非线性变参数无人船艏向$H_infty$鲁棒控制

针对水流冲击引起无人船(unmanned surface vehicle,USV)转艏呈现非线性特点,建立基于转艏运动的非线性变参数(nonlinear parameter-varying,NPV)USV模型,并提出一种NPV $H_\infty$ 艏向控制方法,以提高艏向调节的快速性和鲁棒性.首先,考虑低展弦比机翼理论能较好地描述船体受水流冲击的特点,建立基于水动力阻尼的非线性Fossen模型.通过忽略横荡速度和横流阻力将动力学模型简化为操纵动力学模型,并引入艏向角,建立NPV艏向模型.其次,构造与艏向控制系统状态和纵荡速度变参相关的Lyapunov函数,推导出满足艏向闭环控制系统$H_\infty$鲁棒稳定的非线性控制器求解条件,该条件是一个非线性矩阵不等式(nonlinear matrix inequality,NLMI).由于NLMI难以求解,根据平方和(sums of squares,SOS)理论,用多项式矩阵代替NLMI中的非线性矩阵,并将NLMI 转化为可使用SOS工具求解的多项式线性矩阵不等式.仿真结果表明,NPV $H_\infty$控制器在艏向调节时具有较快的系统响应和更高的准确性.

$H_infty$ robust heading control for nonlinear parameter-varying unmanned surface vehicle

Aiming at the nonlinear characteristics of unmanned surface vehicle(USV) yaw caused by the impact of water flow, a nonlinear parameter-varying(NPV) USV model is established based on yaw motion, and the NPV $H_\infty$ robust heading control method is proposed to improve the rapidity and robustness of heading regulation. Firstly, a nonlinear Fossen model is established based on the hydrodynamic damping by the low aspect-ratio wing theory, which can better describe the characteristics of ship hull impacted by the flow. The dynamics model is simplified into a maneuvering model by ignoring the roll velocity and cross-flow drag, then an NPV heading model is established by introducing the heading. Secondly, a Lyapunov function related to the state of the heading control system and parameter-varying of the surge velocity is constructed to derive the solving conditions of the nonlinear controller, which satisfies the $H_\infty$robust stability of the heading closed-loop control system. This condition is a nonlinear matrix inequality(NLMI). Moreover, since the NLMI is difficult to solve, the nonlinear matrix in the NLMI is replaced with the polynomial matrix based on the sums of squares(SOS) theory to transform into polynomial linear matrix inequalities, which can be solved by SOSTOOLS. Finally, the results of the simulation indicate that the NPV $H_\infty$ controller has fast system response and higher accuracy for heading regulation.