Incorporation of unstructured uncertainty into the horowitz design method

The Horowitz design method has long been known to yield closed loop systems that perform well for plants exhibiting structured or parametric uncertainty. Here it is shown that uncertain plants P(s) = P/sub nom/ (s) + (1 + M(s)) with the asymptotically stable and rational, so called unstructured uncertainty M(s), where IM(iw)jI < m(w) for all frequencies w, naturally fit into the Horowitz design framework. In particular, the realistic case of P(s) having structured uncertainty at low frequencies and unstructured uncertainty at high frequencies is treated. A theorem, giving necessary and sufficient conditions for the Horowitz method to work is presented, by which the interplay between plant knowledge and achievable closed loop specifications is clearly seen.

[1]  D. M. Stimler,et al.  Majorization: a computational complexity reduction technique in control system design , 1988 .

[2]  I. Horowitz,et al.  Optimum synthesis of non-minimum phase feedback systems with plant uncertainty† , 1978 .

[3]  Isaac Horowitz,et al.  Multivariable Flight Control Design with Uncertain Parameters. , 1982 .

[4]  Second-Order Systems,et al.  Some Geometric Questions in the Theory of Linear Systems , 1976 .

[5]  M. Morari,et al.  Unifying framework for control system design under uncertainty and its implications for chemical process control , 1986 .

[6]  Karl Johan Åström,et al.  Adaptive control — A way to deal with uncertainty , 1985 .

[7]  Isaac Horowitz,et al.  A synthesis theory for linear time-varying feedback systems with plant uncertainty , 1975 .

[8]  Quantitative design method for MIMO uncertain plants to achieve prescribed diagonal dominant closed-loop minimum-phase tolerances , 1988 .

[9]  Michael Athans,et al.  Robustness and modeling error characterization , 1984 .

[10]  G. Stein,et al.  Multivariable feedback design: Concepts for a classical/modern synthesis , 1981 .

[11]  R. Nussbaum.  Some remarks on a conjecture in parameter adaptive control , 1983 .

[12]  I. Horowitz.  Quantitative synthesis of uncertain multiple input-output feedback system† , 1979 .

[13]  B. Ghosh.  Some new results on the simultaneous stabilizability of a family of single input, single output systems , 1985 .

[14]  I. Horowitz,et al.  Optimization of the loop transfer function , 1980 .

[15]  R. Brockett.  Some geometric questions in the theory of linear systems , 1975 .

[16]  Isaac Horowitz,et al.  Limitations of non-minimum-phase feedback systems† , 1984 .

[17]  I. Horowitz,et al.  Synthesis of feedback systems with large plant ignorance for prescribed time-domain tolerances† , 1972 .

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

[19]  H. Kimura.  Robust stabilizability for a class of transfer functions , 1983, The 22nd IEEE Conference on Decision and Control.

[20]  P. Gutman,et al.  Robust and adaptive control of a beam deflector , 1988 .

[21]  Marcel Sidi,et al.  Feedback synthesis with plant ignorance, nonminimum-phase, and time-domain tolerances , 1976, Autom..

[22]  J. Garloff,et al.  Stability of polynomials under coefficient perturbation , 1985 .

[23]  I. Horowitz,et al.  Synthesis of cascaded multiple-loop feedback systems with large plant parameter ignorance , 1973 .

[24]  I. Horowitz,et al.  Superiority of transfer function over state-variable methods in linear time-invariant feedback system design , 1975 .

[25]  I. Horowitz,et al.  A quantitative design method for MIMO linear feedback systems having uncertain plants , 1985, 1985 24th IEEE Conference on Decision and Control.

[26]  S. Bhattacharyya,et al.  Robust control , 1987, IEEE Control Systems Magazine.