On Sliding Mode H_∞Control For Offshore Platforms

Abstract：Offshore platforms are large structures used for oil and gasextraction, drilling, transportation and storage.The continuing effect of theexternal loads such as waves, wind, ice and earthquakes in the environ-ment, as well as the nonlinear self-excited wave forces which arises fromthe flexibility of the structure induce the vibration of offshore platforms.Severe vibration will reduce the reliability and security of the platforms.Therefore, vibration control of offshore platforms is of great significancein practice.The active vibration control method for offshore platforms has beenone of the hot topics. This paper studies the observer-based feedback con-trol and sliding mode H∞control for offshore platforms, and further dis-cusses robust sliding mode H∞control method for offshore platforms withuncertainty. Details are as follows:Firstly, we study the observer-based active control for offshore plat-formssubjecttononlinearself-excitedwaveforces. Firstly,afull-dimensionalstate observer and observer-based feedback controller for offshore plat-forms are researched, and a sufficient condition for the existence of theobserver and the controller is obtained; At last, numerical simulations aregiven to illustrate the effectiveness of the proposed controller.Secondly,westudytheslidingmode H∞controlforoffshoresteeljack-et platforms subject to nonlinear self-excited wave forces and external dis-turbances. Firstly, thesimplifiedmodelofoffshoreplatformsundernonlin-ear self-excited wave forces and external disturbances is given, and obtaina sufficient condition for the existence of the sliding mode H∞controller;Further,thedesignmethodofrobustsliding H∞controllerforoffshoreplat-forms under parameter perturbation is discussed; Finally, numerical sim- ulations are given, the simulations results show that: i) Compared withsliding mode controller, the displacements of the system under the slidingmode H∞controller are much smaller, and the required control force ismuch less; ii)It is not difficult to find that the displacement oscillation am-plitude of the system under the sliding mode H∞controller and the pure H∞controller are almost the same, but the the required control force of formercontroller is much smaller than the latter one.Thirdly, based on the positive effect of the time delay, we investigatethe delayed sliding mode H∞control for offshore steel jacket platform-s subject to nonlinear self-excited wave forces and external disturbances.Firstly, by introducing time-delay into the control channel, a delayed s-liding mode H∞controller is obtained. Then, according to the platformswith time varying parameter uncertainty, a robust delayed sliding modeH∞controller is developed. Numerical examples show that: i)The methodof artificially introducing time delay into control channel, can further en-hance the anti-jamming capability of the system, and improve the systemcontrol effect. ii)Compared with the delayed H∞controller and delayedsliding mode controller, the delayed sliding mode H∞controller is moreeffective.