Research Of H_∞ Switched Control For Vessel Dynamic Positioning

After entering twenty-first Century,speeding up the development of marine resources and energy have become an important strategic developmental goal for all the maritime countries in the world.However,the deep-sea environment is complex and changeable.It puts forward new and higher requirements for marine engineering equipment and technology in order to ensure marine engineering structures operate stably in such environment.Among which,dynamic positioning is one of the essential technologies.Due to the interference of the uncertain ocean environment when dynamic positioning ships are navigation or in the operation process,this results in poor stability of ships and affecting navigation and operation.The robust H_∞switched control has a prominent advantage in dealing with the problem of uncertainty and interference suppression.Therefore,two different controllers are designed for the dynamic positioning ship,according to the switching sequence provided by different switching signals and matching a different controller for different models(subsystems),so as to improve the adaptability of the dynamic positioning ship under the disturbance of changeable ocean environment,and finally this system can be controlled stably.In this paper,the dynamic positioning ship is considered as the research object,and the ship motion model and the ocean environment disturbance model are established.Then the ship whole model is transformed into the H_∞standard control problem,and on this basis,the discrete time H_∞switched system with time delay and continuous time H_∞switched system with time delay are studied respectively.Finally for the above two switched systems,two different H_∞controller are designed.The concrete research content is as follows:Firstly,based on the characteristics of ship,the problem how to set up the ship motion model is discussed.At first,two common reference coordinate systems,the North-East-Down coordinate system and the Body-Fixed coordinate system are described.Then,based on them,the kinematic model and dynamic model are established.Lastly,the ocean environmental disturbance model includes wind,first-order and second-order waves interference,and current is also established.Secondly,the problem of H_∞switched output tracking control with time delay for dynamic positioning ship is studied.At first based on a new Lyapunov-Krosavskii function,the process of system stability analysis and the design process of H_∞output tracking controller are given.Then the problem of designing output tracking controller is transformed into an optimization problem with linear matrix inequality(LMI)constraints.Lastly switched controller’s gain matrix is obtained with cone complement linearization(CCL)method.Thirdly,the problem of H_∞asynchronous switched control with time delay for dynamic positioning ship is studied.At first,based on the ship model,a state space equation of continuous time switched systems with time delay is established.Then,based on a piecewise Lyapunov-Krosavskii function,and by combining the average dwell time switching signal and the merging switching signal method,an H_∞asynchronous switching controller is designed,the stability of the closed-loop system is analyzed as well.By means of solving the corresponding sufficient conditions,which are two sets of linear matrix inequalities(LMI),the corresponding controller gain matrix is obtained.The researches and the simulation experiment results indicate that two H_∞switched control methods proposed in this paper effectively ensure the stability of switched control of the dynamic positioning ship.This conclusion has a certain practical value for the safe navigation and operation of the dynamic positioning ship.