Presentation of quasi-linear piecewise selected models simultaneously with designing of bump-less optimal robust controller for nonlinear vibration control of composite plates

The idea of using quasi-linear piecewise models has been established on the decomposition of complicated nonlinear systems, simultaneously designing with local controllers. Since the proper performance and the final system close loop stability are vital in multi-model controllers designing, the main problem in multi-model controllers is the number of the local models and their position not paying attention to which will result in redundancy, estimation complexity and the decreased performance of the system. Determining a specific margin based on nonlinear model characteristics is a good criterion for the classification. The first margin largely depends on the preliminary knowledge of designing the wrong selection of which will add to the redundancy of the local models and the problem’s complexity. In this article, the maximum stability margin parameter which is the main feature in each sub system and the best choice for the local controllers clustering has made the classification possible and also guaranteed close loop stability of the system. Based on the gap metric and the maximum stability margin, an optimal solution for the number of the local controllers and their position can be obtained by the use of genetic algorithm. The cost function is defined by the complementary sensitivity function and the sensitivity function and guarantees the maximum stability margin, the optimal performance, and the close loop stability of the system, respectively. Another challenge in designing multi-model controllers is the transient performance degradation when switching from one local model to another. Soft/hard switching has been suggested as a solution by the researchers before. In this article, given that the nonlinear system input depends on the online controller error signal and feedback coefficient of the offline controller, transient performance degradation in the switching phase will be solved. To evaluate the presented multi-model controller design procedure, a sandwich plate nonlinear vibration suspension with uncertainty in basic equations is proposed.