Design and validation of linear robust controllers for nonlinear plants

Abstract

SUMMARY This paper describes a robust nonlinear control system design procedure inspired by the nonlinear control ideas of Horowitz’s Quantitative Feedback Theory.1 The central concept is the identification of a family of linear time-invariant (LTI) plants that is equivalent to an uncertain nonlinear (and/or time varying) plant in the sense that an LTI controller feasible for this linear plant family is also feasible for the original nonlinear plant. We identify two conditions for evaluating an equivalent linear family (the equivalence condition and the continuity condition) and show that when these two conditions are satisfied an LTI controller that provides satisfactory robust control of an equivalent linear plant family also provides satisfactory robust control for the related uncertain nonlinear plant, independent of the robust design technique used. We then use these two conditions to analyse the validity of the nonlinear QFT design technique published earlier. Our results suggest that nonlinear QFT can be an attractive approach to nonlinear robust control but its validity (in the sense that the linear design solves the nonlinear control problem) can be demonstrated only if additional conditions and contraints not previously reported are satisfied. ( 1998 John Wiley & Sons, Ltd.