A Design of $H_{\infty}$ Controllers Achieving Type 2 Sensitivity Characteristics in type 1 Servo Systems

This paper proposes an $H_{\infty}$ controller design method which realizes a two-degree-of-freedom (2-DOF) control system with lower sensitivity characteristics in the low-frequency range. A control system with a disturbance observer is a 2-DOF control system that can achieve low sensitivity characteristics in the specific low-frequency range. However, the design of a controller with a disturbance observer structure is a non-convex optimization problem if it is considered as an observer gain design problem. In addition, it has not yet been revealed whether a 2-DOF control system with the low sensitivity characteristics of the disturbance observer can be achieved by the $H_{\infty}$ controller design. Therefore, this paper proposes a design method for $H_{\infty}$ controllers that achieves the low-sensitivity characteristics of a type 2 servo system while maintaining the type 1 servo characteristics without specifying the disturbance observer structure. Numerical examples demonstrate the effectiveness of the proposed method.