow linear controls (voltage modecontrol and the current mode controls), and the fast non-linearcontrols (hysteretic control and V

2control). Also, the operation

principle has been described.

The usefulness of the describing function method in orderto obtain the describing function has been presented. Thedescribing function is a linear function that represents the LnLccontrol. On the describing function can be applied the classicallinear stability techniques, allowing to study the LnLc controlfrom the stability point of view. The obtained experimentalresults have validated the theoretical results.

From the analysis of this function and the experimentalresults the following conclusions have been obtained: when theVo is inside the threshold band the LnLc control works like alinear control, keeping the converter stability and low outputvoltage ripple; when the Vo goes out the threshold band, theLnLc control reacts drastically against the perturbationproduced by the load current steps, removing it, and, at thesame time, improving the stability of the whole converter. Ifthe converter with linear control becomes a little bit unstablethe LnLc control is able to stabilize it; if the converter withlinear control becomes totally unstable the LnLc control is ableto stabilize it, operating like a hysteretic control.

In conclusion, the LnLc reduces the output voltage recovery

time; and it improves the transient response making itindependent of the linear control bandwidth. Furthermore, thistype of control guarantees the stability of the converter underload current steps, derating, and bad designs of the linearcontrol. Finally, its implementation is very easy.

ACKNOWLEDGMENT

This work has been supported by the Ministry of Scienceand Technology (Spain) by means of the research projectALDIRA (Code of PN: DPI2001-0748).

VII. REFERENCES

[1] S. Goodfellow, D. Weis, Designing Power System Around ProcessorsSpecifications, Electronic Design, Jan. 1997. Pp. 53-57.

[2] Zhou, X. Zhang, J. Liu, P. Wong, J. Chen, H.Wu, L. Amoroso, F. C. Lee, D. Chen,Investigation of Candidate for Future Microprocessors. IEEE Applied Power

Electronics conference (APEC), 1998.

[3] J. Wei, P. Xu, H. Wu, F. C. Lee, K. Yao, M. Ye, Comparison of Three TopologyCandidates for 12V VRM. IEEE Applied Power Electronics conference (APEC),

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[4] Kaiwei Yao, Yu Meng and Fred C. Lee, Control Bandwidth and TransientResponse of Buck Converters. IEEE Power Electronics Specialist Conference

(PESC). 2002.

[5] Rais Miftakhutdinov An Analytical Comparison of Alternative ControlTechinques for Powering Next-Generation Microprocessors Unitrode Products

from Texas Instruments, Power Supply Desing Seminar. 2001

[6] Angel V. Peterchev and Seth R. Sanders, Low Conversion Ratio VRM Design.IEEE Power Electronics Specialist Conference (PESC). 2002.

[7] Y. Panov and M.M. Jovanovic, Design Considerations for 12-V/1.5-V, 50-AVoltage Regulator Modules. IEEE Applied Power Electronics conference

(APEC). pp 39-46. 2000.

[8] Barrado, R. Vzquez, E. Olas, A. Lzaro, J. Pleite. Fast Transient Response In

Hybrid Sources with Combined Linear-Non-Linear Control, PESC02, pp. 1599-1604, 2002.

[9] Barrado, R. Vzquez, A. Lzaro, J. Pleite, E. Olas. Fast Transient Response withCombined Linear-Non Linear Control applied to Buck Converters. 33th Power

Electronics Specialists Conference, PESC 02, pp.1587-1592, 2002.

[10] Katsuhiko Ogata, Modern Control Engineering (3th Edition) Ed. Prentice Hall;ISBN: 0132273071; 3 edition.

[11] Barrado, R. Vzquez, A. Lzaro, J. Pleite, J. Vzquez, E. Olas. Stability Analysisof Linear-Non Linear Control Applied to Fast Transient Response DC-DC

Converter. 34th Power Electronics Specialists Conference, PESC 03, pp.1175-

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linear-non-linear control (lnlc) for dc-dc buck converters stability and transient response analysis

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