Input–output current regulation of Zeta converter using an optimized dual-loop current controller

Alireza Goudarzian; Adel Khosravi; Navid Reza Abjadi

doi:10.1007/s00202-019-00872-z

Electrical Engineering

pp 1–13 | Cite as

Input–output current regulation of Zeta converter using an optimized dual-loop current controller

Authors
Authors and affiliations

Alireza Goudarzian
Adel Khosravi
Navid Reza Abjadi

Original Paper

First Online: 27 November 2019

9 Downloads

Abstract

In this paper, an optimized dual-loop current controller for current balancing of a Zeta converter is presented and analysed in continuous current mode. The proposed strategy has an inner loop which is defined based on the input inductor current control. The reference signal of the sliding manifold is changed through an outer loop which works to regulate the output current. The stability analysis of the two-loop controllers is established by means of Routh–Hurwitz criterion and the equivalent control method. Then, the gains of the outer loop compensator are optimized using the integral gain maximization method to guarantee the robustness and disturbance rejection of the closed loop system in the presence of model uncertainties. The controller performance is investigated in depth taking into account the parametric variations associated with the converter operation in various equilibrium points. Moreover, a laboratory set-up of the suggested controller has been implemented by using analogue component devices. The experimental results demonstrate the effective performance of the controller.

Keywords

Zeta converter Cascade control strategy PI compensator design Current regulation

This is a preview of subscription content, to check access.

Notes

Appendix A

When the inner loop is nearly constant (i.e. $ \frac{{{\text{d}}I_{E} (t)}}{{{\text{d}}t}} < < \frac{{{\text{d}}i_{O} }}{{{\text{d}}t}} $ and also $ I_{E} (t) = I_{E} $), the ideal equation of the closed loop system in (16) can be expressed as:

$$ \begin{aligned} C\frac{{{\text{d}}v_{C} }}{{{\text{d}}t}} & = - i_{o} \left( {\frac{{v_{C} }}{{E + v_{C} }}} \right) + I_{E} \left( {\frac{E}{{E + v_{C} }}} \right) \\ L_{2} \frac{{{\text{d}}i_{o} }}{{{\text{d}}t}} & = v_{C} - v_{O} \\ \end{aligned} $$

(a.1)

where $ v_{o} = Ri_{O} $. The equilibrium point of the system given by (17) can be rewritten as follows:

$$ I_{L} = I_{E} = \frac{{RI_{O}^{2} }}{E},_{{}} V_{C} = RI_{O}^{2} ,_{{}} I_{O} = I_{d} $$

(a.2)

By using (a.2) and with some manipulations, (a.1) can be expressed as follows:

$$ \begin{aligned} C\frac{{{\text{d}}v_{C} }}{{{\text{d}}t}} & = - i_{o} \left( {\frac{{v_{C} - V_{C} }}{{E + v_{C} }}} \right) - RI_{d} \left( {\frac{{i_{O} - I_{d} }}{{E + v_{C} }}} \right) \\ L_{2} \frac{{{\text{d}}i_{o} }}{{{\text{d}}t}} & = - R(i_{O} - I_{d} ) + (v_{C} - V_{C} ) \\ \end{aligned} $$

(a.3)

Now, select the following positive definite Lyapunov function:

$$ V(v_{C} ,i_{O} ) = \frac{1}{2}C(v_{C} - V_{C} )^{2} + \frac{1}{2}L_{2} (i_{O} - I_{d} )^{2} \ge 0 $$

(a.4)

The time derivative of the defined Lyapanov function is given by:

$$ \mathop V\limits^{.} (v_{C} ,i_{O} ) = - \frac{{i_{O} }}{{E + v_{C} }}(v_{C} - V_{C} )^{2} - \frac{{RI_{d} }}{{E + v_{C} }}(v_{C} - V_{C} )(i_{O} - I_{d} ) - R(i_{O} - I_{d} )^{2} + (v_{C} - V_{C} )(i_{O} - I_{d} ) $$

(a.5)

Expressing (a.5) in form of $ \mathop V\limits^{.} = - XQX^{T} $, leads to:

$$ \dot{V}(v_{C} ,i_{O} ) = - XQX^{T} = - [v_{C} i_{O} ]\left[ {\begin{array}{*{20}c} {\frac{{i_{O} }}{{E + v_{C} }}} & {\frac{{RI_{d} }}{{E + v_{C} }}} \\ { - 1} & R \\ \end{array} } \right][v_{C} i_{O} ]^{T} $$

(a.6)

If $ Q > 0 $; then, $ \mathop V\limits^{.} (v_{C} ,i_{O} ) $ will be negative definite. For the Zeta converter, it is valid: $ R > 0 $ and $ I_{d} > 0 $. If the conditions $ i_{O} > - I_{d} $ and $ v_{C} > - E $ are fulfilled, then $ \mathop V\limits^{.} (v_{C} ,i_{O} ) < 0 $. Therefore, the proposed system is asymptotically stable based on the LaSalle’s stability principles [43].

References

1.
Celebi M (2017) Efficiency optimization of a conventional boost DC/DC converter. Electr Eng 100(2):803–809MathSciNetCrossRefGoogle Scholar
2.
Aylapogu PK, Bhajana VVSK (2017) Modeling and implementation of a new ZCS interleaved bidirectional buck–boost DC/DC converter for energy storage systems. Electr Eng 99(4):1283–1293CrossRefGoogle Scholar
3.
Goudarzian A, Nasiri H, Abjadi N (2016) Design and implementation of a constant frequency sliding mode controller for a Luo converter. Int J Eng 29(2):202–210Google Scholar
4.
Veerachary M (2001) Fourth order buck converter for maximum power point tracking applications. IEEE Trans Aerosp Electron Syst 47(2):896–911CrossRefGoogle Scholar
5.
Hosseinzadeh M, Abjadi N, Kargar A, Arab G (2014) Application of brain emotional learning-based intelligent controller to power flow control with thyristor-controlled series capacitance. IET Gener Transm Dis 9(14):1964–1976CrossRefGoogle Scholar
6.
Naika BB, Mehtab AJ (2017) Sliding mode controller with modified sliding function for DC/DC Buck converter. ISA Trans 70:279–287CrossRefGoogle Scholar
7.
Tang M, Stuart T (2003) Selective buck-boost equalizer for series battery packs. IEEE Trans Aerosp Electron Syst 39(2):521–532CrossRefGoogle Scholar
8.
Almasi O, Fereshtehpoor V, Khooban MH, Blaabjerg F (2017) Analysis, control and design of a non-inverting buck-boost converter: a bump-less two-level T-S fuzzy PI control. ISA Trans 67:515–527CrossRefGoogle Scholar
9.
Chen AS (2012) PI and sliding mode control of a Cuk converter. IEEE Trans Power Electron 27(8):3695–3703CrossRefGoogle Scholar
10.
Veerachary M (2012) Two loop controlled buck-SEPIC converter for input source power management. IEEE Trans Aerosp Electron Syst 59(11):4075–4087Google Scholar
11.
Wu TS, Liang SA, Chen YM (2003) Design optimization for asymmetrical ZVS-PWM zeta converter. IEEE Trans Aerosp Electron Syst 39(2):521–532CrossRefGoogle Scholar
12.
Singh S, Singh B, Bhuvaneswari G, Bist V (2015) Power factor corrected Zeta converter based improved power quality switched mode power supply. IEEE Trans Ind Electron 62(9):5422–5433CrossRefGoogle Scholar
13.
Kumar R, Singh B (2016) BLDC motor-driven solar PV array-fed water pumping system employing Zeta converter. IEEE Trans Ind Appl 52(3):2315–2322CrossRefGoogle Scholar
14.
Singh B, Bist B (2015) Power quality improvements in a Zeta converter for brushless DC motor drives. IET Sci Measur Technol 9(3):351–361CrossRefGoogle Scholar
15.
Surapaneni RK, Rathore AK (2015) A single-stage CCM Zeta microinverter for solar photovoltaic AC module. IEEE J Emerg Select Top Power Electron 3(4):892–900CrossRefGoogle Scholar
16.
Shrivastava A, Singh B, Pal S (2015) A novel wall-switched step-dimming concept in LED lighting systems using PFC Zeta converter. IEEE Trans Ind Electron 62(10):6272–6283CrossRefGoogle Scholar
17.
Veerachary M (2004) General rules for signals flow graph modeling and analysis of DC/DC converters. IEEE Trans Aerosp Electron Syst 40(1):259–271CrossRefGoogle Scholar
18.
Lee C, Yang J, Jiang J (2010) Assessment of PEM fuel cells-based DC/DC power conversion for applications in AUVs. IEEE Trans Aerosp Electron Syst 46(4):1834–1847CrossRefGoogle Scholar
19.
Chou M, Liaw C (2014) PMSM-driven satellite reaction wheel system with adjustable DC-link voltage. IEEE Trans Aerosp Electron Syst 50(2):1359–1373CrossRefGoogle Scholar
20.
Yang S, Wang P, Tang Y (2018) Feedback linearization-based current control strategy for modular multilevel converters. IEEE Trans Power Electron 33(1):161–174Google Scholar
21.
Shi ZY, Zhong YS, Xu WL (2005) Decentralized robust tracking control for uncertain robots. Electr Eng 87(4):217–226CrossRefGoogle Scholar
22.
Bennaoui A, Saadi S (2017) Type-2 fuzzy logic PID controller and different uncertainties design for boost DC/DC converters. Electr Eng 99(1):203–211CrossRefGoogle Scholar
23.
Salimi M, Soltani J, Markadeh GA, Abjadi NR (2013) Indirect output voltage regulation of dc-dc buck/boost converter operating in continuous and discontinuous conduction modes using adaptive backstepping approach. IET Power Electron 6(4):732–741CrossRefGoogle Scholar
24.
Abjadi N, Goudarzian A, Arab Markadeh G, Valipour Z (2018) Reduced-order backstepping controller for POESLL DC/DC converter based on pulse width modulation. Iran J Sci Technol Trans Electr Eng. https://doi.org/10.1007/s40998-018-0096-y(0123456789 CrossRefGoogle Scholar
25.
Wai RJ, Shih LC (2012) Adaptive fuzzy-neural-network design for voltage tracking control of a DC/DC boost converter. IEEE Trans Power Electron 27(4):2104–2115CrossRefGoogle Scholar
26.
Wang Z, Li S, Wang J, Li Q (2017) Robust control for disturbed buck converters based on two GPI observers. Control Eng Pract Elsevier J 66:13–22CrossRefGoogle Scholar
27.
Kim M (2015) Proportional-integral (PI) compensator design of duty-cycle-controlled buck LED driver. IEEE Trans Power Electron 30(7):3852–3859CrossRefGoogle Scholar
28.
Kim M (2018) High-performance current-mode-controller design of buck LED driver with slope compensation. IEEE Trans Power Electron 33(1):641–649CrossRefGoogle Scholar
29.
Abjadi NR (2014) Sliding-mode control of a six-phase series/parallel connected two induction motors drive. ISA Trans 53:1847–1856CrossRefGoogle Scholar
30.
Mohanty P, Panda A (2016) Fixed frequency sliding mode (SM) control scheme based on current control manifold for improved dynamic performance of boost PFC converter. IEEE J Emerg Sel Top Power Electron 5(1):576–586CrossRefGoogle Scholar
31.
Nairi H, Goudarzian A, Pourbagher R, Derakhshandeh SY (2017) PI and PWM sliding mode control of POESLL converter. IEEE Trans Aerosp Electron Syst 53(5):2167–2177CrossRefGoogle Scholar
32.
Mamarelis E, Petrone G, Spagnuolo G (2014) Design of a sliding-mode-controlled SEPIC for PV MPPT applications. IEEE Trans Ind Electron 61(7):3387–3398CrossRefGoogle Scholar
33.
Chincholkar SH, Jiang W, Chan SY (2018) A modified hysteresis-modulation-based sliding mode control for improved performance in hybrid DC/DC boost converter. IEEE Trans Circuits Syst II Exp Briefs 65(11):1683–1687CrossRefGoogle Scholar
34.
Wang Y, Ruan X, Leng Y, Li Y (2018) Hysteresis current control for multilevel converter in parallel-form switch-linear hybrid envelope tracking power supply. Power Electron., To be published, IEEE Trans. https://doi.org/10.1109/TPEL.2018.2835640 CrossRefGoogle Scholar
35.
Silva-Ortigoza R, Hernandez-Guzman V, Antonio Cruz M, Munoz Carrillo D (2015) DC/DC buck power converter as a smooth starter for a DC motor based on a hierarchical control. IEEE Trans Power Electron 30(2):1076–1084CrossRefGoogle Scholar
36.
Ahmadzadeh S, Arab Markadeh G, Blaabjerg F (2017) Voltage regulation of the Y-source boost DC/DC converter considering effects of leakage inductances based on cascaded sliding mode control. IET Power Electron 10(11):1333–1343CrossRefGoogle Scholar
37.
Qi W, Li S, Tan SC, Hui SY (2018) Parabolic modulated sliding mode voltage control of buck converter. IEEE Trans Ind Electron 65(1):844–854CrossRefGoogle Scholar
38.
Goudarzian A, Khosravi A, Abjadi N (2018) Sliding mode current control of NOCULL converter based on hysteresis modulation method in a wide range of operating conditions. ISA Trans. https://doi.org/10.1016/j.isatra.2018.10.007 CrossRefGoogle Scholar
39.
Kessai A, Rahmani L (2014) Ga-Optimized parameters of sliding mode controller based on both output voltage and input current with an application in the PFC of AC/DC converters. IEEE Trans Power Electron 29(6):3159–3165CrossRefGoogle Scholar
40.
Panagopoulos H, Astrom K (1999) “PID control design and loop shaping.” In: Proceedings of the IEEE international conference on control application, Aug, pp 103–108Google Scholar
41.
Panagopoulus H, Astrom K, Hagglund T (2002) Design of PID controllers based on constrained optimisation. IEE Proc Control Theory Appl 149(1):32–40CrossRefGoogle Scholar
42.
Astrom K, Panagopoulus H, Hagglund T (1998) Design of PI controllers based on Non-convex optimization. Automatica 34(5):585–601MathSciNetCrossRefGoogle Scholar
43.
LaSalle J (1976) “The stability of dynamical systems.” In: Proceedings of the regional conference series in applied mathematics, 25Google Scholar

Copyright information

Authors and Affiliations

Alireza Goudarzian
- 1
- 3
Email author
Adel Khosravi
- 1
Navid Reza Abjadi
- 2

1.Department of Electrical Engineering, Faculty of Engineering, Shahrekord BranchIslamic Azad UniversityShahrekordIran
2.Department of Electrical Engineering, Faculty of EngineeringShahrekord UniversityShahrekordIran
3.Young Researchers and Elite Club, Shahrekord BranchIslamic Azad UniversityShahrekordIran

Input–output current regulation of Zeta converter using an optimized dual-loop current controller

Abstract

Keywords

Notes

References

Copyright information

Authors and Affiliations

Personalised recommendations

Cite article