Global Stabilization Approach For Underactuated Surface Vessels

In recent years, control of a class of mechanical systems(Underactuated MechanicalSystems) with fewer control inputs to achieve accurate complex motion in multiplefreedom-degrees has been attracted more and more attention by the control society. Mostsurface ships at sea are not equipped with lateral propulsion equipment, relying solely on thevertical propulsion device (propeller or jet propulsion) and steering the complex motion of theships on the horizontal plane within three degrees of freedom, this class of ships all belongs toclassic underactuated systems. Study of nonlinear control of the Underactuated SurfaceVessels has important practical applications and theoretical significance, and play animportant hole to achieve autonomous control of marine weapons and equipment..We addressed the following questions of underactuaed surfae vessels:(1) In order to solve the point stabilization control problem of the underactuated surfacevessels, a switch control method based on time-invariant state feedback is proposed. First, aglobal diffeomorphism transformation is introduced to decpoupling the strong multivariablecoupling system by transfer the ship’s position to a new coordinate frame rotating with theship. Then the dynamic properties of the new dynamic sytem are analysised by using theLyapunov’s direct method. The analysis result allows us to consider a low-level ordernonlinear subsystem to realize the whole point stabilization control of the underactuatedsurface vessel, which simplifies the controller design, and a swith state-feedback control lawis proposed to achive the globa asymptotically stable by using the backstepping approach.Finally, the global point asymptotic stabilization control of underactuated surface vessel issovled by time-invariant feedback switching control method.(2) In order to overcome the natural non-continuity defects to realizae the smooth controlof underactuated surface vessels, and improve the convergence rate of the state, atime-varying state-feedback decoupling control method is proposed. On the basis of theglobal diffeomorphic transformation, a new time-varying state transformation is introdued todecoupling the dynamic system to a linear subsystem and a time-varying linear subsystem,which enabled us easier to design isolated global exponential stabilizing controllers for thetwo subsystems. A global K-exponential stabilizing controller for the whole system wasfinally constructed for the ship in consideration. Simulation results were provided to validatethe effectiveness of the proposed scheme. (3) In this thesis, a Cascaded-Backstepping approach is proposed to achive the globaltracking control of underactuated surface vessels. Firstly, the tracking erroe dynamics of theconsider ship are derived, and thus the tracking control problem was transformed into astabilization conrol problem of the error dynamic systems. Secondly a cascaded approach wasapplied for the global transformed error dynamic system to subdivide the global trackingcontrol problem into a stabilization problem of two isolated subsystems with a control inputeach. Thirdly, the backstepping method was applied to construct a global exponentialstabilizing controller for one of the two subsystems, while an exponential stabilizingcontroller was easily constructed for the other linear system. Finally, a global K-exponentialtracking controller was presented for the considered vessel with only two controls. Simulationresults were provided to validate the effectiveness of the proposed scheme.(4) According to the geometry of the track track, tracking control of underactuatedsurface vessels can be divided into a straight line trajectory tracking control and curvetrajectory tracking control. From the point of view of the control object, the two trackingcontrol problems are not essentially different. However, the main technical problems of thetracking control of underactuated surface vessels can be summarized as persistent excitation(PE) and is unrelated to the robustness of the design difficulties, namely, whether or not toconsider the model parameter uncertainties and the interference of the external environment,the problem exists, and mainly appeara as heading angular persistent excitation, which makesthe design applies to both straight lines and curves of the trajectory tracking controller is verydifficult, so scholars generally studies straight-line trajectory tracking track and curved trackseparately. This dissertation studies the robust tracking control problem of an underactuatedsurface with parameter uncertainties and external disturbances, and a sliding modemethodology is proposed. In order to guarantee the convergence of the position trackingerrors, desired surge and sway velocities are proposed as virtual control law. Furthermore,actual control laws are constructed to force the real surge and sway velocities convergent tothe desired ones. Finally, an asymptotic tracking result is obtained, and simulation examplesfor a model ship are provided to validate our method.