Design of suboptimal weight using frequency responses guaranteeing performance level of controller for H∞ loop shaping method

The H_∞ loop shaping method is known as one of the robust controller design method. In this method, the design procedure consists of two steps; weight design and derivation of stabilizing controller. The controller is designed to suppress the H_∞ norm of the transfer matrix consisting of a sensitivity function, a complementary sensitivity function, etc. As a result, the closed-loop system achieves good tracking and robustness. However, there is only a guideline for the weight design in the H_∞ loop shaping method, and an explicit index for the weight design has not been proposed. Thereby, a time-consuming and tedious process is often required. This paper provides a new method to design the suboptimal weight for the H_∞ loop shaping method guaranteeing the performance level of the controller. Moreover, the weight is designed using only frequency responses. Accordingly, we can avoid the process of the system identification and reduce the conservativeness caused by an overestimate of the system uncertainty.