Loop Shaping Design Related to LQG/LTR for SISO Minimum Phase Plants

One method of model-based compensator design for linear systems consists of two stages: state feedback design and observer design. A key issue in recent work in multivariable synthesis involves selecting the observer (state feedback) gain so that the final Loop transfer function is the same as the state feedback (observer) loop transfer function. This is called Loop Transfer Recovery (LTR)(1,4,6,7). This paper shows how identification of the internal mechanism of the LTR provides simple design rules with Little algebra for single-input single-output systems. In the SISO case, the LQG/LTR reduces to computation of a compensator that shapes the loop transfer function by 1) cancelling the zeros of the plant with the compensator poles, 2) locating a new set of zeros for the compensator to shape the loop transfer function.