1. JCPEE
  2. All Volumes and Issues
  3. Volume 15, Number 1, 2025
  4. Sensitivity analysis of control systems synthesized by feedback control methods to changes in the moment of inertia of the second mass of a two-mass positioning system

Sensitivity analysis of control systems synthesized by feedback control methods to changes in the moment of inertia of the second mass of a two-mass positioning system

JCPEE.
2025;
Volume 15, Number 1
Authors:
  1. Andriy Lozynskyy
  2. Lidiya Kasha
  3. Stepan Pakizh
  4. Roman Sadovyi
1
Lviv Polytechnic National University, Casimir Pulaski Radom University
2
Lviv Polytechnic National University
3
Lviv Polytechnic National University
4
Lviv Polytechnic National University

In this work, a comprehensive approach to the sensitivity analysis of state-variable control systems is proposed. The advantages of systems synthesized by a feedback linearization method are demonstrated being compared to a system synthesized by the modal control method, both in terms of sensitivity to changes in the moment of inertia of the second mass and in terms of control quality. The influence of applying a PI controller and a PIμ-controller on the sensitivity of the system to changes in the moment of inertia of the second mass and on the speed of response and overshoot of the output coordinate in systems synthesized by the feedback linearization method is analyzed.

feedback linearization method
PI controller
sensitivity function of the synthesized system
two-mass system.
  1. R. Muszynski and J. Deskur, "Damping of Torsional Vibrations in High-Dynamic Industrial Drives," in IEEE Transactions on Industrial Electronics, vol. 57, no. 2, pp. 544-552, Feb. 2010, doi: 10.1109/TIE.2009.2036034.
  2. MA Valenzuela, JM Bentley and RD Lorenz, "Evaluation of torsional oscillations in paper machine sections," in IEEE Transactions on Industry Applications, vol. 41, no. 2, pp. 493-501, March-April 2005, doi: 10.1109/TIA.2005.844383
  3. K. Szabat, T. Orlowska-Kowalska and M. Dybkowski, "Indirect Adaptive Control of Induction Motor Drive System With an Elastic Coupling," in IEEE Transactions on Industrial Electronics, vol. 56, no. 10, pp. 4038-4042, Oct. 2009, doi: 10.1109/TIE.2009.2022514.
  4. Li, J.; Wang, D.; Wu, X.; Xu, K.; Liu, X. Vibration Prediction of the Robotic Arm Based on Elastic Joint Dynamics Modeling. Sensors 2022, 22, 6170.https://doi.org/10.3390/s22166170
  5. Dynamics of two-mass systems of regime stabilization in electric arc furnaces [Text]: monograph / Ya. Yu. Marushchak, A.O. Lozynskyi, A. P. Kushnir;. — L.: Lviv Polytechnic Publishing House, 2011. — 224 p.
  6. SE Saarakkala and M. Hinkkanen, "Identification of Two-Mass Mechanical Systems Using Torque Excitation: Design and Experimental Evaluation," in IEEE Transactions on Industry Applications, vol. 51, no. 5, pp. 4180-4189, Sept.-Oct. 2015, doi: 10.1109/TIA.2015.2416128
  7. T. Tarczewski, R. Szczepanski, K. Erwinski, X. Hu and LM Grzesiak, "A Novel Sensitivity Analysis to Moment of Inertia and Load Variations for PMSM Drives," in IEEE Transactions on Power Electronics, vol. 37, no. 11, pp. 13299-13309, Nov. 2022, doi: 10.1109/TPEL.2022.3188404.
  8. K. Szabat and T. Orlowska-Kowalska, "Vibration Suppression in a Two-Mass Drive System Using a PI Speed ​​Controller and Additional Feedbacks—Comparative Study," in IEEE Transactions on Industrial Electronics, vol. 54, no. 2, pp. 1193-1206, April 2007, doi: 10.1109/TIE.2007.892608
  9. K. Szabat, T. Orłowska-Kowalska, and P. Serkies, “Robust Control of the Two-mass Drive System Using Model Predictive Control”, in Robust Control Theory and Applications, InTech, 2011.
  10. MA Valenzuela, JM Bentley and RD Lorenz, "Computer-Aided Controller Setting Procedure for Paper Machine Drive Systems," in IEEE Transactions on Industry Applications, vol. 45, no. 2, pp. 638-650, March-April 2009, doi: 10.1109/TIA.2009.2013588.
  11. P. Li, G. -R. Duan, B. Zhang and Y. Wang, "High-order Fully Actuated Approach for Output Position Control of Two Mass Systems based on Extended State Observer," 2024 3rd Conference on Fully Actuated System Theory and Applications (FASTA), Shenzhen, China, 2024, pp. 1193-1198, doi: 10.1109/FASTA61401.2024.10595104.
  12. SE Saarakkala and M. Hinkkanen, "State-Space Speed ​​Control of Two-Mass Mechanical Systems: Analytical Tuning and Experimental Evaluation," in IEEE Transactions on Industry Applications, vol. 50, no. 5, pp. 3428-3437, Sept.-Oct. 2014, doi: 10.1109/TIA.2014.2306977
  13. M. Ruderman, "Robust output feedback control of non-collocated low-damped oscillating load," 2021 29th Mediterranean Conference on Control and Automation (MED), PUGLIA, Italy, 2021, pp. 639-644, doi: 10.1109/MED51440.2021.9480239.
  14. R. Saathof, T. Riel, M. Bibl, D. Kohl, HW Yoo and G. Schitter, "Non-parametric robustness analysis for feedback motion control for a high precision stage with large mass uncertainty," 2016 American Control Conference (ACC), Boston, MA, USA, 2016, pp. 2611-2616, doi: 10.1109/ACC.2016.7525310
  15. A. Ansari and T. Murphey, "Minimal parametric sensitivity trajectories for nonlinear systems," 2013 American Control Conference, Washington, DC, USA, 2013, pp. 5011-5016, doi: 10.1109/ACC.2013.6580616.
  16. Liang and H. Yamaura, "Robust stabilization for friction-induced vibration with parameter uncertainties," 2015 IEEE International Conference on Advanced Intelligent Mechatronics (AIM), Busan, Korea (South), 2015, pp. 1373-1377, doi: 10.1109/AIM.2015.7222730.
  17. S. Santra and S. Paul, "PSO based robust power system stabilizer design using mixed sensitivity based H¥output-feedback control in LMI approach," 2017 Third International Conference on Research in Computational Intelligence and Communication Networks (ICRCICN), Kolkata, India, 2017, pp. 273-278, doi: 10.1109/ICRCICN.2017.8234520.
  18. B. -s. Kwon, S. Kim and K. Yi, "Design of a robust yaw stability controller for commercial vehicles with parameter sensitivity reduction and stochastic root locus," 2015 IEEE Intelligent Vehicles Symposium (IV), Seoul, Korea (South), 2015, pp. 1100-1105, doi: 10.1109/IVS.2015.7225831.
  19. AJ den Hamer, GZ Angelis, MJG van de Molengraft and M. Steinbuch, "A practical loop-shaping approach for pole-placement in mechatronic systems," Proceedings of 2005 IEEE Conference on Control Applications, 2005. CCA 2005., Toronto, ON, Canada, 2005, pp. 394-399, doi: 10.1109/CCA.2005.1507157.
  20. A. Accetta, M. Cirrincione, M. Pucci and A. Sferlazza, "Feedback Linearization Based Nonlinear Control of SynRM Drives Accounting for Self- and Cross-Saturation," in IEEE Transactions on Industry Applications, vol. 58, no. 3, pp. 3637-3651, May-June 2022, doi: 10.1109/TIA.2022.3155511
  21. A. Lozynskyy, L. Kasha, S. Pakizh, R. Sadovyi. Synthesis of PI- and PID-regulators in control systems derived by the feedback linearization method. Energy Engineering and Control Systems, 2024, Vol. 10, No. 2, pp. 120 - 130.https://doi.org/10.23939/jeecs2024.02.120
  22. P. Serkies and K. Szabat, "Predictive position control of the induction two-mass drive system," 2014 IEEE 23rd International Symposium on Industrial Electronics (ISIE), Istanbul, Turkey, 2014, pp. 871-876, doi: 10.1109/ISIE.2014.6864726
  23. M. Mola, M. Dehghani, A. Khayatian and SM Mola, "LPV modeling and position control of two mass systems with variable backlash using LMIs," 2016 6th IEEE International Conference on Control System, Computing and Engineering (ICCSCE), Penang, Malaysia, 2016, pp. 141-146, doi: 10.1109/ICCSCE.2016.7893560
  24. G. Vinnicombe, "Frequency domain uncertainty and the graph topology," in IEEE Transactions on Automatic Control, vol. 38, no. 9, pp. 1371-1383, Sept. 1993, doi: 10.1109/9.237648.
  25. Richard C. Dorf, Robert H. Bishop. Modern Control Systems, 14th edition, Pearson, 2021 - 1024 p.
  26. Gustavo Asumu Mboro Nchama, Angela Leon Mecías, Mariano Rodriguez Richard. The Caputo-Fabrizio Fractional Integral to Generate Some New Inequalities// Information Sciences Letters 8, No. 2, 73-80 (2019)