Abstract
This paper concerns with the optimal state derivative feedback LQR controller design for vibration control of an offshore steel jacket platform having active tuned mass damper against the wave induced disturbances. Considering that the state derivative signals such as acceleration and velocity are easier to measure rather than the state variables such as displacement, state derivative feedback control strategy is proposed to obtain practically applicable and easily realizable synthesis method. On the basis of convex optimization approach, state derivative feedback LQR controller design is formulated in Linear Matrix Inequalities (LMIs) form to get an optimal feasible solution set. Finally, an offshore steel jacket platform subject to nonlinear self excited wave force is used to illustrate the effectiveness of the proposed approach through simulations. The results show that proposed state derivative LQR controller is very effective in reducing vibration amplitudes of each floor of modeled offshore steel jacket platform and achieves compitable control performance to classical LQR controller design.
Highlights
The offshore steel jacket platforms play an important role in the oil exploration and drilling operation in the oceans [1]
Closed loop system order has not been increased, since the state derivative feedback controllers are static and memoryless with no additional state variables. This situation motivates us with the fact that there exist still more room obtaining practically applicable optimal state derivative feedback LQR controller synthesis to attenuate the vibrations of offshore platforms
Active Tuned Mass Damper (ATMD) is used as an active control mechanism to supress structural vibrations, which is installed on the top floor of the offshore steel jacket platform
Summary
The offshore steel jacket platforms play an important role in the oil exploration and drilling operation in the oceans [1]. Closed loop system order has not been increased, since the state derivative feedback controllers are static and memoryless with no additional state variables This situation motivates us with the fact that there exist still more room obtaining practically applicable optimal state derivative feedback LQR controller synthesis to attenuate the vibrations of offshore platforms. To the best of authors’ knowledge it can be seen that there is no result has been given in the literature on the active vibration control of offshore steel jacket platform by the use of state derivative feedback approach, so far. Because of the state derivative signals are easier to measure, an LMI based optimal state derivative LQR controller is developed to control of the offshore steel jacket platform having nonlinear wave disturbances. Diag{M1,...,Mn} stands for a diagonal matrix with elements M1,...,Mnappearing on its diagonal
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