Nonminimum-Phase Zeros

IEEE Control Systems

Volumn 27, Issue 3, 2007, Pages 45-57

  Hoagg, Jesse B ^a   Bernstein, Dennis S ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

POLES AND ZEROS; ROBUSTNESS (CONTROL SYSTEMS); STEP RESPONSE;

INITIAL ERROR GROWTH; NONMINIMUM-PHASE ZEROS;

FEEDBACK CONTROL;

EID: 34249915526     PISSN: 1066033X     EISSN: None     Source Type: Journal    
DOI: 10.1109/MCS.2007.365003     Document Type: Article

References (76)

1. J.D. Barrow, The Book of Nothing. London: Jonathan Cape, 2000.
2. R. Kaplan, The Nothing That Is: A Natural History of Zero. London: Oxford Univ. Press, 2000.
3. C. Seife, Zero: The Biography of a Dangerous Idea. New York: Viking, 2000.
4. D.E. Duncan, Calendar: Humanity's Epic Struggle to Determine a True and Accurate Year. New York: Avon, 1998.
5. R.A. Horn and C.R. Johnson, Matrix Analysis. Cambridge, U.K.: Cambridge Univ. Press, 1985.
6. D.S. Bernstein, Matrix Mathematics: Theory, Facts, and Formulas with Application to Linear Systems Theory. Princeton, NJ: Princeton Univ. Press, 2005.
7. T. Norimatsu and M. Ito, “On the zero non-regular control system,” J. Inst. Elect. Eng. Japan, vol. 81, pp. 566-575,1961.
8. T. Mita and H. Yoshida, “Undershooting phenomenon and its control in linear multivariable servomechanisms,” IEEE Trans. Automat. Contr., vol. 26, pp. 402-407, 1981.
9. M. Vidyasagar, “On undershoot and nonminimum phase zeros,” IEEE Trans. Automat. Contr., vol. 31, p. 440,1986.
10. G. Oriolo, A. De Luca, and M. Vendittelli, “WMR control via dynamic feedback linearization: design, implementation, and experimental validation,” IEEE Trans. Contr. Syst. Technol., vol. 10, pp. 835–852, 2002.
11. E. Yang, D. Au, T. Mita, and H. Hu. “Nonlinear tracking control of a car-like mobile robot via dynamic feedback linearization,” Proc. Contr. 2004, U. of Bath, UK, ID-218, 2004.
12. D. Karnopp, Vehicle Stability. New York: Marcel Dekker, 2004.
13. R.F. Stengel, Flight Dynamics. Princeton, NJ: Princeton Univ. Press, 2004.
14. D.S. Bernstein, “What makes some control problems hard?,” IEEE Contr. Syst. Mag., vol. 22, pp. 8–19, August 2002.
15. J. Hong and D.S. Bernstein, “Bode integral constraints, colocation, and spillover in active noise and vibration control,” IEEE Trans. Contr. Syst. Technol., vol. 6, pp. 111-120,1998.
16. E.H. Maslen, “Positive real zeros in flexible beams,” Shock and Vibration, vol. 2, pp. 429-435,1995.
17. D.K. Miu, Mechatronics: Electromechanics and Contromechanics. New York: Springer-Verlag, 1993.
18. J. Chandrasekar, J.B. Hoagg, and D.S. Bernstein, “On the zeros of asymptotically stable serially connected structures,” in Proc. Conf. Decision Control, Paradise Island, The Bahamas, Dec. 2004, pp. 2638–2643.
19. J.B. Hoagg and D.S. Bernstein, “On the zeros, initial undershoot, and relative degree in lumped-mass structures,” in Proc. American Control Conf., Minneapolis, MN, June 2006, pp. 394–399.
20. J.B. Hoagg, J. Chandrasekar, and D.S. Bernstein, “On the zeros, initial undershoot, and relative degree of collinear, lumped-parameter structures,” ASME J. Dyn. Syst. Meas. Contr., submitted for publication.
21. S. Skogestad and I. Postlethwaite, Multivariable Feedback Control: Analysis and Design. New York: Wiley, 1996.
22. B.R. Holt and M. Morari, “Design of resilient processing plants-VI. The effect of right-half-plane zeros on dynamic resilience,” Chem. Eng. Sci., vol. 40, pp. 59-74,1985.
23. H.H. Rosenbrock, State Space and Multivariable Theory. Camden, NJ: Nelson, 1970.
24. S. Skogestad and I. Postlethwaite, Multivariable Feedback Control: Analysis and Design, 2nd ed. Hoboken, NJ: Wiley, 2005.
25. B.A. Leon de la Barra, “On undershoot in SISO systems,” IEEE Trans. Automat. Contr., vol. 39, pp. 578-581,1994.
26. M. El-Khoury, O.D. Crisalle, and R. Longchamp, “Influence of zero locations on the number of step-response extrema,” Automatica, vol. 29, pp. 1571-1574,1993.
27. G.C. Goodwin, S.F. Graebe, and M.E. Salgado, Control System Design. Englewood Cliffs, NJ: Prentice-Hall, 2001.
28. J.C. Doyle, B.A. Francis, and A.R. Tannenbaum, Feedback Control Theory. New York: Macmillan, 1992.
29. P. Dorato, Analytic Feedback System Design: An Interpolation Approach. Pacific Grove, CA: Brooks/Cole, 2000.
30. M. Vidyasagar, Control System Synthesis: A Factorization Approach. Cambridge, MA: MIT Press, 1985.
31. R.H. Middleton, “Trade-offs in linear control system design,” Automatica, vol. 27, pp. 281-292,1991.
32. I. Mareels, “A simple selftuning controller for stably invertible systems,” Syst. Control Lett., vol. 4, pp. 5-16,1984.
33. J.B. Hoagg and D.S. Bernstein, “Direct adaptive stabilization of minimum-phase systems with bounded relative degree,” in Proc. Conf. Decision Control, Paradise Island, The Bahamas, Dec. 2004, pp. 183–188.
34. H. Kwakernaak and R. Sivan, Linear Optimal Control Systems. New York: Wiley, 1972.
35. L. Qiu and E.J. Davison, “Performance limitations of non-minimum phase systems in the servomechanism problem,” Automatica, vol. 29, pp. 337-349,1993.
36. J.S. Freudenberg and D.P. Looze, “Right half plane poles and zeros and design tradeoffs in feedback systems,” IEEE Trans. Autom. Contr., vol. AC-30, pp. 555-565,1985.
37. D.P. Looze and J.S. Freudenberg, “Limitations of feedback properties imposed by open-loop right half plane poles,” IEEE Trans. Automat. Contr., vol. 36, pp. 736-739,1991.
38. J. Chen, “Sensitivity integral relations and design tradeoffs in linear multivariable feedback systems,” IEEE Trans. Automat. Contr., vol. AC-40, pp. 1700-1716,1995.
39. M.M. Seron, J.H. Braslavsky, and G.C. Goodwin, Fundamental Limitations in Filtering and Control. New York: Springer-Verlag, 1997.
40. J. Chen, L. Qiu, and Q. Toker, “Limitations on maximal tracking accuracy,” IEEE Trans. Automat. Contr., vol. 45, pp. 326-331,2000.
41. K. Lau, R.H. Middleton, and J.H. Braslavsky, “Undershoot and settling time tradeoffs for nonminimum phase systems,” IEEE Trans. Automat. Contr., vol. 48, pp. 1389-1393,2003.
42. ∞ controllers,” IEEE Trans. Automat. Contr., vol. 37, pp. 1261-1265,1992.
43. K.S. Narendra and A.M. Annaswamy, Stable Adaptive Systems. Englewood Cliffs, NJ: Prentice-Hall, 1989.
44. K. Zhou, J.C. Doyle, and K. Glover, Robust and Optimal Control. Englewood Cliffs, NJ: Prentice-Hall, 1996.
45. S. Kahne, “Pole-zero cancellations in SISO linear feedback systems,” IEEE Trans. Educ., vol. 33, pp. 240-243,1990.
46. A.G.J. MacFarlane and N. Karcanias, “Poles and zeros of linear multivariable systems: A survey of the algebraic, geometric and complex-variable theory,” Int. J. Control, vol. 24, pp. 33-74,1976.
47. B. Kouvaritakis and A.G.J. MacFarlane, “Geometric approach to analysis and synthesis of system zeros. Part 1. Square systems,” Int. J. Control, vol. 23, pp. 149-166,1976.
48. B. Kouvaritakis and A.G.J. MacFarlane, “Geometric approach to analysis and synthesis of system zeros. Part 1. Non-square systems,” Int. J. Control, vol. 23, pp. 167-181,1976.
49. A. Emami-Naeini, “Computation of zeros of linear multivariable systems,” Automatica, vol. 18, pp. 415-430,1982.
50. M.K. Sain and C.B. Schrader, “Research on system zeros: A survey,” Int. J. Control, vol. 50, pp. 1407-1433,1989.
51. C.B. Schrader and M.K. Sain, “The role of zeros in the performance of multiinput, multioutput feedback systems,” IEEE Trans. Educ., vol. 33, pp. 244-257,1990.
52. B.F. Wyman and M.K. Sain, “On the zeros of a minimal realization,” Lin. Alg. Applicat., vol. 50, pp. 621-637,1983.
53. B.F. Wyman, M.K. Sain, G. Conte, and M.A. Perdon, “On the zeros and poles of a transfer function,” Lin. Alg. Applicat., vol. 122–124, pp. 123–144, 1989.
54. B.F. Wyman, M.K. Sain, G. Conte, and M.A. Perdon, “Poles and zeros of matrices of rational functions,” Lin. Alg. Applicat., vol. 157, pp. 113-139,1991.
55. M.J. Corless and A.E. Frazho, Linear Systems and Control. New York: Marcel Dekker, 2003.
56. T. Kailath, Linear Systems. Englewood Cliffs, NJ: Prentice-Hall, 1980.
57. J.M. Maciejowski, Multivariable Feedback Design. Reading, MA: Addison-Wesley, 1989.
58. G.W. Stewart and J. Sun, Matrix Perturbation Theory. New York: Academic, 1990.
59. A. Emami-Naeini and P. Van Dooren, “Computation of zeros of linear multivariable systems,” Automatica, vol. 18, pp. 415-430,1982.
60. J.M. Berg and H.G. Kwatny, “Unfolding the zero structure of a linear control system,” Lin. Alg. Applicat., vol. 258, pp. 19-39,1997.
61. B.L. De La Barra, M. El-Khoury, and M. Fernandez, “On undershoot in scalar discrete-time systems,” Automatica, vol. 32, pp. 255-259,1996.
62. Y. Fu and G.A. Dumont, “Choice of sampling to ensure minimum-phase behavior,” IEEE Trans. Automat. Contr., vol. 34, pp. 560-563,1989.
63. T. Hagiwara, “Analytic study on the intrinsic zeros of sampled-data systems,” IEEE Trans. Automat. Contr., vol. 41, pp. 261-263,1996.
64. K.J. Astrom and B. Wittenmark, Computer-Controlled Systems, 3rd ed. Englewood Cliffs, NJ: Prentice-Hall, 2005.
65. K.J. Astrom, P. Hagander, and J. Sternby, “Zeros of sampled data systems,” Automatica, vol. 20, pp. 31-38,1983.
66. U. Holmberg, P. Myszkorowski, and R. Longchamp, “On compensation of nonminimum-phase zeros,” Automatica, vol. 31, pp. 1433-1441,1995.
67. J. Tokarzewski, “System zeros via the Moore-Penrose pseudoinverse and SVD of the first nonzero Markov parameter,” IEEE Trans. Automat. Contr., vol. 43, pp. 1285-1291,1998.
68. J. Tokarzewski, Finite Zeros in Discrete Time Control Systems. New York: Springer-Verlag, 2006.
69. D.S. Bayard, “Stable direct adaptive periodic control using only plant order knowledge,” Int. J. Adapt. Control Signal Process., vol. 43, pp. 551-570,1996.
70. P.T. Kabamba, “Control of linear systems using generalized sampled-data hold functions,” IEEE Trans. Automat. Contr., vol. AC-32, pp. 772-783,1987.
71. L.B. Jemaa and E.J. Davison, “Performance limitations in the robust servomechanism problem for discrete-time LTI systems,” IEEE Trans. Automat. Contr., vol. 48, pp. 1299–1311, 2003.
72. W. Su, L. Qiu, and J. Chen, “Fundamental limit of discrete-time systems in tracking multi-tone sinusoidal signals,” Automatica, vol. 43, pp. 15–30, 2007.
73. K.J. Astrom and B. Wittenmark, Adaptive Control, 2nd ed. Reading, MA: Addison-Wesley, 1995.
74. G.C. Goodwin and K.S. Sin, Adaptive Filtering, Prediction, and Control. Englewood Cliffs, NJ: Prentice-Hall, 1984.
75. P. Ioannou and J. Sun, Robust Adaptive Control. Englewood Cliffs, NJ: Prentice-Hall, 1996.
76. I.D. Landau, Adaptive Control: The Model Reference Approach. New York: Marcel Dekker, 1979.