Multi-objective optimal design of fuzzy controller for structural vibration control using Hedge-algebras approach

In this paper, the problem of multi-objective optimal design of hedge-algebras-based fuzzy controller (HAC) for structural vibration control with actuator saturation is presented. The main advantages of HAC are: (i) inherent order relationships among linguistic values of each linguistic variable are always ensured; (ii) instead of using any fuzzy sets, linguistic values of linguistic variables are determined by an isomorphism mapping called semantically quantifying mapping (SQM) based on a few fuzziness parameters of each linguistic variable and hence, the process of fuzzy inference is very simple due to SQM values occurring in the fuzzy rule base and (iii) when optimizing HAC, only a few design variables which are above fuzziness parameters are needed. As a case study, a HAC and optimal HACs ( op HACs) based on multi-objective optimization view point have been designed to active control of a benchmark structure with active bracing system subjected to earthquake excitation. Control performance of controllers is also discussed in order to shown advantages of the proposed method.