Intrinsic performance limits of linear feedback control

Nevanlinna-Pick interpolation techniques are employed in this paper to derive for multivariable systems exact expressions and bounds for the best attainable H ∞ norms of the sensitivity and complementary sensitivity functions. These results improve the previously known performance bounds and provide intrinsic limits on the performance of feedback systems irreducible via compensator design, leading to new insights toward the understanding of fundamental limitations in feedback control. It becomes clear that in a multivariable system the best achievable performance is constrained by plant nonminimum phase zeros and unstable poles, and additionally, is dependent on the mutual orientation of the zero and pole directions.

[1]  Jie Chen.  Sensitivity Integral Relations and Design Tradeoffs in Linear Multivariable Feedback Systems , 1993 .

[2]  H. Kwakernaak,et al.  The maximally achievable accuracy of linear optimal regulators and linear optimal filters , 1972 .

[3]  J. Freudenberg,et al.  Right half plane poles and zeros and design tradeoffs in feedback systems , 1985 .

[4]  Evanghelos Zafiriou,et al.  Robust process control , 1987 .

[5]  P. Khargonekar,et al.  Non-Euclidian metrics and the robust stabilization of systems with parameter uncertainty , 1985 .

[6]  Rick H. Middleton,et al.  Trade-offs in linear control system design , 1991, Autom..

[7]  Jie Chen.  Sensitivity Integral Relations and Design Tradeoffs in Linear Multivariable Feedback Systems , 1993, 1993 American Control Conference.

[8]  Carl N. Nett,et al.  Sensitivity integrals for multivariable discrete-time systems , 1995, Autom..

[9]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[10]  David Q. Mayne,et al.  Feedback limitations in nonlinear systems: from Bode integrals to cheap control , 1999, IEEE Trans. Autom. Control..

[11]  Jie Chen.  Multivariable gain-phase and sensitivity integral relations and design trade-offs , 1998, IEEE Trans. Autom. Control..

[12]  Graham C. Goodwin,et al.  Fundamental Limitations in Filtering and Control , 1997 .

[13]  Graham C. Goodwin,et al.  Trade-offs in linear filter design , 1995, Autom..

[14]  Edward J. Davison,et al.  Performance limitations of non-minimum phase systems in the servomechanism problem, , 1993, Autom..

[15]  H. W. Bode,et al.  Network analysis and feedback amplifier design , 1945 .

[16]  G. Zames,et al.  Feedback, minimax sensitivity, and optimal robustness , 1983 .

[17]  S. Hara,et al.  Constraints on sensitivity characteristics in linear multivariable discrete-time control systems , 1989 .

[18]  Shinji Hara,et al.  Properties of complementary sensitivity function in SISO digital control systems , 1989 .

[19]  Li Qiu,et al.  Limitations on maximal tracking accuracy. I. Tracking step signals , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[20]  Stephen P. Boyd,et al.  Subharmonic functions and performance bounds on linear time-invariant feedback systems , 1984, IEEE Conference on Decision and Control.

[21]  R. Middleton,et al.  Inherent design limitations for linear sampled-data feedback systems , 1995 .

[22]  Shinji Hara,et al.  Properties of sensitivity and complementary sensitivity functions in single-input single-output digital control systems , 1988 .