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


[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 field reconstruction of boiler drum based on fuzzy adaptive Kalman filter 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 identification 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 fluid 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: Definition, tuning, digital realization and some applications”, Int. J. Control Autom., 13(1), pp. 81-90 (2015).
[19]    Merrikh-Bayat, F. “A uniform LMI formulation for tuning PID, multi-term fractional-order PID, and tilt-integral-derivative (TID) for integer and fractional-order 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, 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 tradeoff 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).