LQG/LTR based robust youla parameterized adaptive vibration control for the supporting platform of rotating liquid mirror

Abstract

In mechatronic systems, the vibrations which commonly consist of band-limited random signals mixed with large multiple narrow-band deterministic signals may negatively impact the system performance. For example, due to the incomplete matching of the mechanism and the rotation of the motor, random and deterministic vibration disturbance may occur in the supporting platform of the rotating liquid mirror. In this paper, a robust Youla ( Q) parameterized adaptive regulation approach has been proposed to minimize such kind of vibration signals for the rotating platform system with model uncertainties. Firstly, the inner-loop robust controller with linear quadratic Gaussian with loop transfer recovery ( LQG/LTR) is optimally designed by choosing the suitable weighting functions to achieve the trade-off between robust stability and control performance to deal with random vibration signals. Then the Youla parameter is augmented to construct a set of Q-parameterized stabilizing controllers, and the robust stability of the system is analyzed through dual-Youla parameterization of the uncertain model. The recursive least squares (RLS) adaptive algorithm is developed to tune the Q parameter online to construct a desired adaptive controller for further residual vibration elimination. An experimental evaluation of the controller in reducing the vibration of the supporting platform of a rotating liquid mirror has been carried out, and the results illustrate that the proposed adaptive robust vibration regulation approach can effectively suppress the band-limited random and narrow-band deterministic vibration signals.