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PIλDµ Controllers for Suppression of Limit Cycle in a Plant with Time Delay and Backlash Nonlinearity

Year 2024, Volume: 8 Issue: 4, 506 - 526, 31.12.2024

Biresh Kumar Dakua , Bibhuti Bhusan Pati

https://doi.org/10.30939/ijastech..1471847

Abstract

This paper evaluates the existence of a periodic limit cycle oscillation in a system with backlash nonlinearity in the presence of time delay. An armature voltage-controlled DC motor system is studied in this regard whose output signifies accuracy in position control. An analytical solution for the limit cycle based on the Describing Function (DF) method is obtained whose authenticity is verified with the Nyquist contour-based graphical method and the digital simulations. The effect of parametric changes on the magnitude and frequency of the limit cycle is examined in this article. Integer and non-integer order proportional-integral-derivative (PID) controllers are designed to eliminate these undesirable periodic oscillations present in the system. Multiple optimization techniques considering error-based, time domain specification-based objective functions are scrutinized through statistical tests towards the parameter estimation of the applied controllers. Observations reveal that while the Moth flame optimizer (MFO) with Integral time absolute error (ITAE) produces superior results for the PID controller, the MFO with the Integral time square error (ITSE) provides better results for the FOPID controller. Further, the gain and phase margin-based loop shaping method is also used for an analytical calculation of the controller parameters. Out of the five loop shaping constraints, superior results are obtained by considering robustness towards gain variation constraint as an objective function, and the rest as nonlinear constraints. Simulation studies suggest the efficiency of the utilized controllers in quenching the periodic limit cycle oscillations. The superiority of the FOPID controller over the PID controller is validated by considering suitable performance-based comparisons. The effectiveness of the designed controllers is also tested against the variations in system parameters. Further, the physical realizations of the integer and fractional order PID controllers are performed through Oustaloup recursive filter approximation.

Keywords

Describing function FOPID controllers Limit cycle Nonlinear Systems Time-delay systems

References

  • [1] Atherton DP. Nonlinear control engineering. Van Nostrand Rheinhold. 1975. ISBN:9780442300173.
  • [2] Gopal M. Control systems: principles and design. McGraw-Hill Science, Engineering & Mathematics; 2008. ISBN: 9780073529516.
  • [3] Dakua BK, Pati BB. Prediction and suppression of limit cycle oscillation for a plant with time delay and backlash nonlinearity. In2020 IEEE International Symposium on Sustainable Energy, Signal Processing and Cyber Security (iSSSC) 2020 Dec 16 (pp. 1-5). IEEE. https://doi.org/10.1109/iSSSC50941.2020.9358900.
  • [4] Kesarkar AA, Selvaganesan N, Priyadarshan H. A novel framework to design and compare limit cycle minimizing controllers: demonstration with integer and fractional-order controllers. Nonlinear Dynamics. 2014; 78: 2871-82. https://doi.org/10.1007/s11071-014-1632-6.
  • [5] Kesarkar AA, Selvaganesan N, Priyadarshan H. Novel controller design for plants with relay nonlinearity to reduce amplitude of sustained oscillations: Illustration with a fractional controller. ISA transactions. 2015;57:295-300. https://doi.org/10.1016/j.isatra.2015.01.005.
  • [6] Perumal S, Selvaganesan N. Input dependent Nyquist plot for limit cycle prediction and its suppression using fractional order controllers. Transactions of the Institute of Measurement and Control. 2019;41(13) 3847-60. https://doi.org/10.1177/0142331219841113.
  • [7] Mbitu ET, Chen SC. Designing limit-cycle suppressor using dithering and dual-input describing function methods. mathematics. 2020;8(11):1978. https://doi.org/10.3390/math8111978.
  • [8] Yeroglu C, Tan N. Limit cycle prediction for fractional order systems with static nonlinearities. IFAC Proceedings Volumes. 2010;43(11):144-9. https://doi.org/10.3182/20100826-3-TR-4016.00029.
  • [9] Atherton DP, Tan N, Yeroglu C, Kavuran G, Yüce A. Limit cycles in nonlinear systems with fractional order plants. Machines. 2014;2(3):176-201. https://doi.org/10.3390/machines2030176.
  • [10] Atherton DP, Tan N, Yeroglu C, Kavuran G, Yüce A. Computation of limit cycles in nonlinear feedback loops with fractional order plants. InICFDA'14 International Conference on Fractional Differentiation and Its Applications 2014. Jun 23 (pp. 1-6). IEEE. https://doi.org/10.1109/ICFDA.2014.6967404.
  • [11] Yüce A, Tan N, Atherton DP. Limit cycles in relay systems with fractional order plants. Transactions of the Institute of Measurement and Control. 2019;41(15):4424-35. https://doi.org/10.1177/0142331219860302.
  • [12] Dakua BK, Pati BB. Computation of Limit Cycle in a Nonlinear Fractional-Order Feedback Control Plant with Time Delay. In2021 1st Odisha International Conference on Electrical Power Engineering, Communication and Computing Technology (ODICON) 2021 Jan 8 (pp. 1-6). IEEE. https://doi.org/10.1109/ODICON50556.2021.9428950.
  • [13] Patra KC, Dakua BK. Investigation of limit cycles and signal stabilization of two dimensional systems with memory type nonlinear elements. Archives of Control Sciences. 2018;2:285-330. https://doi.org/10.24425/123461.
  • [14] Patra KC, Kar N. Suppression limit cycles in 2× 2 nonlinear systems with memory type nonlinearities. International Journal of Dynamics and Control. 2022;10(3):721-33. https://doi.org/10.1007/s40435-021-00860-x.
  • [15] Patra KC, Patnaik A. Investigation of the Existence of Limit Cycles in Multi Variable Nonlinear Systems with Special Attention to 3X3 Systems. Int. Journal of Applied Mathematics, Computational Science and System Engineering. 2023;5:93-114. https://doi.org/10.37394/232026.2023.5.9.
  • [16] Patra KC, Patnaik A. Possibility of Quenching of Limit Cycles in Multi Variable Nonlinear Systems with Special Attention to 3X3 Systems. WSEAS Transactions on Systems and Control. 2023;18:677-95. https://doi.org/10.37394/23203.2023.18.69.
  • [17] Cominos P, Munro N. PID controllers: recent tuning methods and design to specification. IEE Proceedings-Control Theory and Applications. 2002;149(1):46-53. https://doi.org/10.1049/ip-cta:20020103.
  • [18] Petráš I. Fractional-order nonlinear systems: modeling, analysis and simulation. Springer Science & Business Media; 2011 May 30. ISSN 1867-8440.
  • [19] Boudjelıda L, Hisar Ç, Sefa I. Design and Control of a Permanent Magnet Assisted Synchronous Reluctance Motor. International Journal of Automotive Science and Technology. 2023;7(4):332-9. https://doi.org/10.30939/ijastech..1366882.
  • [20] Kuyu YÇ. Trajectory Tracking Control Using Evolutionary Approaches for Autonomous Driving. International Journal of Automotive Science And Technology. 2024;8(1):110-7. https://doi.org/10.30939/ijastech..1354082.
  • [21] Karakaş O, Şeker UB, Solmaz H. Modeling of an electric bus Using MATLAB/Simulink and determining cost saving for a realistic city bus line driving cycle. Engineering Perspective. 2021;1(2):52-62. http://dx.doi.org/10.29228/eng.pers.51422.
  • [22] Arslan TA, Aysal FE, Çelik İ, Bayrakçeken H, Öztürk TN. Quarter Car Active Suspension System Control Using Fuzzy Controller. Engineering Perspective. 2022;2(4):33-9. http://dx.doi.org/10.29228/eng.pers.66798.
  • [23] Dakua BK, Pati BB. PIλ-PDμController for Suppression of Limit Cycle in Fractional-Order Time Delay System with Nonlinearities. In2021 1st Odisha International Conference on Electrical Power Engineering, Communication and Computing Technology (ODICON) 2021 Jan 8 (pp. 1-6). IEEE. https://doi.org/10.1109/ODICON50556.2021.9428971.
  • [24] Xue D, Li T, Liu L. A MATLAB toolbox for multivariable linear fractional-order control systems. In2017 29th Chinese Control And Decision Conference (CCDC) 2017 May 28 (pp. 1894-1899). IEEE. https://doi.org/10.1109/CCDC.2017.7978826.
  • [25] Tepljakov A, Petlenkov E, Belikov J. FOMCON toolbox for modeling, design and implementation of fractional-order control systems. Applications in control. 2019 Feb 19; 6:211-36. https://doi.org/10.1515/9783110571745-010.
  • [26] Podlubny I. Fractional-order systems and PI/sup/spl lambda//D/sup/spl mu//-controllers. IEEE Transactions on automatic control. 1999;44(1):208-14. https://doi.org/10.1109/9.739144.
  • [27] Oustaloup A, Levron F, Mathieu B, Nanot FM. Frequency-band complex noninteger differentiator: characterization and synthesis. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications. 2000;47(1):25-39. https://doi.org/10.1109/81.817385.
  • [28] Krishna BT. Studies on fractional order differentiators and integrators: A survey. Signal processing. 2011;91(3):386-426. https://doi.org/10.1016/j.sigpro.2010.06.022.
  • [29] Krishna BT. Various methods of realization for fractional-order elements. ECTI Transactions on Electrical Engineering, Electronics, and Communications. 2023;28(1):1-10. https://doi.org/10.37936/ecti-eec.2023211.248544.
  • [30] Monje CA, Vinagre BM, Feliu V, Chen Y. Tuning and auto-tuning of fractional order controllers for industry applications. Control engineering practice. 2008;16(7):798-812. https://doi.org/10.1016/j.conengprac.2007.08.006.
  • [31] Yeroglu C, Tan N. Note on fractional-order proportional–integral–differential controller design. IET control theory & applications. 2011 Nov 17;5(17):1978-89. https://doi.org/10.1049/iet-cta.2010.0746.
  • [32] Deniz FN, Yüce A, Tan N, Atherton DP. Tuning of fractional order PID controllers based on integral performance criteria using Fourier series method. IFAC-PapersOnLine. 2017;50(1):8561-6. https://doi.org/10.1016/j.ifacol.2017.08.1417.
  • [33] Birs I, Muresan C, Mihai M, Dulf E, De Keyser R. Tuning guidelines and experimental comparisons of sine based auto-tuning methods for fractional order controllers. IEEE Access. 2022;10:86671-83. https://doi.org/10.1109/ACCESS.2022.3198943.
  • [34] Paducel I, Safirescu CO, Dulf EH. Fractional order controller design for wind turbines. Applied Sciences. 2022;12(17):8400. https://doi.org/10.3390/app12178400.
  • [35] Ionescu CM, Dulf EH, Ghita M, Muresan CI. Robust controller design: Recent emerging concepts for control of mechatronic systems. Journal of the Franklin Institute. 2020;357(12):7818-44. https://doi.org/10.1016/j.jfranklin.2020.05.046.
  • [36] Kesarkar AA, Selvaganesan N. Superiority of fractional order controllers in limit cycle suppression. International Journal of Automation and Control. 2013;7(3):166-82. https://doi.org/10.1504/IJAAC.2013.057057.
  • [37] Dakua BK, Pati BB. A deterministic design approach of tilt integral derivative controller for integer and fractional-order system with time delay. Engineering Research Express. 2024;6(3):035331. https://doi.org/10.1088/2631-8695/ad6ca5.
  • [38] Kumar P, Chatterjee S, Shah D, Saha UK, Chatterjee S. On comparison of tuning method of FOPID controller for controlling field controlled DC servo motor. Cogent Engineering. 2017;4(1):1357875. https://doi.org/10.1080/23311916.2017.1357875.
  • [39] Ekinci S, Izci D, Hekimoğlu B. Optimal FOPID speed control of DC motor via opposition-based hybrid manta ray foraging optimization and simulated annealing algorithm. Arabian Journal for Science and Engineering. 2021;46(2):1395-409. https://doi.org/10.1007/s13369-020-05050-z.
  • [40] Hekimoğlu B. Optimal tuning of fractional order PID controller for DC motor speed control via chaotic atom search optimization algorithm. IEEE access. 2019;7:38100-14. https://doi.org/10.1109/ACCESS.2019.2905961.
  • [41] Ersali C, Hekimoğlu B. FOPID controller design for a buck converter system using a novel hybrid cooperation search algorithm with pattern search for parameter tuning. Gazi University Journal of Science Part A: Engineering and Innovation. 2023;10(4):417-41. https://doi.org/10.54287/gujsa.1357216.
  • [42] Mirjalili S, Lewis A. The whale optimization algorithm. Advances in engineering software. 2016;95:51-67. https://doi.org/10.1016/j.advengsoft.2016.01.008.
  • [43] Kennedy J, Eberhart R. Particle swarm optimization. InProceedings of ICNN'95-international conference on neural networks 1995 Nov 27 (Vol. 4, pp. 1942-1948). ieee. https://doi.org/10.1109/ICNN.1995.488968.
  • [44] Mirjalili S. The ant lion optimizer. Advances in engineering software. 2015;83:80-98. https://doi.org/10.1016/j.advengsoft.2015.01.010.
  • [45] Mirjalili S, Mirjalili SM, Lewis A. Grey wolf optimizer. Advances in engineering software. 2014;69:46-61. https://doi.org/10.1016/j.advengsoft.2013.12.007.
  • [46] Mirjalili S. Moth-flame optimization algorithm: A novel nature-inspired heuristic paradigm. Knowledge-based systems. 2015;89:228-49. https://doi.org/10.1016/j.knosys.2015.07.006.
  • [47] Gaing ZL. A particle swarm optimization approach for optimum design of PID controller in AVR system. IEEE transactions on energy conversion. 2004;19(2):384-91. https://doi.org/10.1109/TEC.2003.821821.

Year 2024, Volume: 8 Issue: 4, 506 - 526, 31.12.2024

Biresh Kumar Dakua , Bibhuti Bhusan Pati

https://doi.org/10.30939/ijastech..1471847

Abstract

References

  • [1] Atherton DP. Nonlinear control engineering. Van Nostrand Rheinhold. 1975. ISBN:9780442300173.
  • [2] Gopal M. Control systems: principles and design. McGraw-Hill Science, Engineering & Mathematics; 2008. ISBN: 9780073529516.
  • [3] Dakua BK, Pati BB. Prediction and suppression of limit cycle oscillation for a plant with time delay and backlash nonlinearity. In2020 IEEE International Symposium on Sustainable Energy, Signal Processing and Cyber Security (iSSSC) 2020 Dec 16 (pp. 1-5). IEEE. https://doi.org/10.1109/iSSSC50941.2020.9358900.
  • [4] Kesarkar AA, Selvaganesan N, Priyadarshan H. A novel framework to design and compare limit cycle minimizing controllers: demonstration with integer and fractional-order controllers. Nonlinear Dynamics. 2014; 78: 2871-82. https://doi.org/10.1007/s11071-014-1632-6.
  • [5] Kesarkar AA, Selvaganesan N, Priyadarshan H. Novel controller design for plants with relay nonlinearity to reduce amplitude of sustained oscillations: Illustration with a fractional controller. ISA transactions. 2015;57:295-300. https://doi.org/10.1016/j.isatra.2015.01.005.
  • [6] Perumal S, Selvaganesan N. Input dependent Nyquist plot for limit cycle prediction and its suppression using fractional order controllers. Transactions of the Institute of Measurement and Control. 2019;41(13) 3847-60. https://doi.org/10.1177/0142331219841113.
  • [7] Mbitu ET, Chen SC. Designing limit-cycle suppressor using dithering and dual-input describing function methods. mathematics. 2020;8(11):1978. https://doi.org/10.3390/math8111978.
  • [8] Yeroglu C, Tan N. Limit cycle prediction for fractional order systems with static nonlinearities. IFAC Proceedings Volumes. 2010;43(11):144-9. https://doi.org/10.3182/20100826-3-TR-4016.00029.
  • [9] Atherton DP, Tan N, Yeroglu C, Kavuran G, Yüce A. Limit cycles in nonlinear systems with fractional order plants. Machines. 2014;2(3):176-201. https://doi.org/10.3390/machines2030176.
  • [10] Atherton DP, Tan N, Yeroglu C, Kavuran G, Yüce A. Computation of limit cycles in nonlinear feedback loops with fractional order plants. InICFDA'14 International Conference on Fractional Differentiation and Its Applications 2014. Jun 23 (pp. 1-6). IEEE. https://doi.org/10.1109/ICFDA.2014.6967404.
  • [11] Yüce A, Tan N, Atherton DP. Limit cycles in relay systems with fractional order plants. Transactions of the Institute of Measurement and Control. 2019;41(15):4424-35. https://doi.org/10.1177/0142331219860302.
  • [12] Dakua BK, Pati BB. Computation of Limit Cycle in a Nonlinear Fractional-Order Feedback Control Plant with Time Delay. In2021 1st Odisha International Conference on Electrical Power Engineering, Communication and Computing Technology (ODICON) 2021 Jan 8 (pp. 1-6). IEEE. https://doi.org/10.1109/ODICON50556.2021.9428950.
  • [13] Patra KC, Dakua BK. Investigation of limit cycles and signal stabilization of two dimensional systems with memory type nonlinear elements. Archives of Control Sciences. 2018;2:285-330. https://doi.org/10.24425/123461.
  • [14] Patra KC, Kar N. Suppression limit cycles in 2× 2 nonlinear systems with memory type nonlinearities. International Journal of Dynamics and Control. 2022;10(3):721-33. https://doi.org/10.1007/s40435-021-00860-x.
  • [15] Patra KC, Patnaik A. Investigation of the Existence of Limit Cycles in Multi Variable Nonlinear Systems with Special Attention to 3X3 Systems. Int. Journal of Applied Mathematics, Computational Science and System Engineering. 2023;5:93-114. https://doi.org/10.37394/232026.2023.5.9.
  • [16] Patra KC, Patnaik A. Possibility of Quenching of Limit Cycles in Multi Variable Nonlinear Systems with Special Attention to 3X3 Systems. WSEAS Transactions on Systems and Control. 2023;18:677-95. https://doi.org/10.37394/23203.2023.18.69.
  • [17] Cominos P, Munro N. PID controllers: recent tuning methods and design to specification. IEE Proceedings-Control Theory and Applications. 2002;149(1):46-53. https://doi.org/10.1049/ip-cta:20020103.
  • [18] Petráš I. Fractional-order nonlinear systems: modeling, analysis and simulation. Springer Science & Business Media; 2011 May 30. ISSN 1867-8440.
  • [19] Boudjelıda L, Hisar Ç, Sefa I. Design and Control of a Permanent Magnet Assisted Synchronous Reluctance Motor. International Journal of Automotive Science and Technology. 2023;7(4):332-9. https://doi.org/10.30939/ijastech..1366882.
  • [20] Kuyu YÇ. Trajectory Tracking Control Using Evolutionary Approaches for Autonomous Driving. International Journal of Automotive Science And Technology. 2024;8(1):110-7. https://doi.org/10.30939/ijastech..1354082.
  • [21] Karakaş O, Şeker UB, Solmaz H. Modeling of an electric bus Using MATLAB/Simulink and determining cost saving for a realistic city bus line driving cycle. Engineering Perspective. 2021;1(2):52-62. http://dx.doi.org/10.29228/eng.pers.51422.
  • [22] Arslan TA, Aysal FE, Çelik İ, Bayrakçeken H, Öztürk TN. Quarter Car Active Suspension System Control Using Fuzzy Controller. Engineering Perspective. 2022;2(4):33-9. http://dx.doi.org/10.29228/eng.pers.66798.
  • [23] Dakua BK, Pati BB. PIλ-PDμController for Suppression of Limit Cycle in Fractional-Order Time Delay System with Nonlinearities. In2021 1st Odisha International Conference on Electrical Power Engineering, Communication and Computing Technology (ODICON) 2021 Jan 8 (pp. 1-6). IEEE. https://doi.org/10.1109/ODICON50556.2021.9428971.
  • [24] Xue D, Li T, Liu L. A MATLAB toolbox for multivariable linear fractional-order control systems. In2017 29th Chinese Control And Decision Conference (CCDC) 2017 May 28 (pp. 1894-1899). IEEE. https://doi.org/10.1109/CCDC.2017.7978826.
  • [25] Tepljakov A, Petlenkov E, Belikov J. FOMCON toolbox for modeling, design and implementation of fractional-order control systems. Applications in control. 2019 Feb 19; 6:211-36. https://doi.org/10.1515/9783110571745-010.
  • [26] Podlubny I. Fractional-order systems and PI/sup/spl lambda//D/sup/spl mu//-controllers. IEEE Transactions on automatic control. 1999;44(1):208-14. https://doi.org/10.1109/9.739144.
  • [27] Oustaloup A, Levron F, Mathieu B, Nanot FM. Frequency-band complex noninteger differentiator: characterization and synthesis. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications. 2000;47(1):25-39. https://doi.org/10.1109/81.817385.
  • [28] Krishna BT. Studies on fractional order differentiators and integrators: A survey. Signal processing. 2011;91(3):386-426. https://doi.org/10.1016/j.sigpro.2010.06.022.
  • [29] Krishna BT. Various methods of realization for fractional-order elements. ECTI Transactions on Electrical Engineering, Electronics, and Communications. 2023;28(1):1-10. https://doi.org/10.37936/ecti-eec.2023211.248544.
  • [30] Monje CA, Vinagre BM, Feliu V, Chen Y. Tuning and auto-tuning of fractional order controllers for industry applications. Control engineering practice. 2008;16(7):798-812. https://doi.org/10.1016/j.conengprac.2007.08.006.
  • [31] Yeroglu C, Tan N. Note on fractional-order proportional–integral–differential controller design. IET control theory & applications. 2011 Nov 17;5(17):1978-89. https://doi.org/10.1049/iet-cta.2010.0746.
  • [32] Deniz FN, Yüce A, Tan N, Atherton DP. Tuning of fractional order PID controllers based on integral performance criteria using Fourier series method. IFAC-PapersOnLine. 2017;50(1):8561-6. https://doi.org/10.1016/j.ifacol.2017.08.1417.
  • [33] Birs I, Muresan C, Mihai M, Dulf E, De Keyser R. Tuning guidelines and experimental comparisons of sine based auto-tuning methods for fractional order controllers. IEEE Access. 2022;10:86671-83. https://doi.org/10.1109/ACCESS.2022.3198943.
  • [34] Paducel I, Safirescu CO, Dulf EH. Fractional order controller design for wind turbines. Applied Sciences. 2022;12(17):8400. https://doi.org/10.3390/app12178400.
  • [35] Ionescu CM, Dulf EH, Ghita M, Muresan CI. Robust controller design: Recent emerging concepts for control of mechatronic systems. Journal of the Franklin Institute. 2020;357(12):7818-44. https://doi.org/10.1016/j.jfranklin.2020.05.046.
  • [36] Kesarkar AA, Selvaganesan N. Superiority of fractional order controllers in limit cycle suppression. International Journal of Automation and Control. 2013;7(3):166-82. https://doi.org/10.1504/IJAAC.2013.057057.
  • [37] Dakua BK, Pati BB. A deterministic design approach of tilt integral derivative controller for integer and fractional-order system with time delay. Engineering Research Express. 2024;6(3):035331. https://doi.org/10.1088/2631-8695/ad6ca5.
  • [38] Kumar P, Chatterjee S, Shah D, Saha UK, Chatterjee S. On comparison of tuning method of FOPID controller for controlling field controlled DC servo motor. Cogent Engineering. 2017;4(1):1357875. https://doi.org/10.1080/23311916.2017.1357875.
  • [39] Ekinci S, Izci D, Hekimoğlu B. Optimal FOPID speed control of DC motor via opposition-based hybrid manta ray foraging optimization and simulated annealing algorithm. Arabian Journal for Science and Engineering. 2021;46(2):1395-409. https://doi.org/10.1007/s13369-020-05050-z.
  • [40] Hekimoğlu B. Optimal tuning of fractional order PID controller for DC motor speed control via chaotic atom search optimization algorithm. IEEE access. 2019;7:38100-14. https://doi.org/10.1109/ACCESS.2019.2905961.
  • [41] Ersali C, Hekimoğlu B. FOPID controller design for a buck converter system using a novel hybrid cooperation search algorithm with pattern search for parameter tuning. Gazi University Journal of Science Part A: Engineering and Innovation. 2023;10(4):417-41. https://doi.org/10.54287/gujsa.1357216.
  • [42] Mirjalili S, Lewis A. The whale optimization algorithm. Advances in engineering software. 2016;95:51-67. https://doi.org/10.1016/j.advengsoft.2016.01.008.
  • [43] Kennedy J, Eberhart R. Particle swarm optimization. InProceedings of ICNN'95-international conference on neural networks 1995 Nov 27 (Vol. 4, pp. 1942-1948). ieee. https://doi.org/10.1109/ICNN.1995.488968.
  • [44] Mirjalili S. The ant lion optimizer. Advances in engineering software. 2015;83:80-98. https://doi.org/10.1016/j.advengsoft.2015.01.010.
  • [45] Mirjalili S, Mirjalili SM, Lewis A. Grey wolf optimizer. Advances in engineering software. 2014;69:46-61. https://doi.org/10.1016/j.advengsoft.2013.12.007.
  • [46] Mirjalili S. Moth-flame optimization algorithm: A novel nature-inspired heuristic paradigm. Knowledge-based systems. 2015;89:228-49. https://doi.org/10.1016/j.knosys.2015.07.006.
  • [47] Gaing ZL. A particle swarm optimization approach for optimum design of PID controller in AVR system. IEEE transactions on energy conversion. 2004;19(2):384-91. https://doi.org/10.1109/TEC.2003.821821.
There are 47 citations in total.

Details

Primary Language English
Subjects Automotive Mechatronics and Autonomous Systems
Journal Section Articles
Authors

Biresh Kumar Dakua 0000-0003-2921-5948

Bibhuti Bhusan Pati This is me 0000-0003-0215-388X

Publication Date December 31, 2024
Submission Date April 22, 2024
Acceptance Date September 11, 2024
Published in Issue Year 2024 Volume: 8 Issue: 4

Cite

APA Dakua, B. K., & Pati, B. B. (2024). PIλDµ Controllers for Suppression of Limit Cycle in a Plant with Time Delay and Backlash Nonlinearity. International Journal of Automotive Science And Technology, 8(4), 506-526. https://doi.org/10.30939/ijastech..1471847
AMA Dakua BK, Pati BB. PIλDµ Controllers for Suppression of Limit Cycle in a Plant with Time Delay and Backlash Nonlinearity. IJASTECH. December 2024;8(4):506-526. doi:10.30939/ijastech.1471847
Chicago Dakua, Biresh Kumar, and Bibhuti Bhusan Pati. “PIλDµ Controllers for Suppression of Limit Cycle in a Plant With Time Delay and Backlash Nonlinearity”. International Journal of Automotive Science And Technology 8, no. 4 (December 2024): 506-26. https://doi.org/10.30939/ijastech. 1471847.
EndNote Dakua BK, Pati BB (December 1, 2024) PIλDµ Controllers for Suppression of Limit Cycle in a Plant with Time Delay and Backlash Nonlinearity. International Journal of Automotive Science And Technology 8 4 506–526.
IEEE B. K. Dakua and B. B. Pati, “PIλDµ Controllers for Suppression of Limit Cycle in a Plant with Time Delay and Backlash Nonlinearity”, IJASTECH, vol. 8, no. 4, pp. 506–526, 2024, doi: 10.30939/ijastech..1471847.
ISNAD Dakua, Biresh Kumar - Pati, Bibhuti Bhusan. “PIλDµ Controllers for Suppression of Limit Cycle in a Plant With Time Delay and Backlash Nonlinearity”. International Journal of Automotive Science And Technology 8/4 (December 2024), 506-526. https://doi.org/10.30939/ijastech. 1471847.
JAMA Dakua BK, Pati BB. PIλDµ Controllers for Suppression of Limit Cycle in a Plant with Time Delay and Backlash Nonlinearity. IJASTECH. 2024;8:506–526.
MLA Dakua, Biresh Kumar and Bibhuti Bhusan Pati. “PIλDµ Controllers for Suppression of Limit Cycle in a Plant With Time Delay and Backlash Nonlinearity”. International Journal of Automotive Science And Technology, vol. 8, no. 4, 2024, pp. 506-2, doi:10.30939/ijastech. 1471847.
Vancouver Dakua BK, Pati BB. PIλDµ Controllers for Suppression of Limit Cycle in a Plant with Time Delay and Backlash Nonlinearity. IJASTECH. 2024;8(4):506-2.


International Journal of Automotive Science and Technology (IJASTECH) is published by Society of Automotive Engineers Turkey

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