Anti-pitching Control For High-speed Multihull Without Velocity Measurements

With the advantages of large loading capacity,high speed and good seakeeping performance,high-speed multihulls have attracted wide attention in the fields of military operation and marine transportation.However,the vertical motion of highspeed multihulls is severe under the disturbance of sea waves,i.e.,the amplitude of heave and pitch motion are too large.It is easy to result in stall,hull structural damage,bow slam,and even “buried bow” movement,which threat to the navigation safety of ships greatly.Severe vertical motion will also cause seasickness,equipment failure and other phenomena.Therefore,effective control measures should be taken to restrain the vertical motion of the multihull,namely longitudinal anti-pitching control.The installation of active T-foil and flaps is an important means of anti-pitching control.The longitudinal restoring force and moment can be significantly increased by designing appropriate control strategy to adjust the attack angle of T-foil and flaps in real time,so as to achieve pitch reduction.In anti-pitching control system,introducing pitch angular velocity and heave velocity into multi-loop feedback control has more obvious effect.However,due to the limitations of technology and cost,the actual inertial navigation platform installed on high-speed multihull can only measure heave displacement and pitch angle,but not heave velocity and pitch angular velocity directly.Therefore,it is of certain theoretical value and practical significance to study antipitching control of multihull without velocity measurements.The main contents of this paper are as follows:(1)The vertical motion model for high-speed multihull was established.The North-East-Down frame and hull coordinate system were introduced.With active T-foil and flaps as the anti-pitching appendages,force analysis for multihull was taken.A nonlinear mathematical model of the multihull vertical motion was established.The fluid memory effect was quantified in the form of convolution,and the multihull vertical motion was simulated by Cummins equation.The Pierson-Moskowitz spectrum was used to simulate the random motion of level-4 waves to establish the wave disturbance model.Based on Froude scaling law,the computational fluid dynamics was used to analyze the variation of hydrodynamic coefficients with encounter frequency.(2)Aiming at the problems that heave and pitch angular velocities of multihull cannot be measured directly,an anti-pitching controller based second-order approximate differential without velocity estimation was proposed.Only using heave displacement and pitch angle to construct the second-order approximate differential system and design linear feedback control law.To ensure its dynamic and steady-state performance,the parameters were selected based on regional pole assignment theory.On this basis,in order to further improve the ability to suppress sea wave disturbance,two kinds of measures to deal with the lumped uncertainty were designed: nonlinear feedback control and feedforward compensation based on the extended state observer.The convergence of the estimated error of the extended state observer was analyzed,and the stability of the system was analyzed based on Lyapunov theory.Finally,the effectiveness of the algorithm was verified by simulation.(3)In order to further improve the effect of pitch reduction,the optimization was introduced into the anti-pitching control,and the algebraic model predictive controller with less computation was proposed.First,the heave and pitch angular velocities were estimated by the Kalman filter based on kinematics,which reduced the dependence of signal estimation on the system model.Second,in order to reduce the computation amount of traditional prediction model with equally spaced numerical iteration,a prediction model of state transition matrix based on characteristic roots was proposed,which can guarantee the accuracy of prediction model and reduce the number of prediction points effectively.Finally,a disturbance observer based on second-order low-pass filter was proposed to estimate the uncertainty of the multihull model and the irregular wave interference,which would be introduced into predictive control law for feedforward compensation to improve the robustness of the system.Based on Lyapunov theory,the convergence of estimation error of the observer and the stability of closedloop system were analyzed.The simulation results show that heave motion was reduced by about 60% and pitch motion by about 70%.(4)In order to solve the problems of model uncertainty and strong wave disturbance,a super twisting sliding mode anti-pitching controller was proposed.A fixed-time convergent perturbation observer,a high-order sliding mode observer and a finite time extended state observer were designed to estimate heave velocity,pitch angular velocity and lumped uncertainty.Then the super twisting sliding mode antipitching controller was designed.Its stability was analyzed based on Lyapunov theory.The effectiveness of the proposed algorithm was verified by digital simulation.