Robustness analysis of responses of vibration control structures with uncertain parameters using interval algorithm

Variations in system parameters due to uncertainties may result in system performance deterioration. Uncertainties in modeling of structures are often considered to ensure that control system is robust with respect to response errors. Hence, the uncertain concept plays an important role in vibration control of the engineering structures. The paper discusses the robustness of responses of vibration control systems with the uncertain parameters. The vibration control problem of an uncertain system is approximated by a deterministic one. The uncertain parameters are described by interval variables. The uncertain state matrix is constructed directly using system physical parameters and avoided to use bounds in Euclidean norm. The feedback gain matrix is determined based on the deterministic systems, and then it is applied to the actual uncertain systems. A method to calculate the upper and lower bounds of responses of the closed-loop system with uncertain parameters is presented. The upper bounds of responses can be used to estimate the robustness of responses of the controlled system with uncertain parameters. Two numerical examples are given to illustrate the applications of the present approach.