Actuator placement robust optimization for vibration control system with interval parameters

Actuator configuration and optimization are of great significance in active control of vibration and noise. This paper proposes an actuator position optimization method for active control system with uncertainties. The uncertain parameters were modeled by interval numbers. Based on interval analysis, the boundaries of eigenvalues of the controllability grammian are obtained and uncertainty propagation analysis method for actuator configuration is presented. Mathematical operation on the eigenvalues of controllability grammian is considered to be the optimization criterion in order to maximize the norm of controllability grammian. Both nominal value and radius of the performance index are considered in the optimization model proposed in this paper. The uncertain optimization model for actuator configuration is transformed into a deterministic optimization model based on weighted processing. Node index number on the finite element mesh is selected as design variable. Since the objective function is non-convexity, genetic algorithm is adopted to get the optimal solution. The feasibility of the robust optimization method is demonstrated by two examples.