基于线性矩阵不等式的船舶动力定位滑模控制

为了解决具有非线性和环境干扰的船舶动力定位系统的控制问题, 提出了一种基于线性矩阵不等式的滑模控制算法; 将跟踪误差设计为滑模函数, 设计线性矩阵不等式, 求解状态反馈增益; 基于二次型Lyapunov函数证明了闭环系统的稳定性; 设计切换函数, 使系统对不确定性和外加干扰具有较强的鲁棒性, 避免出现抖振现象; 对基于线性矩阵不等式的滑模控制器进行仿真, 计算出动力定位船舶在无扰动的匀速运动和有外界环境扰动的变速运动2种不同情况下的前进速度、横荡速度、艏向角速度、前进加速度、横荡加速度、艏向角加速度、前进控制力、横荡控制力和艏向控制力矩等; 分析了状态反馈增益线性矩阵、边界层、切换项增益等参数对控制性能的影响。研究结果表明: 采用基本滑模控制使前进速度达到期望值所需的上升时间为29s, 而新算法为15s, 节约了48.28%;采用基本滑模控制使横荡速度达到期望值所需的上升时间为24s, 而新算法为14s, 节约了41.67%;采用基本滑模控制使艏向角速度达到期望值所需的上升时间为13s, 而新算法为10s, 节约了23.08%。可见, 设计的控制器对有非线性和环境干扰的船舶动力定位系统都具有较强的鲁棒性, 具有控制输入连续、控制抖振小、不存在过高增益等特点。

Sliding mode control for ship dynamic positioning based on linear matrix inequality

In order to solve the control problem of ship dynamic positioning systems with nonlinear and environmental disturbances, a sliding mode control algorithm based on the linear matrix inequality (LMI) was proposed.The tracking error was designed as a sliding mode function, and a linear matrix inequality was designed to solve the state feedback gain.Based on the quadratic Lyapunov function, the stability of the closed-loop system was proved.The switching function was designed to make the system robust to uncertainties and external disturbances and to avoid chattering.The sliding mode controller based on the LMI was simulated, and the forward speed, sway speed, heading angular speed, forward acceleration, sway acceleration, heading angular acceleration, forward control force, sway control force, and heading control moment of a dynamic-positioning ship were calculated under two different conditions, namely, uniform motion without disturbance and variable-speed motion with external environment disturbance.The effects of parameters such as the linear matrix of state feedbackgain, boundary layer, and switching gain on control performance were analyzed and compared.Analysis result indicates that it takes 29 sfor the forward speed to reach the expected value by using the basic sliding mode control, whereas the new algorithm saves 48.28% at 15 s.It takes24 sfor the sway speed to reach the expected value by using the basic sliding mode control, whereas the new algorithm saves 41.67%at 14 s.It takes 13 sfor the heading angular speed to reach the expected value by using the basic sliding mode control, whereas the new algorithm saves 23.08%at 10 s.Thus, the designed controller has strong robustness for the ship dynamic positioning system with nonlinear and environmental disturbances, and has the characteristics of continuous control input, no control chattering, and no high gain.