A linear matrix inequality approach to discrete-time finite impulse response controller design for integrating time-delay processes

Document Type : Article


Department of Electrical and Computer Engineering, University of Zanjan, Zanjan, P.O. Box 45371-38791, Iran


Short-term memory discrete-time finite impulse response (FIR) controller design along with an optimized tuning method is presented in this paper. For this purpose, the loop shaping scheme is employed in the linear matrix inequalities (LMIs) framework for adjusting some characteristics of the open-loop frequency response such as phase margin and bandwidth to the desired values at appropriate frequencies. Unlike the conventional methods which work based on state-space models, the proposed procedure generates LMIs directly in the frequency domain. The proposed controller design procedure was applied to several integrating time-delay systems to illustrate its performance and the results were compared with some other competing methods


References  1. Mishra, P., Kumar, V., and Rana, K.P.S. A fractional  order fuzzy PID controller for binary distillation column  control", Expert Syst. Appl., 42(22), pp. 8533{  8549 (2015).  2. Shamsuzzoha, M. IMC based robust PID controller  tuning for disturbance rejection", J. Cent. South  Univ., 23(3), pp. 581{597 (2016).  3. Wang, X., Wang, G., Chen, H., et al. Real-time  temperature _eld reconstruction of boiler drum based  on fuzzy adaptive Kalman _lter and order reduction",  Int. J. Ther. Sci., 113, pp. 145{153 (2017).  4. Pachauri, N., Singh, V., and Rani, A. Two degree  of freedom PID based inferential control of continuous  bioreactor for ethanol production", ISA T., 68, pp.  235{250 (2017).  5. Masroor, S. and Peng, C. Agent-based consensus  on speed in the network-coupled DC motors", Neural  Comput. Appl., 30(5), pp. 1647{1656 (2018).  6. Pai, N.S., Chang, S.C., and Huang, C.T. Tuning  PI/PID controllers for integrating processes with deadtime  and inverse response by simple calculations", J.  Process Contr., 20(6), pp. 726{733 (2010).  7. Matausek, M.R. and Sekara, T.B. PID controller  frequency-domain tuning for stable, integrating and  unstable processes, including dead-time", J. Process  Contr., 21(1), pp. 17{27 (2011).  8. Mercader, P. and Banos, A. A PI tuning rule for  integrating plus dead time processes with parametric  uncertainty", ISA T., 67, pp. 246{255 (2017).  9. Martins, M.A., Yamashita, A.S., Santoro, B.F., et al.  Robust model predictive control of integrating time  delay processes", J. Process Contr., 23(7), pp. 917{  932 (2013).  10. Gonzalez, A.H., Marchetti, J.L., and Odloak, D.  Robust PID control using generalized KYP synthesis:  direct open-loop shaping in multiple frequency  ranges", IEEE Contr. Syst. Mag., 26(1), pp. 80{91  (2006).  11. Hara, S., Iwasaki, T., and Shiokata, D. Robust model  predictive control of integrating time delay processes",  J. Process Contr., 23(7), pp. 917{932 (2013).  12. Grassi, E., Tsakalis, K.S., Dash, S., et al. Integrated  system identi_cation and PID controller tuning by  frequency loop-shaping", IEEE T. Contr. Syst. T.,  9(2), pp. 285{294 (2001).  13. Ojaghi, P., Bigdeli, N., and Rahmani, M. An LMI  approach to robust model predictive control of nonlinear  systems with state-dependent uncertainties", J.  Process Contr., 47, pp. 1{10 (2016).  14. Argha, A., Li, L., Su, S.W., et al. On LMI-based sliding  mode control for uncertain discrete-time systems",  J. Frankl. Inst., 353(15), pp. 3857{3875 (2016).  15. Wang, Q.G., Lin, C., Ye, Z., et al. A quasi-LMI  approach to computing stabilizing parameter ranges of  multi-loop PID controllers", J. Process Contr., 17(1),  pp. 59{72 (2007).  16. Wu, Z., Iqbal, A., and Amara, F.B. LMI-based  multivariable PID controller design and its application  to the control of the surface shape of magnetic uid  deformable mirrors", IEEE T. Contr. Syst. T., 19(4),  pp. 717{729 (2011).  17. Wang, D., Liu, T., Sun, X., et al. Discrete-time  domain two-degree-of-freedom control design for integrating  and unstable processes with time delay", ISA  T., 63, pp. 121{132 (2016).  18. Merrikh-Bayat, F., Mirebrahimi, N., and Khalili,  M.R. Discrete-time fractional-order PID controller:  De_nition, tuning, digital realization and some applications",  Int. J. Control Autom., 13(1), pp. 81{90  (2015).  1578 H. Naja_zadegan and F. Merrikh-Bayat/Scientia Iranica, Transactions D: Computer Science & ... 28 (2021) 1570{1578  19. Merrikh-Bayat, F. A uniform LMI formulation for  tuning PID, multi-term fractional-order PID, and tiltintegral-  derivative (TID) for integer and fractionalorder  processes", ISA T., 68, pp. 99{108 (2017).  20. Monje, C.A., Vinagre, B.M., Feliu, V., et al. Tuning  and auto-tuning of fractional order controllers for  industry applications", Control Eng. Pract., 16, pp.  798{812 (2008).  21. VanAntwerp, J.G. and Braatz, R.D. A tutorial on  linear and bilinear matrix inequalities", J. Process  Contr., 10(4), pp. 363{385 (2000).  22. Skogestad, S. and Postlethwaite, I., Multivariable Feedback  Control: Analysis and Design, Wiley, Chichester,  New York (2005).  23. Jin, Q.B. and Liu, Q. Analytical IMC-PID design in  terms of performance/robustness tradeo_ for integrating  processes: from 2-Dof to 1-Dof", J. Process Contr.,  24(3), pp. 22{32 (2014).  24. Kumar, D.S. and Sree, R.P. Tuning of IMC based PID  controllers for integrating systems with time delay",  ISA T., 63, pp. 242{255 (2016).  25. Anil, C. and Sree, P.R. Tuning of PID controllers  for integrating systems using direct synthesis method",  ISA T., 57, pp. 211{219 (2015).  26. Lee, J., Cho, W., and Edgar, T.F. Simple analytic  PID controller tuning rules revisited", Ind. Eng. Chem.  Res., 53(13), pp. 5038{5047 (2014).