Robust Longitudinal Motion Control For A Supercavitating Vehicle

In underwater environment, a vehicle encounters greater resistance than in the air,this makes it hard for the increase of the vehicle speed. As an effective method on resistance reduction, the supercavitation technology recently attracts more and more scholars' interests.As is known to us all, the mathematical modeling and control design are one of the most critical technologies in the study of a supercavitating weapon. The whole package within the cavity, on one hand, introduces a great resistance reduction for the vehicle body and so that the vehicle can reach a high velocity range, on the other hand, also changes the balance of the hydrodynamic force and respective moments, which makes it quite difficult for the modeling and maneuvering of the vehicle. Hence it is quite important to study the mathematical modeling and control design of a supercavitating vehicle. This paper pays its attention to the modeling research of the longitudinal motion of a supercavitating vehicle,and base on the resulting model, some controllers are designed to achieve the longitudinal motion stability and reference tracking purpose, simulations are also conducted to evaluate the effectiveness of the designed controllers.Firstly the body coordinate system is established with its origin fixed at the nose of the vehicle body. Under this frame forces and the respective moments, including the gravity, the cavitator force, the fins force, the planing force and the moments corresponding to the force,are analysed. Great efforts are given to the analysis of the two modeling methods of the planing force, which is generated by the interaction of the vehicle body and the cavity wall.Based on the previous forces and moments analysis,nonlinear motion equations and dynamical equations are established for the longitudinal motion of a supercavitating vehicle.Secondly a nonlinear control design is proposed for the supercavitating vehicle based on absolute stability method in frequency domain. The system model is expressed as a form of feedback connections which contains linear parts and nonlinear parts. A circle criterion based feedback controller is designed. Simulations are conducted to evaluate its performance under the situations that the planing force expression faces modeling uncertainties and parameter uncertainties, respectively. Then by studying the characters of the vehicle model, a circle criterion based backstepping controller is designed. Simulations are also conducted under the same situations metioned above so as to compare the control performance of the resulting controller and that of the previous one.Thirdly an absolute stability control method is given for the longitudinal motion control of a supercavitating cehicle. The system model is first also expressed as a form of feedback connections which contains linear parts and nonlinear parts, by expressing the nonlinear characters of the planing force as a sector bounded condition, the controller is synthesized by using Lyapunov method together with the sector bounded condition. It is noted that the controller is proposed in the form of linear matrix inequality(LMI), hence can be solved efficiently. Simulations are conducted to evaluate its robustness under the situation that the system faces noise disturbance.Finally three linear parameter varying(LPV) controllers are proposed for asupercavitating vehicle. By modeling the planing force as the product of a time-varying parameter and the state variable, the original system is translated to an LPV model whose system matrix depends affinely on the time-varying parameter. Based on this model, a constant gain controller and a gain scheduled controller and a backstepping LPV controller are proposed. Simulations are conducted to evaluate their performances under the situation that the system faces noise disturbance,respectively. Comparisons are also conducted to show their goodness and badness.