LQG Control for Dynamic Positioning of Floating Caissons Based on the Kalman Filter

This paper presents the application of an linear quadratic gaussian (LQG) control strategy for concrete caisson deployment for marine structures. Currently these maneuvers are carried out manually with the risk that this entails. Control systems for these operations with classical regulators have begun to be implemented. They try to reduce risks, but they still need to be optimized due to the complexity of the dynamics involved during the sinking process and the contact with the sea bed. A linear approximation of the dynamic model of the caisson is obtained and an LQG control strategy is implemented based on the Kalman filter (KF). The results of the proposed LQG control strategy are compared to the ones given by a classic controller. It is noted that the proposed system is positioned with greater precision and accuracy, as shown in the different simulations and in the Monte Carlo study. Furthermore, the control efforts are less than with classical regulators. For all the reasons cited above, it is concluded that there is a clear improvement in performance with the control system proposed.

LQG control of linear lossless positive-real systems: the continuous-time and discrete-time cases

Lossless positive-real systems have been widely studied in the literature. They are systems in which the energy is entirely transferred between input and output. In this paper, new aspects related to the linear quadratic gaussian (LQG) control of lossless positive-real systems are reported including both the continuous-time and the discrete-time cases. Direct formulas for the calculation of the optimal gains will be introduced and the properties of the different structures of the LQG compensator obtained for the continuous-time and the discrete-time cases will be emphasized, also in view of designing positive-real LQG compensators. Numerical examples related to low-damped structures are also discussed to verify the possibility to design the LQG compensator on the basis of a lossless approximation.