Robust Performance Limitations and Design of Controlled Delayed Systems

[+] Author and Article Information
O. Yaniv

Faculty of Engineering, Department of Electrical Engineering Systems, Tel Aviv University, Tel Aviv 69978, Israel e-mail: yaniv@eng.tau.ac.il

M. Nagurka

Department of Mechanical and Industrial Engineering, Marquette University, Milwaukee, WI 53201 e-mail: mark.nagurka@marquette.edu

J. Dyn. Sys., Meas., Control 126(4), 899-904 (Mar 11, 2005) (6 pages) doi:10.1115/1.1849246 History: Received November 29, 2003; Revised February 25, 2004; Online March 11, 2005
Copyright © 2004 by ASME
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Ziegler,  J., and Nichols,  N. B., 1942, “Optimum Settings for Automatic Controllers,” Trans. ASME, 64, pp. 759–765.
Cohen,  G., and Coon,  G. A., 1953, “Theoretical Consideration of Retarded Control,” Trans. ASME, 75, pp. 827–834.
Hang,  C., Tan,  C. H., and Chan,  W. P., 1980, “A Performance Study of Control Systems With Dead Time,” IEEE Trans. Ind. Electron. Control Instrum., 27(3), pp. 234–241.
Chwee,  T., and Sirisena,  H. R., 1988, “Self-Tuning PID Controllers for Dead Time Processes,” IEEE Trans. Ind. Electron., 35(1), pp. 119–125.
Hang, C., Lee, T. H., and Ho, W. K., 1993, Adaptive Control, ISA, Research Triangle Park, NC.
Astrom, K., and Wittenmark, B., 1995, Adaptive Control, 2nd ed., Addison-Wesley, Reading, MA.
Shafiei,  Z., and Shenton,  A. T., 1994, “Tuning of PID-Type Controllers for Stable and Unstable Systems With Time Delay,” Automatica, 30(10), pp. 1609–1615.
Tsang,  K., Rad,  A. B., and Lo,  W. L., 1994, “PID Controllers for Dominant Time Delay Systems,” Control Comput.,22(3), pp. 65–69.
Lee,  Y., Lee,  M., Park,  S., and Brosilow,  C., 1998, “PID Controller Tuning for Desired Closed-Loop Responses for SISO Systems,” AIChE J., 44(1), pp. 106–115.
Khan,  B., and Lehman,  B., 1996, “Setpoint PI Controllers for Systems With Large Normalized Dead Time,” IEEE Trans. Control Syst. Technol., 4(4), pp. 459–466.
Alexander,  C., and Trahan,  R. E., 2001, “A Comparison of Traditional and Adaptive Control Strategies for Systems With Time Delay,” ISA Trans., 40, pp. 353–368.
Abbas,  A., 1997, “A New Set of Controller Tuning Relations,” ISA Trans., 36(3), pp. 183–187.
Lee,  Y., Lee,  J., and Park,  S., 2000, “PID Controller Tuning for Integrating and Unstable Processes With Time Delay,” Chem. Eng. Sci., 55, pp. 3481–3493.
Mann,  G., Hu,  B. G., and Gosine,  R. G., 2001, “Time-Domain Based Design and Analysis of New PID Tuning Rules,” IEE Proc.: Control Theory Appl., 148(3), pp. 251–262.
Ho,  W. K., Hang,  C. C., and Cao,  L. S., 1995, “Tuning of PID Controllers Based on Gain and Phase Margin Specifications,” Automatica, 31(3), pp. 497–502.
Ho,  W. K., Lim,  K. W., and Xu,  W., 1998, “Optimal Gain and Phase Margin Tuning for PID Controllers,” Automatica, 34(8), pp. 1009–1014.
Astrom,  K. J., Panagopoulos,  H., and Hagglund,  T., 1998, “Design of PI Controllers Based on Non-Convex Optimization,” Automatica, 34(5), pp. 585–601.
Horowitz,  I., and Sidi,  M., 1972, “Synthesis of Feedback Systems With Large Plant Ignorance for Prescribed Time-Domain Tolerances,” Int. J. Control, 16(2), pp. 287–309.
Sidi,  M., 1976, “Feedback Synthesis With Plant Ignorance, Non-Minimum Phase, and Time-Domain Tolerances,” Automatica, 12, pp. 265–271.
Horowitz,  I., and Sidi,  M., 1978, “Optimum Synthesis of Non-Minimum Phase Feedback Systems With Plant Uncertainty,” Int. J. Control, 27(3), pp. 361–386.
Sidi,  M., 1984, “On Maximization of Gain-Bandwidth in Sampled Systems,” Int. J. Control, 32, pp. 1099–1109.
Horowitz,  I., and Liau,  Y., 1984, “Limitations of Non-Minimum Phase Feedback Systems,” Int. J. Control, 122(3), pp. 889–919.
Francis,  B. A., and Zames,  G., 1984, “On H-Infinity Optimal Sensitivity Theory for SISO Feedback Systems,” IEEE Trans. Autom. Control, 29, pp. 9–16.
Freudenberg,  J., and Looze,  D. P., 1985, “Right Half Plane Poles and Zeros and Design Tradeoffs in Feedback Systems,” IEEE Trans. Autom. Control, 30(6), pp. 555–565.
Freudenberg,  J., and Looze,  D. P., 1987, “A Sensitivity Tradeoff for Plants With Time Delay,” IEEE Trans. Autom. Control, 32(2), pp. 99–104.
Middleton,  R. H., 1991, “Trade-Offs in Linear Control System Design,” Automatica, 27, pp. 281–292.
Astrom, K., 1996, Fundamental Limitations of Control System Performance, Kluwer Academic, Dordrecht (Mathematical Engineering: A Kailath Festschrift).
Seron, M., Braslavsky, J., and Goodwin, G. C., 1997, Fundamental Limitations in Filtering and Control, Springer-Verlag, New York.
Bode, H., 1945, Network Analysis and Feedback Amplifier Design, Van Nostrand, New York.
Horowitz, I., 1963, Synthesis of Feedback Systems, Academic Press, New York.
Yaniv, O., 1999, Quantitative Feedback Design of Linear and Nonlinear Control Systems, Kluwer Academic, Dordrecht.
Seron, M., and Goodwin, G., 1995, “Design Limitations in Linear Filtering,” Proceedings of the 34th CDC, New Orleans, LA, December.


Grahic Jump Location
Nichols plot for M=1.46 and K=3.16, corresponding to at least 40 deg phase margin and at least 14.5 dB gain margin (4.5 dB due to M and 10 dB due to plant gain uncertainty). Frequencies are marked in rad/s for chosen Ts=0.001 s. The open-loop transfer function must not enter the shaded region in order to satisfy the gain and phase margin constraints.
Grahic Jump Location
Maximum a,ab and crossover frequency (rad/s) versus M and its associated guaranteed phase margin (deg) (indicated at top) for the approximate solution.
Grahic Jump Location
Boundary curves of (a,b) values that satisfy (1) with K=1 where L is replaced by L(Z) of (16). Marked on the right of each curve is its M value and corresponding lower bound of phase margin (PM) and gain margin (GM in dB) for K=1, according to (3) and (4).
Grahic Jump Location
Boundary curves of (a,b) values that satisfy (1) with K=1 for L of (6) and change of variables (7). Marked on the right of each curve is its M value and corresponding lower bound of phase margin (PM) and gain margin (GM in dB) for K=1, according to (3) and (4).
Grahic Jump Location
Region of (a,b) values for M=1.46, equivalent to at least 40 deg phase margin (PM) and at least 4.5 dB gain margin (GM) for K=1 (both shaded regions). Lower shaded region is for M=1.46 with additional 6 dB plant gain uncertainty (K=2).
Grahic Jump Location
Boundary curves of (a,b) values showing comparison between exact and approximate solutions for M=1.93 (phase margin, PM, of at least 30 deg) and for M=1.18 (PM of at least 50 deg). Gain margin, GM, indicated in dB.



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