Nonlinear identification and control of building structures equipped with magnetorheological dampers

A new system identification algorithm, multiple autoregressive exogenous (ARX) inputs-based Takagi-Sugeno (TS) fuzzy model, is developed to identify nonlinear behavior of structure-magnetorheological (MR) damper systems. It integrates a set of ARX models, clustering algorithms, and weighted least squares algorithm with a TS fuzzy model. Based on a set of input-output data that is generated from building structures equipped with MR dampers, premise parameters of the ARX-TS fuzzy model are determined by clustering algorithms. Once the premise part is constructed, consequent parameters of the ARX-TS fuzzy model are optimized by the weighted least squares algorithm. To demonstrate the effectiveness of the proposed ARX-TS fuzzy model, it is applied to a three-, an eight-, a twenty-story building structures. It is demonstrated from the numerical simulation that the proposed ARX-TS fuzzy algorithm is effective to identify nonlinear behavior of seismically excited building structures equipped with MR dampers. A new semiactive nonlinear fuzzy control (SNFC) algorithm is developed through integration of multiple Lyapunov-based state feedback gains, a Kalman filter, and a converting algorithm with TS fuzzy interpolation method. First, the nonlinear ARX-TS fuzzy model is decomposed into a set of linear dynamic models that are operated in only a local linear operating region. Based on the decomposed models, multiple Lyapunov-based state feedback controllers are formulated in terms of linear matrix inequalities (LMIs) such that the structure-MR damper system is globally asymptotically stable and the performance on transient responses is guaranteed. Then, the state feedback controllers are integrated with a Kalman filter and a converting algorithm using a TS fuzzy interpolation method to construct semiactive output feedback controllers. To demonstrate the effectiveness of the proposed SNFC algorithm, it is applied to a three-, an eight-, and a twenty-story building structures. It is demonstrated from the numerical simulation that the proposed SNFC algorithm is effective to control responses of seismically excited building structures equipped with MR dampers. In addition, it is shown that the proposed SNFC system is better than a traditional optimal algorithm, H2/linear quadratic Gaussian-based semiactive control strategy.