A convex optimization framework for hybrid simulation

Hybrid simulation is a dynamic response evaluation technique which involves the partitioning of the structure into parts-physical and numerical subsystems. The interaction between the two subsystems is realized with the help of a transfer system (an actuator or a shake table). The objective of the hybrid simulation is to find control input to the transfer system such that the impedance of the transfer system is close to the numerical subsystem. The physical limitations of the system needs to be accounted while designing controller for hybrid simulation. This paper presents a framework which enables to pose controller synthesis for hybrid simulation as a multi-objective convex optimization problem using linear matrix inequalities (LMIs). Different control system tools based on LMIs which can be used for abstract formulation are described. A mathematical model based on the linear control theory is presented for the hybrid simulation of a three degrees of freedom system using shake table. The controller obtained from the solution of optimization is used to evaluate the frequency response of the closed loop hybrid system. It is observed that the accuracy of the hybrid simulation decreases with the decrease in the control effort.