Arka Biswas, Arindam Mondal, Prasanta Sarkar

DOI Number
First page
Last page


This paper presents the design and implementation of a discrete-time controller for a DC-DC Buck converter in the complex delta domain. Whenever any continuous-time system is sampled to get a corresponding discrete-time system with a very high sampling rate, the shift operator parameterized discrete-time system fails to provide meaningful information. There is another discrete-time operator called delta operator. In the delta operator parameterized discrete-time system, the discrete-time results and continuous-time results can be obtained hand to hand, rather than in two special cases at a very high sampling rate. The superior property of the delta operator is capitalized in this paper to design the proposed controller in the discrete domain. The Proportional plus Integral (PI) controller designed in the delta domain is used to maintain the output voltage of the Buck converter at the load end for varying load and varying supply voltage conditions. The controller is designed and implemented using the DS1202 dSPACE board. The output voltage of the Buck converter is scaled to feed to the onboard analogue to digital converter of DS1202. Under the different disturbances, the error between the desired output voltage and the actual output voltage is measured and the delta PI controller is used to manipulate the duty cycle of the converter. The duty cycle of this pulse width modulation (PWM) signal is generated using a DS1202 board and is applied to the gate of the Metal Oxide Semiconductor field-effect transistor (MOSFET) via a suitable driver such that the output voltage of the Buck converter remains at its desired value.


Buck converter, delta domain, digital controller, dSPACE board, PI controller

Full Text:



N. Mohan, T. M. Undeland, & W. P. Robbins, Power Electronics: Converters, Applications, and Design, John Willey & Sons, New York, 2002.

G. Dileep & S. N. Singh, "Selection of non-isolated DC-DC converters for solar photo voltaic system", Renewable Sustainable Energy Review, vol. 76, pp. 1230-1247, 2017.

A. Bhaumik, Y. Kumar, S. Srivastava, & M. Islam, 2016, "Performance studies of a separately excited DC motor speed control fed by a buck converter using optimized PIλDμ controller", In Proceedings of the Int. Conf. Circuit, Power Comput. Technol. (ICCPCT), Nagercoil, India, 2016.

M. Hassanalieragh, T. Soyata, A. Nadeau, & G. Sharma, "UR-SolarCap: An open-source intelligent auto-wakeup solar energy harvesting system for supercapacitor-based energy buffering", IEEE Access, vol. 4, pp. 542-557, 2016.

Q. Xu, C. Zhang, C. Wen, & P. Wang, "A novel composite nonlinear controller for stabilization of constant power load in DC microgrid, IEEE Trans. Smart Grid", vol.10, no. 1, pp. 752-761, 2010.

D. Kumar, F. Zare, & A. Ghosh, "DC microgrid technology: System architectures, AC grid interfaces, grounding schemes, power quality, communication networks, applications, and standardizations aspects", IEEE Access, vol. 5, pp. 12230-12256, 2017.

Liu Qingpeng, Research on Buck converter based on linear feedback control [D], Northeast Petroleum University, 2012.

M. Ghamari, H. Mollaee, F. Khavari, "Robust self-tuning regressive adaptive controller design for a DC–DC BUCK converter", Measurement, vol. 174, 109071, 2021.

C. Deekshitha & K. Latha Shenoy, "Design and Simulation of Synchronous Buck Converter for LED Application", In Proceedings of the 2nd IEEE International Conference on Recent Trends In Electronics Information & Communication Technology, Bangalore, India, 2017, pp. 142-146.

Z. Yichen, X. Hejin & L. Deming, "Feedback control of fractional PIλDμ for DC/DC Buck converters", In Proceedings of the International Conference on Industrial Informatics -Computing Technology, Intelligent Technology, Industrial Information Integration, Wuhan, China, 2017, pp. 219-222.

A. M. AbdurRaqueeb, A. A. AL-Shamma’a, A. Alkhuhyali, A. M. Noman, K.E. Addoweesh, "RST Digital Robust Control for DC/DC Buck Converter Feeding Constant Power Load", Mathematics, vol. 10, id. 1782, p. 15, 2022.

G. Abbas, J. Gu, U. Farooq, M. Irfan Abid, A. Raza, M. Asad, V. E. Balas and M. E. Balas, "Optimized Digital Controllers for Switching-Mode DC-DC Step-Down Converter", Electronics, vol. 7, no. 12, id. 412, p. 25, 2018.

G. Abbas, M. Nazeer, V. Balas, T.-C. Lin, M. Balas, M. Asad, A. Raza, M. Shehzad, U. Farooq and J. Gu, "Derivative-Free Direct Search Optimization Method for Enhancing Performance of Analytical Design Approach-Based Digital Controller for Switching Regulator", Energies, vol. 12, no. 11, id. 2183, p. 18, 2019.

K. R. Kumar & S. Jeevananthan, "Design of Sliding Mode Control for Negative Output Elementary Super Lift Luo Converter operated in Continuous Conduction Mode", In proceedings of the Communication Control and Computing Technologies (ICCCCT), Ramanthapuram, India, 2010. pp. 138-148.

K. Sharma & D. K. Palwalia, 2017, "Design of Digital PID Controller for Voltage ModeControl of DC-DC Converters", In Proceedings of the International conference on Microelectronic Devices, Circuits and Systems (ICMDCS), Vellore, India, 2017.

L. H. Guang, W. Bo & L. G. You, 2005, "Delta Operator Control and its Robust Control Theory Basis (M), National Defence Industry Press, Beijing.

R. H. Middleton & G. C. Goodwin, 1990, Digital Control and Estimation-A Unified Approach, Prentice-Hall, Englewood Cliffs. New Jersey.

R. H. Middleton & G. C. Goodwin, 1986, "Improved finite wordlength characteristics in digital control using delta operators", IEEE Transactions on Automatic Control, vol. 31, no. 11, pp. 1015-1021.

J. Cortes-Romero, A. luviana-Juarez & H. Sira-Ramirez, 2013, "A Delta Operator Approach for the Discrete-Time Active Disturbance Rejection Control on Induction Motors", Mathematical Problems in Engineering, vol. 2013, id. 572026, p. 9, 2013.

G. Maione, "High-Speed Digital Realisation of Fractional Operators in Delta Domain", IEEE Transactions on Automatic Control, vol. 56, no. 3, pp. 697-702, 2011.

S. Ganguli, G. Kaur & P. Sarkar, "A hybrid intelligent technique for model order reduction in the delta domain: a unified approach", Springer Nature, Soft Computing, vol. 23, pp. 4801-4814, 2018.

Y. Zhao & D. Zhang, "H∞ Fault Detection for Uncertain Delta Operator Systems with Packet Dropout and Limited Communication", In Proceedings of the American Control Conference, Seattle, WA, USA, 2017, pp. 4772-4777.

J. Gao, S. Chai, M. Shuai, B. Zhang & L. Cui, "Detecting False Data Injection attack on cyber-physical system based on Delta Operator", In Proceedings of the 37th Chinese Control Conference, Wuhan China, 2018.

J. Zhou, D. Zhang, IEEE Access, Multidisciplinary, vol. 7, id. 94448, 2019.

A. Mondal, P. Sarkar, A. Hazra, "A unified approach for PI controller design in delta domain for indirect field-oriented control of induction motor derive", Journal of Engineering Research, vol. 8, no. 3, pp. 118-134, 2020.

B. L. Eidson, 2010, An Experimental Evaluation of Delta Operator in Digital Control, Auburn, Alabama.

I. Laoprom, S. Tunyasrirut, "Design of PI Controller for Voltage Controller of Four-Phase Interleaved Boost Converter Using Particle Swarm Optimization", Journal of Control Science and Engineering, id. 9515160, p. 13, 2020.

K. S. Rao, R. Mishra, "Comparative study of P, PI and PID controller for speed control of VSI-fed induction motor", International Journal of Engineering Development and Research, vol. 2, no. 2, pp. 2740-2744, 2014.

L. A. Quezada-Téllez, L. Franco-Pérez, "Guillermo Fernandez-Anaya, 2020, Controlling Chaos for a Fractional-Order Discrete System", IEEE Open Journal of Circuit and Systems, vol. 1, pp. 263-269, 2020.

P. Hu, S. Chen, H. Huang, G. Zhang, L. Liu, "Improved alpha-guided grey wolf optimizer", IEEE Access, vol. 7, pp. 5421-5437, 2018.

T. S. Anandhi, K. Muthukumar & S.P. Natarajan, "dSPACE Based Implementation of PID Controller for Buck Converter", In Proceedings of the dSPACE User Conference, 2012.

V. R, R. G, K. K. B & A. K. G, "dSPACE Based 12/24v Closed Loop Boost Converter for Low Power Applications", In Proceedings of the International conference on computation of power, energy, information and communication, Chennai, India, 2014, pp. 213-217.

Ogata. K, Modern Control System, 1987, University of Minnesota, Prentice Hall.

N Pillai, P.A. Govender, Particle Swarm Optimization approach for model independent tuning of PID control loop, IEEE Africon, IEEE Catalog: 04CH37590C, 2007.


  • There are currently no refbacks.

ISSN: 0353-3670 (Print)

ISSN: 2217-5997 (Online)

COBISS.SR-ID 12826626