Extended LQG/LTR design of disturbance cancelation controllers for a class of output disturbances

This study develops an optimal design of the disturbance cancelation controllers for the output disturbances consisting of step, ramp and/or sinusoidal signals. A disturbance model with a particular structure is utilized to handle the three types of disturbance signals in a unified manner. A new quadratic performance index is introduced for the deviation from steady‐state behavior of the plant with disturbance. An optimal full‐state feedback control to minimize the new performance index is obtained by the parametric LQ approach with the aid of the explicit solution of related eigenstructure assignment problem. Additionally, an optimal output feedback controller of linear quadratic Gaussian (LQG) type is constructed using Kalman filter to estimate the plant and disturbance state variables. The classical LQG/LTR procedure is extended to achieve a systematic two‐step design of optimal disturbance cancelation controllers. A numerical design example is presented to illustrate the flexibility of the proposed design procedure.