Call For Paper - Upcoming Conferences
Research Article | Open Access | Download PDF
Volume 13 | Issue 6 | Year 2026 | Article Id. IJEEE-V13I6P107 | DOI : https://doi.org/10.14445/23488379/IJEEE-V13I6P107

Frequency Response-Based Design of PI and PID Controllers for a Quadratic Boost Converter

Telvi Armaliany, Krismadinata, Asnil, Remon Lapisa, Fandi Oktasendra, Heru Dibyo Laksono

Received Revised Accepted Published
16 Mar 2026 15 Apr 2026 14 May 2026 29 Jun 2026

Citation :

Telvi Armaliany, Krismadinata, Asnil, Remon Lapisa, Fandi Oktasendra, Heru Dibyo Laksono, "Frequency Response-Based Design of PI and PID Controllers for a Quadratic Boost Converter," International Journal of Electrical and Electronics Engineering, vol. 13, no. 6, pp. 91-103, 2026. Crossref, https://doi.org/10.14445/23488379/IJEEE-V13I6P107

Abstract

Quadratic Boost Converters (QBCs) may produce high voltage gains without excessive duty cycles, making them ideal for high step-up DC-DC conversion. However, QBCs' multistage construction and high-order dynamics make voltage regulation difficult, especially under input voltage and load changes. A systematic, frequency-response-based design and comparison of PI and PID controllers for a QBC is presented in this work. The work starts with QBC hardware parameter design, then state-space modeling, and small-signal duty-to-output transfer function formulation. PI and PID controllers are tuned using Bode-plot analysis to establish a target phase margin, gain crossover frequency, and predicted transient response. With a 33 kHz switching frequency, the converter steps up 40 V to 400 V at 400 W. MATLAB simulates open-loop, closed-loop, and PI and PID controller operations. The analysis covers rise time, settling time, overshoot, steady-state error, gain/phase margins, and input voltage step variations. Both PI and PID controllers stabilize the QBC and meet transient-response criteria. The PID controller has a shorter rising time (0.456 s compared to 0.7509 s), faster settling (0.808 s versus 1.293 s), and reduced steady-state error (0.007% versus 0.08%) than the PI controller, with almost no overshoot for a 400 V reference. PID controllers dampen and recover faster from input-voltage perturbations. These findings demonstrate that frequency-response-based PID design can regulate high-order QBCs efficiently.

Keywords

QBC, PI and PID Controller, Frequency Response, Bode Plot, DC-DC Conversion.

References

  1. Dharani Kolantla et al., “Critical Review on Various Inverter Topologies for PV System Architectures,” IET Renewable Power Generation, vol. 14, no. 17, pp. 3418-3438, 2020.
    [CrossRef] [Google Scholar] [Publisher Link]
  2. V. Arun, and I. Kumaraswamy, “DC-DC Converters in Solar PV System,” International Journal of Innovative Technology and Exploring Engineering, vol. 9, no. 3, pp. 1692-1699, 2020.
    [CrossRef] [Google Scholar] [Publisher Link]
  3. Farzad Karimian, Ali Nahavandi, and Pouria Pakbaz, “A Novel Structure of High Voltage Gain DC-DC Converters for Photovoltaic (PV) Applications,” Engineering Reports, vol. 7, no. 1, pp. 1-18, 2025.
    [CrossRef] [Google Scholar] [Publisher Link]
  4. Wei Jiang, and Babak Fahimi, “Multi-Port Power Electric Interface for Renewable Energy Sources,” 2009 Twenty-Fourth Annual IEEE Applied Power Electronics Conference and Exposition, Washington, DC, USA, pp. 347-352, 2009.
    [CrossRef] [Google Scholar] [Publisher Link]        
  5. Moien A. Omar, and Marwan M. Mahmoud, “Design and Simulation of DC/DC Boost Converter with Maximum Power Point Tracking for Grid Connected PV Inverter Considering the Nonlinearity of the PV Generator,” International Journal on Energy Conversion, vol. 7, no. 6, pp. 241-242, 2019.
    [CrossRef] [Google Scholar] [Publisher Link]    
  6. Ferdian Ronilaya, and Hajime Miyauchi, “Frequency and Voltage Control for an Autonomous Distributed Variable-Speed Wind Turbine based on a PID-Type Fuzzy Controller with Battery Support,” International Review on Modelling and Simulations, vol. 7, no. 2, pp. 271-278, 2014.
    [Google Scholar] [Publisher Link]               
  7. Ezhilarasan Ganesan, and Subhransu Sekhar Dash, “A New Approach in Modelling and Control of Distributed Energy Resources for Performance Optimisation and Reliability Improvement in a Micro Grid,” International Review on Modelling and Simulations, vol. 8, no. 1, pp. 26-40, 2015.
    [CrossRef] [Publisher Link]          
  8. A.S. Valarmathy, and M. Prabhakar, “High Gain Interleaved Boost-Derived DC-DC Converters-A Review on Structural Variations, Gain Extension Mechanisms and Applications,” E-Prime - Advances in Electrical Engineering, Electronics and Energy, vol. 8, pp. 1-15, 2024.
    [CrossRef] [Google Scholar] [Publisher Link]               
  9. A. Gopi, N.S. Harikrishna, and R. Saravanakumar, “Isolated High Boost Dc-Dc Flyback Converter,” International Review on Modelling and Simulations, vol. 6, no. 2, pp. 336-341, 2013.
    [Google Scholar] [Publisher Link]        
  10. Madhav Kumar et al., “A Critical Analysis of Quadratic Boost based High-Gain Converters for Electric Vehicle Applications: A Review,” Sensors, vol. 24, no. 7, pp. 1-36, 2024.
    [CrossRef] [Google Scholar] [Publisher Link]     
  11. Anindya Sundar Jana et al., “A High Gain Modified Quadratic Boost DC-DC Converter with Voltage Stress Half of Output Voltage,” Applied Sciences, vol. 12, no. 10, pp. 1-25, 2022.
    [CrossRef] [Google Scholar] [Publisher Link]            
  12. Preeti Sharma, Sara Hasanpour, and Rajneesh Kumar, “Ultra-High Voltage Gain Achieved with Quadratic DC/DC Converter Design,” Scientific Reports, vol. 14, no. 1, pp. 1-20, 2024.
    [CrossRef] [Google Scholar] [Publisher Link]               
  13. Tole Sutikno et al., “A Review on Non-Isolated Low-Power DC-DC Converter Topologies with High Output Gain for Solar Photovoltaic System Applications,” Clean Energy, vol. 6, no. 4, pp. 557-572, 2022.
    [CrossRef] [Google Scholar] [Publisher Link]          
  14. Babak Allahverdinejad, Ali Ajami, and Ali Makaremi, “Coupled Inductor based Quadratic High-Gain DC-DC Converter with Wide Range of CCM Operation for Photovoltaic Applications,” IET Renewable Power Generation, vol. 19, no. 1, pp. 1-14, 2025.
    [CrossRef] [Google Scholar] [Publisher Link]              
  15. Francesco Alonge et al., “Sliding Mode Control of Quadratic Boost Converters based on Min-Type Control Strategy,” IEEE Access, vol. 11, pp. 39176-39184, 2023.
    [CrossRef] [Google Scholar] [Publisher Link]        
  16. Nesrine Boujelben, Mohamed Djemel, and Nabil Derbel, “Analysis of a Quadratic Boost Converter using Sliding Mode Controller,” 2020 17th International Multi-Conference on Systems, Signals and Devices (SSD), Monastir, Tunisia, pp. 969-973, 2020.
    [CrossRef] [Google Scholar] [Publisher Link] 
  17. Saban Ozdemir, Necmi Altin, and Ibrahim Sefa, “Fuzzy Logic based MPPT Controller for High Conversion Ratio Quadratic Boost Converter,” International Journal of Hydrogen Energy, vol. 42, no. 28, pp. 17748-17759, 2017.
    [CrossRef] [Google Scholar] [Publisher Link]
  18. Francesco Alonge et al., “Nonlinear Robust Control of a Quadratic Boost Converter in a Wide Operation Range, based on Extended Linearization Method,” Electronics, vol. 11, no. 15, pp. 1-21, 2022.
    [CrossRef] [Google Scholar] [Publisher Link]
  19. F. Alonge et al., “Dynamic Modelling of a Quadratic DC/DC Single-Switch Boost Converter,” Electric Power Systems Research, vol. 152, pp. 130-139, 2017.
    [CrossRef] [Google Scholar] [Publisher Link]
  20. Said Oucheriah, “Robust Controller for a Quadratic Boost Converter,” Research Square, pp. 1-7, 2023.
    [CrossRef] [Google Scholar] [Publisher Link]
  21. Durgesh Sarankar, and Ashish Kumar Shinghal, “Designing of Higher Order DC-DC Converter,” IRE Journals, vol. 1, no. 9, pp. 116-121, 2018.
    [Google Scholar] [Publisher Link]
  22. G. Nethajig, and J. Kathirvelan, “Performance Comparison Between PID and Fuzzy Logic Controllers for the Hardware Implementation of Traditional High Voltage DC-DC Boost Converter,” Heliyon, vol. 10, no. 17, pp. 1-21, 2024.
    [CrossRef] [Google Scholar] [Publisher Link]
  23. Sigurd Skogestad, and Ian Postlethwaite, Multivariable Feedback Control Analysis and Design, 2nd ed., Wiley, 2005.
    [Google Scholar] [Publisher Link]
  24. Ramakant S. Patil, Sharad P. Jadhav, and Machhindranath D. Patil, “Review of Intelligent and Nature-Inspired Algorithms-based Methods for Tuning PID Controllers in Industrial Applications,” Journal of Robotics and Control, vol. 5, no. 2, pp. 336-358, 2024.
    [CrossRef] [Google Scholar] [Publisher Link]
  25. Aytekin Bağiş, and Halit Şenberber, “ABC Algorithm based PID Controller Design for Higher Order Oscillatory Systems,” Electronics and Electrical Engineering, vol. 23, no. 6, pp. 3-9, 2017.
    [CrossRef] [Google Scholar] [Publisher Link]
  26. Stephen Bassi Joseph et al., “Metaheuristic Algorithms for PID Controller Parameters Tuning: Review, Approaches and Open Problems,” Heliyon, vol. 8, no. 5, pp. 1-29, 2022.
    [CrossRef] [Google Scholar] [Publisher Link]
  27. Khadiza Akter et al., “Design and Investigation of High-Power Quality PV Fed DC-DC Boost Converter,” E-Prime - Advances in Electrical Engineering, Electronics and Energy, vol. 9, pp. 1-18, 2024.
    [CrossRef] [Google Scholar] [Publisher Link]
  28. Siavash Shirali, Saeed Zolfaghari Moghaddam, and Mortaza Aliasghary, “An Interval Type-2 Fuzzy Fractional-Order PD-PI Controller for Frequency Stabilization of Islanded Microgrids Optimized with CO Algorithm,” International Journal of Electrical Power and Energy Systems, vol. 164, pp. 1-10, 2025. [CrossRef] [Google Scholar] [Publisher Link]
  29. Emad A. Mohamed et al., “An Optimized Hybrid Fractional Order Controller for Frequency Regulation in Multi-Area Power Systems,” IEEE Access, vol. 8, pp. 213899-213915, 2020.
    [CrossRef] [Google Scholar] [Publisher Link]
  30. Heru Dibyo Laksono, et al., “Performance Evaluation of Load Frequency Control in Reheat Power Systems with Filtered PID Controllers,” Andalas Journal of Electrical and Electronic Engineering Technology, vol. 5, no. 1, pp. 23-30, 2025.
    [CrossRef]  [Google Scholar] [Publisher Link]
  31. Cihan Ersali, Baran Hekimoğlu, and Musa Yilmaz, “Designing A Filtered Proportional–Integral–Derivative Controller with Disturbance Rejection for a Nonideal Buck Converter Utilizing an Upgraded Genetic Algorithm and Pattern Search,” Advanced Control for Applications: Engineering and Industrial Systems, vol. 7, no. 1, pp. 1-18, 2025.
    [CrossRef] [Google Scholar] [Publisher Link]
  32. B. Saidi et al., “Digital Design of Robust Fractional PID Controller for Uncertain Systems,” International Review on Modelling and Simulations, vol. 9, no. 5, pp. 389-398, 2016.
    [CrossRef] [Google Scholar] [Publisher Link]
  33. Farag Elghabsi et al., “An Enhanced Voltage Gain Techniques in Quadratic Boost Converters - A Systematic Review,” ELEKTRIKA-Journal of Electrical Engineering, vol. 23, no. 2, pp. 144-156, 2024.
    [CrossRef] [Google Scholar] [Publisher Link]
  34. Oswaldo Lopez-Santos et al., “Quadratic Boost Converter with Low-Output-Voltage Ripple,” IET Power Electronics, vol. 13, no. 8, pp. 1605-1612, 2020.
    [CrossRef] [Google Scholar] [Publisher Link]
  35. Majid Hosseinpour et al., “A Novel Interleaved Nonisolated High Gain DC–DC Boost Converter based on Voltage Multiplier Rectifier,” Scientific Report, vol. 15, no. 1, pp. 1-29, 2025.
    [CrossRef] [Google Scholar] [Publisher Link]
  36. Souheyb Mohammed Belhadj et al., “Control of Multi-Level Quadratic DC-DC Boost Converter for Photovoltaic Systems using Type-2 Fuzzy Logic Technique-Based MPPT Approaches,” Heliyon, vol. 11, no. 3, pp. 1-25, 2025.
    [CrossRef] [Google Scholar] [Publisher Link]
  37. Modou Badiane et al., “Quadratic Boost Converter: An Analysis with Passive Components Losses,” Open Journal of Applied Sciences, vol. 11, no. 2, pp. 202-215, 2021.
    [CrossRef] [Google Scholar] [Publisher Link]
  38. R. Selva Kumar et al., “Design and Comparison of Quadratic Boost Converter with Boost Converter,” International Journal of Engineering Research and Technology, vol. 5, no. 1, pp. 877-881, 2016.
    [Google Scholar] [Publisher Link]
  39. Xinxin Zhang, Marcin B. Kaczmarek, and S. Hassan HosseinNia, “Frequency Response Analysis for Reset Control Systems: Application to Predict Precision of Motion Systems,” Control Engineering Practice, vol. 152, pp. 1-18, 2024.
    [CrossRef] [Google Scholar] [Publisher Link]
  40. Xiaoqiang Li et al., “Stability Design of Single-Loop Voltage Control with Enhanced Dynamic for Voltage-Source Converters with a Low LC-Resonant-Frequency,” IEEE Transactions on Power Electronics, vol. 33, no. 11, pp. 9937-9951, 2018.
    [CrossRef] [Google Scholar] [Publisher Link]
  41. Jorge Alberto Morales-Saldana et al., “Average Current-Mode Control Scheme for a Quadratic Buck Converter with a Single Switch,” IEEE Transactions on Power Electronics, vol. 23, no. 1, pp. 485-490, 2008.
    [CrossRef] [Google Scholar] [Publisher Link]
  42. Mikulas Huba et al., “Making the PI and PID Controller Tuning Inspired by Ziegler and Nichols Precise and Reliable,” Sensors, vol. 21, no. 18, pp. 1-26, 2021.
    [CrossRef] [Google Scholar] [Publisher Link]
  43. Tarakanath Kobaku et al., “Experimental Verification of Robust PID Controller under Feedforward Framework for a Nonminimum Phase DC-DC Boost Converter,” IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 9, no. 3, pp. 3373-3383, 2021.
    [CrossRef] [Google Scholar] [Publisher Link]
  44. Deepa Somasundaram, and Samuel Babu, “A Closed Loop Control of Quadratic Boost Converter using PID-Controller,” International Journal of Engineering, vol. 27, no. 11, pp. 1653-1662, 2014.
    [Google Scholar] [Publisher Link]
  45. I. Ketut Wiryajati, Ade Safitra, and Muh. Izzul Islam, “Comparative Analysis of the Performance of Linear Quadratic Regulator and State Feedback Control on DC-DC Shunt Boost Converter,” Journal of Computer Science and Informatics Engineering, vol. 8, no. 2, pp. 128-135, 2024.
    [CrossRef] [Google Scholar] [Publisher Link]
  46. Wentao Jiang, Satyajit Hemant Chincholkar, and Chok-You Chan, “Modified Voltage-Mode Controller for the Quadratic Boost Converter with Improved Output Performance,” IET Power Electronics, vol. 11, no. 14, pp. 2222-2231, 2018.
    [CrossRef] [Google Scholar] [Publisher Link]
  47. Hari Agus Sujono et al., “Quadratic Boost Converter with Proportional Integral Control in the Mini Photovoltaic System for Grid,” Electrotechnical Review, vol. 96, 2020.
    [CrossRef] [Google Scholar] [Publisher Link]
  48. Fatema A. Mohammed et al., “Design of a Maximum Power Point Tracking-based PID Controller for DC Converter of Stand-Alone PV System,” Journal of Electrical Systems and Information Technology, vol. 9, no. 1, pp. 1-15, 2022.
    [CrossRef] [Google Scholar] [Publisher Link]
  49. Charles L. Phillips, and Royce D. Habor, Feedback Control Systems, Simon and Schuster, Inc., United States, 1995.
    [Google Scholar] [Publisher Link]
  50. Juan Garrido et al., “Design of Multivariable PID Control using Iterative Linear Programming and Decoupling,” Electronics, vol. 13, no. 4, pp. 1-24, 2024.
    [CrossRef] [Google Scholar] [Publisher Link]
  51. Johannes Günther et al., “Interpretable PID Parameter Tuning for Control Engineering using General Dynamic Neural Networks: An Extensive Comparison,” PLOS One, vol. 15, no. 12, pp. 1-17, 2020.
    [CrossRef] [Google Scholar] [Publisher Link]
  52. Arun R. Pathiran, “Improving the Regulatory Response of PID Controller using Internal Model Control Principles,” International Journal of Control Science and Engineering, vol. 9, no. 1, pp. 9-14, 2019.
    [Google Scholar] [Publisher Link]
  53. V.M. Alfaro, and R. Vilanova, “PID Control: Resilience with Respect to Controller Implementation,” Frontiers in Control Engineering, vol. 3, pp. 1-13, 2022.
    [CrossRef] [Google Scholar] [Publisher Link]
  54. Zhijun Li, Hangwei Zhang, and Wen Tan, “Comparison of PI/PID/PIDD2 Controllers for Higher Order Processes,” IFAC-PapersOnLine, vol. 58, no. 7, pp. 340-345, 2024.
    [CrossRef] [Google Scholar] [Publisher Link]
  55. Driss Khouili, “Design of a Robust Nonlinear PID Controller: Simulation and Experimental Validation for a Computer Aided Aerothermic System,” International Review of Automatic Control, vol. 15, no. 1, 2022.
    [    CrossRef] [Google Scholar] [Publisher Link]
  56. Charles L. Phillips, and H. Troy Nagle, Digital Control System Analysis and Design, Prentice Hall Press, United States, 2007.
    [Google Scholar] [Publisher Link]