FOREX Press I. J. of Electrical & Electronics Research
Support Open Access
  • Home/
  • IJEER-100437

Research Article |

Describing Function Approach with PID Controller to Reduce Nonlinear Action

Author(s): Khalaf S Gaeid1, Raad Z. Homod2, Yousif Al Mashhadany3, Takialddin Al Smadi4, Mohammed Shweesh Ahmed5 and Aws Ezzulddin Abbas6

Published In : International Journal of Electrical and Electronics Research (IJEER)        Volume 10, Issue 4

Publisher : FOREX Publication

Published : 12 November 2022

e-ISSN : 2347-470X

Page(s) : 976-983

DOI: https://doi.org/10.37391/IJEER.100437

Abstract

The nonlinear effect in the control system is so important and it may have a hard or soft effect on the electrical, mechanical, biological, and many other systems. This paper analyzes the describing function (DF) which is the transfer function of the nonlinear (NL) control systems of many NL elements found such as saturation, and backlash. The effect of the NL on the third-order delayed system is considered. The PID controller is considered the heart of the control system and continuously finds the error between input and output, and formulates the desired signal for the actuator to control the plant. Experimental tanning of PID controller with the saturation NL as a case study with buffer Operation Amplifier (Op-Amp) to maintain the gain and phase shift. In addition, a low pass filter (LPF) is used in the feedback to minimize and attenuate the effect of the NL in the closed-loop control system. The Fourier series is used to analyze the DF. The results show the effectiveness of the proposed algorithm.

Keywords: Nonlinear, PID controller, Describing function, Fourier transform, Third-order delayed system .




Khalaf S Gaeid*, Department of Electrical Engineering, Tikrit University, Tikrit, Iraq; Email: gaeidkhalaf@gmail.com

Raad Z. Homod, Department of Oil and Gas Engineering, Basrah University for Oil and Gas, Iraq; Email: raadahmood@yahoo.com

Yousif Al Mashhadany, Electrical Engineering department, University of Anbar, Anbar, Iraq; Email: yousif.mohammed@uoanbar.edu.iq

Takialddin Al Smadi, Faculty of Engineering, Jerash University, Jordan; Email: dsmaditakialddin@gmail.com

Mohammed Shweesh Ahmed, College of Petroleum Processes Engineering/Tikrit University, Iraq; Email: mohammed.shwash@tu.edu.iq

Aws Ezzulddin Abbas, AlZawra State Company, Ministry of Industry, Baghdad, Iraq; Email: awaazz@gmail.com

    [1] Jamshed Iqbal, Mukhtar Ullah, Said Ghani Khan, Baized Khelifa and Saa ukovic "Nonlinear control systems - A brief overview of historical and recent advances" Nonlinear Engineering, vol. 6, no. 4, 2017, pp. 301-312.[Cross Ref]
    [2] R. Pupeikis, D. Navakauskas, L. Ljung" Identification of Wiener systems with hard and discontinuous nonlinearities" Report no.: LiTH-ISY-R-2501, 2003.[Cross Ref]
    [3] G. Abeloos, F. Muller, E. Ferhatogluc, M. Scheel, C. Collettea,G. Kerschena, M.R.W. Braked, P. Tisoe, L. Rensonf, andM. Krack. A Consistency Analysis of Phase-Locked-Loop Testing and Control-Based Continuation for a Geometrically Nonlinear Frictional System. Mechanical Systems and Signal Processing, 170 (2022), 108820. doi: 10.1016/j.ymssp.2022.108820.[Cross Ref]
    [4] N Karbasizadeh, S. Hassan Hossein Nia. Complex-order Reset Control System. arXiv:2205.01378v1 [cs.SY], 2022. [Cross Ref]
    [5] Richard M. Murray "Describing function analysis "Python Control Systems Toolbox, 2021.[Cross Ref]
    [6] Jau-Woei Perng, Bing-Fei Wu, Tien-Yu Liao & Tsu-Tian Lee "Robust Stability Analysis of a Fuzzy Vehicle Lateral Control System Using Describing Function Method "Analysis and Design of Intelligent Systems using Soft Computing Techniques. Advances in Soft Computing, vol 41. Springer, Berlin, Heidelberg, 2007.[Cross Ref]
    [7] V. Sesar; I. Mikovi; T. ijak "Use of describing functions in analysis of systems with neural networks and dominant nonlinearities "The 33rd International Convention MIPRO, Croatia,2010.[Cross Ref]
    [8] Abidaoun Hamdan ShallalRawaa A. KarimOsama Y. Al-Rawi. A Novel Method for Tuning PID Controller. Diyala Journal of Engineering Sciences. Vol. 06, No. 01, pp. 62-74 March 2013.[Cross Ref]
    [9] Khalaf S. Gaeid Anas A. Hussien, Mehdi J Marie. Effect of Fuzzy PID Controller on Feedback Control Systems Based on Wireless Sensor Network. International Journal of Electrical and Computer Engineering.10 (3/1), 2020.[Cross Ref]
    [10] Roland Büchi" PID Controller Parameter Tables for Time-Delayed Systems Optimized Using Hill-Climbing" Signals, 3(1), 146-156, 2022.[Cross Ref]
    [11] Katsuhiko Ogata" Modern Control Engineering" Fifth Edition. Prentice Hall, 2010.[Cross Ref]
    [12] Ghanshyam Prasad Dubey, Rakesh Kumar Bhujade" Information Gain and Correlation on the Performance of Error Back Propagation Based IDS" International Journal of Electrical and Electronics Research (IJEER), Vol9, no.3, pp 27-34, 2021.[Cross Ref]
    [13] Xiao Laui , Rui-Lain Chua "Direct digital control scheme for controlling hybrid dynamic systems using ANN state estimator and inverse dynamics controller" International Journal of Electrical and Electronics Research (IJEER), Vol. 8, no.1 ,pp 1-9,2020.[Cross Ref]
    [14] Juhi Khan Afridi, Awadhesh Gupta, Vandana Vikas Thakre" Adjustable Spectral Characteristics to Design FIR Filter Using Two-Variable Window Function" International Journal of Electrical and Electronics Research (IJEER), Vol. 8, no.1, pp 19-25, 2020.[Cross Ref]
    [15] Samarajit Ghosh "Control systems theory and applications" Pearson Education India, 2004.[Cross Ref]
    [16] Abidaoun Hamdan Shallal" Comparison Performance of Different PID Controllers for DC Motor" Diyala Journal of Engineering Sciences, 5(1): 121-230, 2012.[Cross Ref]
    [17] Zhang, H.; Holden, A.V.; Kodama, I.; Honjo, H.; Lei, M.; Varghese, T.; Boyett, M.R. Mathematical models of action potentials in the periphery and center of the rabbit sinoatrial node. Am. J. Physiol. Heart Circ. Physiol. 2000, 279, H397-H421.[Cross Ref]
    [18] Saha, S.; Chatterjee, D.; Sarkar, B. The ramification of dynamic investment on the promotion and preservation technology for inventory management through a modified flower pollination algorithm. J. Retail. Con. Ser. 2021, 58, 102326.[Cross Ref]
    [19] Cheng Zhao, Lei Guo. Extended PID Control of Nonlinear Uncertain Systems. arXiv:1901.00973v2,2019.[Cross Ref]
    [20] https://www.public.asu.edu/~kirkwood/sysdyn/SDIntro/ch-6.pdf[Cross Ref]
    [21] Simon Bramble and Gabino Alonso .Loop Gain and its Effect on Analog Control Systems. Analog device .2022.[Cross Ref]
    [22] Scott Zhuge. PID Control Theory. Crystal Instruments, 2020.[Cross Ref]
    [23] S. Tavakoli and M. Safaei. Analytical PID control design in time domain with performance-robustness trade-off. Electronics Letters, Vol. 54, No. 13 pp. 815-817, 2018.[Cross Ref]
    [24] http://pc-textbook.mcmaster.ca/Marlin-Ch09.pdf[19] Cheng Zhao, Lei Guo. Extended PID Control of Nonlinear Uncertain Systems. arXiv:1901.00973v2,2019.[Cross Ref]
    [25] Zdenek Uredn cek, Describing functions and prediction of limit cycles. WSEAS Transactions on Systems and Control.2018.[Cross Ref]
    [26] Z. Chen, J. Huang.: Stabilization and Regulation of Nonlinear Systems, Springer International Publishing, Switzerland, ISBN 978-3-319- 08833-4 (2015).[Cross Ref]
    [27] Zdenek Uredn cek" Nonlinear systems - describing functions analysis and using" MATEC Web of Conferences; Les Ulis, Vol. 210, (2018).[Cross Ref]

Khalaf S Gaeid, Raad Z. Homod, Yousif Al Mashhadany, Takialddin Al Smadi, Mohammed Shweesh Ahmed, Aws Ezzulddin Abbas (2022), Describing Function Approach with PID Controller to Reduce Nonlinear Action. IJEER 10(4), 976-983. DOI: 10.37391/IJEER.100437.