Design of an optimal state derivative feedback LQR controller and its application to an offshore steel jacket platform

Abstract

This paper concerns with the optimal state derivative feedback LQR controllerdesign for vibration control of an offshore steel jacket platform having active tunedmass damper against the wave induced disturbances. Considering that the statederivative signals such as acceleration and velocity are easier to measure ratherthan the state variables such as displacement, state derivative feedback controlstrategy is proposed to obtain practically applicable and easily realizable synthesismethod. On the basis of convex optimization approach, state derivative feedbackLQR controller design is formulated in Linear Matrix Inequalities (LMIs) form toget an optimal feasible solution set. Finally, an offshore steel jacket platformsubject to nonlinear self excited wave force is used to illustrate the effectivenessof the proposed approach through simulations. The results show that proposedstate derivative LQR controller is very effective in reducing vibration amplitudesof each floor of modeled offshore steel jacket platform and achieves compitablecontrol performance to classical LQR controller design.