Abstract
This paper shows a synthesis of LQG control system with frequency-shaped weights (FWLQG) in which a state-estimator is added to LQR with frequency-shaped weights (FWLQR). It is seen from the robustness analysis of FWLQR and FWLQG in the frequency domain that the frequency-shaped weight for the controlled variable is useful to improve the response property and the disturbance rejection, while the weight for the input can give the loop transfer function a specified roll-off property. According to the consideration, a synthesis of FWLQG compensator is shown. In this synthesis, the loop transfer recovery is also included to recover reduced control performance with adding a state-estimator.
In a numerical example of a one-link flexible arm, both FWLQG and LQG syntheses are applied to the second-order nominal plant in which only the first vibration mode of the arm is considered. FWLQG compensator which both frequency-shaped weights for the controlled variable and the input give good response property and stability robustness. That is, more exact plant in which five vibration modes of the arm are included can be stabilized by FWLQG compensator and not by LQG one.
