| Currently,most marine surface vessels(USVs)are usually equipped with propeller and rudder,in which the rudder yaw moment is used to control the heading angle and yaw velocity of USVs,and the longitudinal propeller is used to maintain the longitudinal velocity,resulting to the typical underactuated characteristic.When navigating at sea,the USVs are often influenced by sophisticated sea environment disturbances such as wind,wave and current,which results to the large roll motion.It will not only affect the normal operation of the vessel equipment and cause goods damage,but also deteriorate the stability and safety of the control system,even lead to the shipwreck.Due to the large response difference between roll and yaw,the roll moment caused by the rudder operation can be used to reject the roll disturbance moment caused by wind,wave and current.However,the main function of the rudder is to control the heading angle,resulting to a strong coupling between path following and rudder roll stabilization.Considering the path following of USVs with roll constraints,model predictive control(MPC)is mainly used in this paper,in order to realize the coordinated control of path following and roll rejection.The main contents in this paper are as follows:(1)Based on the four degrees of freedom nonlinear path following model with coupled roll,the piecewise linear affine system is applied to replace the nonlinear system.Considering the non-minimum phase characteristics of the rudder roll stabilization system,the output redefinition method is used to convert it into a minimum phase system for the control design.In order to improve the system robustness,the disturbance observer is used to estimate the disturbances and linearization modeling errors,then the feed-forward compensation is designed.Based on the MPC strategies of receding horizon optimization and state space prediction,the analytical predictive control law can be obtained.The roll constraint is ensured by the linear programming method.The controller effectiveness is verified by simulations.(2)The controller for path following with roll constraints is designed using LMI(Linear Matrix Inequality)method.Consider the roll angle constraint as the system state constraint,together with the input constraint of the rudder device due to inherent mechanical properties,these constraints are combined with the constraints for the performance index and system stability.Using Schur complement principle,all above constraints can be transformed into a convex LMI optimization problem,and the controller can be easy to obtain.In order to solve the computation burden in online constrained optimization of MPC using LMI method,the control strategy of off-line calculation and online synthesis is proposed to improve the real-time performance.In this method,the invariant ellipsoid set is applied to the constrained set of MPC,then the feasibility and stability of the control system can be guaranteed by shortening the distance from the equilibrium origin.The state feedback control law is determined by off-line calculation,and online search of the data table is performed to apply the saved control gain.For the single input condition with the rudder angle,with the consideration of the double inputs model combing with the propeller speed,the predictive controller is designed based on LMI,and the simulations compared with the single input are performed.(3)For path following with the external disturbances such as wind,wave and current,the polytopic modeling is applied to the original nonlinear model,and a robust predictive controller is designed based on the mixed H2/H∞ approach.Among them,the index H2 ensures the good performance of path following in the control system,and the index H∞ can make the control system able to restrain the lumping disturbance,so as to improve the robustness of the control system.On the basis of simulation results,the experiments of the unmanned surface vessel HEU-Ⅱ are carried out to verify the algorithm validity. |
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