Stability Analysis of A Third Order DC to DC Converter by Considering Input Current as Output Vector


  • J. Barnabas Paul Glady
  • K. Manjunath



Luo converter, state space averaging, root locus, transfer function, PID controller, Lead compensator, notch filter


Luo converters are used in various application because of low ripple, high voltage gain with less number of components. In the literature Luo converter was analysed for voltage gain, output voltage control etc. but the stability of the third order system was not analysed. In this paper the stability was analysed by root locus method. Initially the state space modelling was applied by considering input current as the output vector and the input to output transfer function is obtained. The transfer function reveals that the third order system falls under the category of marginally stable system. In order to bring it in to a stable system a PID controller was designed for the third order system. The performance of the PID system for the third order system was compared with  that of the transfer function when it was split in to first order and second order transfer function. For the marginally stable second order transfer function a PID controller, lead compensator and notch filter was designed. The split transfer function performance of lead, notch filter was compared with the PID of the third order system. 



[1] F.L.Luo and H.Ye, “Positive output super lift converters,†IEEE Transaction on power electronics, Vol.18, No. 1, pp. 105-113, January 2003.

[2] Positive output cascade boost converters F. L. Luo; H. Ye IEE Proceedings - Electric Power Applications Y ear: 2004, Volume: 151, Issue: 5 Pages: 590 - 606

[3] Analysis, design and control of zero-voltage switching quasi-resonant-positive output super lift Luo converter E. Jayashree; G. Uma IET Power Electronics Year: 2011, Volume: 4, Issue: 1 Pages: 21 – 28

[4] Design and implementation of zero-voltageswitching quasi-resonant positive-output Luo converter using analog resonant controller UC3861 E. Jayashree; G. Uma IET Power Electronics Year: 2011, Volume: 4, Issue: 1 Pages: 81 - 88

[5] PI and PWM Sliding Mode Control of POESLL Converter Hadi Nasiri Jazi; Alireza Goudarzian; Rohallah Pourbagher; Sayed Yaser Derakhshandeh IEEE Transactions on Aerospace and Electronic Systems Year: 2017, Volume: 53, Issue: 5 Pages: 2167 – 2177

[6] K. Ramash Kumar and S. Jeevananthan, “A Sliding Mode Control for Positive Output Elementary Luo Converter,†Journal of Electrical Engineering, Vol.10, No.4, pp. 115-127, December 2010.

[7] K. Ramash Kumar and S. Jeevananthan,†Hysteresis Modulation Based Sliding Mode Control for Positive Output Elementary Super Lift Luo Converterâ€, International Journal of Electrical and Electronics Engineering 2:3. pp 131-138, 2009.

[8] K.Ramash Kumar and S.Jeevananthan, “Sliding Mode Control for Current Distribution Control in Paralleled Positive Output Elementary Super Lift Luo Convertersâ€, Journal of Power Electronics, vol. 11, no.5-3, pp.639-654, 2011.

[9] Comparative study of current-mode controllers for the positive output elementary Luo converter via state-space and frequency response approaches Satyajit Hemant Chincholkar; Chok-You Chan IET Power Electronics Year: 2015, Volume: 8, Issue: 7 Pages: 1137 - 1145

[10] Implementation of dual-loop controller for positive output elementary luo converter Shama Ravichandran; Sanjib Kumar Patnaik IET Power Electronics Year: 2013, Volume: 6, Issue: 5 Pages: 885 – 893

[11] Hybrid split capacitors and split inductors applied in positive output super-lift Luo-converters Fang Lin Luo; Hong Ye IET Power Electronics Year: 2013, Volume: 6, Issue: 9 Pages: 1759 – 1768.

[12] Ayyappa Swamy, Y,G. Nagarajan, “Implementation of Non-Isolated High Voltage Gain Input-Parallel Output-Series Dc/Dc Converter with Switched Capacitor†Volume 8 (5),pp 2111-2118,2015.

[13] MuhammedShafi. P,Selvakumar.S*, Mohamed Shakeel.P, “An Efficient Optimal Fuzzy C Means (OFCM) Algorithm with Particle Swarm Optimization (PSO) To Analyze and Predict Crime Dataâ€, Journal of Advanced Research in Dynamic and Control Systems, Issue: 06,2018, Pages: 699-707

[14] Selvakumar, S & Inbarani, Hannah & Mohamed Shakeel, P. (2016). A hybrid personalized tag recommendations for social E-Learning system. 9. 1187-1199.

[15] P Hemkumarand, G Nagarajanâ€Current Fed Full Bridge Soft Switching Grid Connected Solar Based Push Pull Inverterâ€ARPN Journal of Engineering and Applied Sciences ,Vol-11 (13), pp8389-8394,2016.

View Full Article: