Polynomial-based Stability Analysis of Modified IMC-PID Controller for Piezoelectric Actuator System in Time Delay Environment

References

• P.  Lambert, A. Valentini, and B. P. D. Lagrange Delchambre, “Design and performances of a one-degree-of-freedom guided nano-actuator,” Robot. Comput. Integr. Manuf., Vol. 19, pp. 89–98, 2003.
   Web of Science ®Google Scholar
• K. F. Hii, R. R. Vallance, and M. P. Mengu, “Design, operation, and motion characteristics of a precise piezoelectric linear motor,” Precis. Eng, Vol. 34, pp. 231–41, 2010.
   Web of Science ®Google Scholar
• U. M. Nath, C. Dey, and R. K. Mudi, “Review on IMC-based PID controller design approach with experimental validations,” IETE. J. Res., pp. 1–21, Feb. 2021. doi:10.1080/03772063.2021.1874839.
   Web of Science ®Google Scholar
• S. Mohith, A. R. Upadhya, N. Karanth, S. M. Kulkarni, and M. Rao, “Recent trends in piezoelectric actuators for precision motion and their applications: A review,” Smart Mater. Struct, Vol. 30, pp. 013002, 2021.
   Web of Science ®Google Scholar
• J. Peng, and X. Chen, “A survey of modeling and control of piezoelectric actuators,” Mod. Mech. Eng., Vol. 3, pp. 1–20, 2013.
   Google Scholar
• Y. Shengdong, M. Jinyu, W. Hongtao, and K. Shengzheng, “Robust precision motion control of piezoelectric actuators using fast nonsingular terminal sliding mode with time delay estimation,” Meas. Control, Vol. 52, pp. 11–9, 2019.
   Web of Science ®Google Scholar
• C. Yang, N. Verbeek, F. Xia, Y. Wang, and K. Youcef-Toumi, “Modeling and control of piezoelectric hysteresis: A polynomial-based fractional order disturbance compensation approach,” IEEE Trans. Ind. Electron., Vol. 68, pp. 3348–58, April 2021. doi:10.1109/TIE.2020.2977567.
   Web of Science ®Google Scholar
• K. A. Naik, P. Srikanth, and P. Negi, “IMC tuned PID governor controller for hydro power plant with water hammer effect,” Procedia Technol., Vol. 4, pp. 845–53, 2012.
   Google Scholar
• A. Kanasottu, S. Pullabhatla, and V. R. Mettu, “IMC design based optimal tuning of a PID-filter governor controller for hydro power plant,” Commun. Comput. Inf. Sci., Vol. 148, pp. 34–42, 2011.
   Google Scholar
• P. Negi, “Frequency domain analysis of optimal tuned IMC-PID controller for continuous stirred tank reactor,” CSTR, Vol. 2, pp. 34–9, 2014.
   Google Scholar
• P. K. Paul, C. Dey, and R. K. Mudi, “Design of fuzzy based IMC-PID controller for IPD process,” in 2013 International Symposium on Computational and Business Intelligence, 2013, pp. 111–4. doi:10.1109/ISCBI.2013.30.
   Google Scholar
• S. A. Geddes, “Internal model control (IMC) of a fruit drying system,” University of Southern Queensland, 2006.
   Google Scholar
• V. Avithra, G. Mary, and R. Jansi, “Boiler drum level control using internal model controller,” Int. J. Innov. Res. Technol. (IJIRT), Vol. 1, pp. 2349-6002, 2015.
   Google Scholar
• M. M. Awais, “Application of internal model control methods to industrial combustion,” Appl. Soft. Comput., Vol. 5, pp. 223–33, 2005.
   Web of Science ®Google Scholar
• G. Hou, Y. Huang, H. Du, J. Zhang, and X. Zheng, “Design of internal model controller based on ITAE index and its application in boiler combustion control system,” in 12th IEEE Conference on Industrial Electronics and Applications (ICIEA), pp. 2078–83. Siem Reap. doi:10.1109/ICIEA.8283180, 2017
   Google Scholar
• T. Liu, and F. Gao, “Enhanced IMC design of load disturbance rejection for integrating and unstable processes with slow dynamics,” ISA Trans., Vol. 50, pp. 239–48, 2011.
   PubMed Web of Science ®Google Scholar
• D. Rupp, and L. Guzzella, “Iterative tuning of internal model controllers with application to air/fuel ratio control,” IEEE Trans. Control Syst. Technol., Vol. 18, pp. 177–84, 2010.
   Web of Science ®Google Scholar
• M. Kumar, D. Prasad, and R. S. Singh, “Performance enhancement of IMC-PID controller design for stable and unstable second-order time delay processes,” J. Cent. South Univ., Vol. 27, pp. 88–100, Jan. 31, 2020. doi:10.1007/s11771-020-4280-7.
   Web of Science ®Google Scholar
• K. Gu, “An integral inequality in the stability problem of time-delay systems,” in Proceedings of the 39th IEEE Conference on Decision and Control vol.3, Sydney, NSW, 2000, pp. 2805–10.
   Google Scholar
• R. Curtain, and A. J. Pritchard. Infinite dimensional linear systems theory. Lecture Notes in Control and Information Sciences. Springer, 1978.
   Google Scholar
• X. fu, Z. Xiao, and D. Lu, “On stability analysis of nonlinear time-delay systems on time scales,” Syst. Control. Lett., Vol. 131, pp. 104–498, 2019.
   Web of Science ®Google Scholar
• J. Peng, M. Xiang, L. Li, H. Sun, and X. Wang, “Time-delayed feedback control of piezoelectric elastic beams under superharmonic and subharmonic excitations,” Appl. Sci., Vol. 9, pp. 1557, 2019. doi:10.3390/app9081557.
   Google Scholar
• Y. Shengdong, M. Jinyu, W. Hongtao, and K. Shengzheng, “Robust precision motion control of piezoelectric actuators using fast nonsingular terminal sliding mode with time delay estimation,” Measurement and Control, Vol. 52, pp. 11–9, 2018. doi:10.1177/0020294018811336.
   Web of Science ®Google Scholar
• W. Huang, “Generalization of liapunov's theorem in a linear delay system,” J. Math. Anal. Appl., Vol. 142, pp. 83–94, 1989.
   Web of Science ®Google Scholar
• S. S. F´ulvia, D. Oliveira, S. O. Fernando, and M. Reinaldo Palhares, “PID tuning for time-varying delay systems based on modified smith predictor,” IFAC Pap. On Line, Vol. 50, pp. 1269–274, 2017.
   Google Scholar
• A. M. Leonardo, and O. Souza, “Fernando PID tuning under uncertain conditions: robust LMI design for second-order plus time-delay transfer functions,” IFAC Proc., Vol. 46, pp. 120–5, 2013.
   Google Scholar
• M. Parada, A. Renato, D. Borges, P. Sbarbaro, and L. D. Peres, “Robust PID design for second-order processes with time-delay and structured uncertainties,” in IFAC Proceedings of the 18th World Congress, 2011, pp. 4614–9.
   Google Scholar
• S. Xu, and J. Lam, “A survey of linear matrix inequality techniques in stability analysis of delay systems,” Int. J. Syst. Sci., Vol. 95, pp. 1095–113, 2008. doi:10.1080/00207720802300370.
   Google Scholar
• S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, “Linear matrix inequalities in system and control theory,” in Studies in Applied Mathematics Society for Industrial and Applied Mathematics, Vol. 15. SIAM. ISBN 0-89871-334-X, 1994.
   Google Scholar
• S. Shome, S. Jana, A. Mukherjee, P. Bhattarcharjee, and U. Datta, “Bio inspired modified internal model control approach for improved disturbance rejection of piezo micro manipulator,” Stud. Inf. Control, Vol. 27, pp. 295–306, 2018. doi:10.24846/v27i3y201805.
   Web of Science ®Google Scholar
• Q. Xu, and Y. Li, “Dahl model-based hysteresis compensation and precise positioning control of an XY parallel micromanipulator with piezoelectric actuation,” J. Dyn. Syst. Measure. Contr. ASME, Vol. 132, pp. 041011, 2010.
   Web of Science ®Google Scholar
• S. K. Shome, A. Mukherjee, P. Karmakar, and U. Datta. “Adaptive feed-forward controller of piezoelectric actuator for micro/nano-positioning,” sadhana, pp. 43–10, Article ID 0158 October 2018.
   Google Scholar
• M. Morari, and E. Zafirious. Robust Process Control, Prentice-Hall.
   Google Scholar
• S. K. Shome, et al., “Model-based control for second-order piezo-actuator system with hysteresis in time-delay environment,” Turk. J. Electr. Eng. Comput. Sci., Vol. 29, pp. 1495–508, 2021. doi:10.3906/elk-1907-28.
   Web of Science ®Google Scholar
• M. Yadav, and H. K. G. Patel, “Sensitivity analysis of IMC-PID controller with smith predictor using different filters,” in 2020 IEEE 17th India Council International Conference (INDICON), 2020, pp. 1–6.
   Google Scholar
• S. Shome, S. Jana, A. Mukherjee, and P. Bhattarcharjee, “Sensitivity function based robustness evaluation of hysteretic piezo electric actuator Using Internal Model principle,” UPB Sci. Bull. Ser. C Electr. Eng., Vol. 81, pp. 169–182, 2019.
   Google Scholar