Cross-Optimization Aspects Concerning the Extended Symmetrical Optimum Method

Abstract

The paper presents cross-optimization aspects in controller parameter tuning in the case of the Extended Symmetrical Optimum (briefly, ESO) method - introduced by the authors (Preitl and Precup, 1996, 1999a) - for a class of systems characterized by an open-loop transfer function H 0 (s): H 0 ( s ) = k 0 ( 1 + sTc ) s 2 ( 1 + sT ∑ ) . The following optimization criteria were taken into consideration: - ISE–I 2e I 2e = ∫ 0 ∞ e 2 ( t ) dt , - generalized ISE – I 2g : I 2 g = ∫ 0 ∞ e 2 ( t ) + τ 2 e . 2 ( t ) dt , - cross-optimization criterion (index) – I 2c I 2 c = ∫ 0 ∞ e 2 ( t ) + ρ 2 u 2 ( t ) dt . Generally speaking, it is relatively difficult to express these three indices and the obtained results are not conclusive. It is proved in the paper that the generalization of the Symmetrical Optimum (SO) method to the form of ESO method determines that the use of the indices I 2e , I 2g and I 2c becomes no more necessary.