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PERFORMANCE FUNCTIONS AND SUBLEVEL SETS FOR FREQUENCY DOMAIN DESIGN OF SINGLE LOOP FEEDBACK CONTROL SYSTEMS WITH PLANT UNCERTAINTY
Author(s) -
Bailey F. N.,
Helton J. William,
Merino Orlando
Publication year - 1997
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/(sici)1099-1239(199703)7:3<227::aid-rnc212>3.0.co;2-c
Subject(s) - transfer function , parametric statistics , frequency domain , closed loop transfer function , control theory (sociology) , loop (graph theory) , function (biology) , constraint (computer aided design) , frequency response , closed loop pole , domain (mathematical analysis) , mathematical optimization , computer science , mathematics , control (management) , engineering , mathematical analysis , artificial intelligence , evolutionary biology , electrical engineering , full state feedback , biology , statistics , geometry , combinatorics
The frequency domain design of control systems involves the fitting of a designable complex function of frequency (e.g., loop transfer function, compensator transfer function) to specification derived constraints in the design space ℂ×ℝ. In the classical Bode approach and its recent modifications the designable function is the loop transfer function, the specifications lead to constraints on the magnitude of the loop transfer function and the constraints have circular cross‐sections in ℂ. In more recent design procedures (e.g., H ∞ optimization or QFT) the specifications lead to more complex constraint surfaces in ℂ×ℝ and the design procedure must fit the designable function to these constraints. In this paper we develop explicit representations of some important ℂ×ℝ constraint surfaces encountered in the design of SISO control systems with both non‐parametric (unstructured) and parametric plant uncertainty and study the characteristics of their frequency axis cross‐sections or level sets: important information use in the fitting process. The results are presented in two systems of co‐ordinates (i.e., designable functions): nominal closed loop transfer function T o ( j ω) and and nominal open loop transfer function L o ( j ω). While the results in T o co‐ordinates are more useful when using mathematical optimization (e.g., H ∞ optimization techniques), the results in L o co‐ordinates have significant advantages of insight and ease of graphical manipulation as demonstrated in QFT. The inclusion of results in both sets of co‐ordinates increases their utility for workers in both areas and also reveals some links between these two different approaches. © 1997 by John Wiley & Sons, Ltd.