Design of optimal disturbance cancellation controllers via modified loop transfer recovery

The authors proposed a modified loop transfer recovery (LTR) method for designing the disturbance cancellation controllers where the disturbances were assumed to be step functions and the optimality of the controllers was not considered. This paper discusses the extension of their work to a more general class of disturbances with optimality consideration. It is assumed that the plant is minimum phase and the disturbances entering the plant input side are generated by function generators with unknown initial conditions. A quadratic performance index explicitly representing the disturbance cancellation requirement is introduced. The optimal disturbance cancellation controller minimizing the performance index is constructed by the separation principle. As a target for the LTR design, the optimal disturbance cancellation controller based on the measurement of the plant state is chosen. It is shown that the target feedback property can be recovered in the output feedback controller by a simple modification of the standard LTR procedure. A numerical example is presented to illustrate the effectiveness of the proposed optimal design.