3-RSR波浪补偿平台T-S模糊控制策略

T-S fuzzy control strategy for the 3-RSR wave compensation platform

关键词:  3-RSR并联平台  波浪补偿  T-S模糊系统  TNL函数观测器  鲁棒控制  凸优化  线性矩阵不等式

Key words:  3-RSR parallel platform  wave compensation  T-S fuzzy system  TNL function observer  robust control  convex optimization  linear matrix inequality

摘要:

为提高并联机器人波浪补偿控制的抗干扰能力与控制精度,针对复杂海洋环境下现有方法鲁棒性不足的问题,以3-RSR并联机器人为对象,提出新型TNL函数观测器和T-S模糊控制策略。首先,基于机构运动特性构建了包含支链约束的运动学模型,推导关节空间与操作空间的雅可比矩阵；通过虚功原理和牛顿欧拉法建立非线性动力学模型,阐明惯性力、科氏力与重力的耦合机制。其次,针对系统的高度非线性特性,采用T-S模糊模型对动力学方程进行精确逼近,实现基于隶属度函数的局部线性化建模。创新性设计了TNL函数观测器,结合Lyapunov稳定性理论构建LMI表征的鲁棒稳定性条件,解决系统状态不可测问题。最后,通过协同设计观测器与模糊控制器,构建抗扰闭环系统,利用凸优化求解满足H∞性能指标的控制器参数,保障扰动下的动态稳定性。仿真结果表明,TNL函数观测器较传统类型具有更优性能指标。该架构能有效解决非线性状态估计与鲁棒控制难题,为海洋工程装备波浪补偿提供了创新方案,对提升舰船转载、海上救援等作业性能具有重要实践价值。

Abstract:

To improve the anti-interference ability and control accuracy of wave compensation control for parallel robots, and to address the problem of insufficient robustness of existing methods in complex marine environments, this study proposes a novel TNL function observer and a T-S fuzzy control strategy for a 3-RSR parallel robot. Firstly, a kinematic model incorporating limb constraints is constructed based on the kinematic characteristics of the mechanism, and the Jacobi matrices between the joint and operational spaces are deduced; a nonlinear dynamics model is established through the principle of virtual work and the Newton-Euler method to elucidate the coupling mechanism of inertial, Coriolis, and gravitational forces. Secondly, to address the highly nonlinear characteristics of the system, the T-S fuzzy model is adopted to accurately approximate the dynamical equations, thereby realizing local linearization modeling based on membership functions. The TNL function observer is innovatively designed, and the robust stability condition characterized by LMIs is constructed by combining the Lyapunov stability theory to solve the problem of unmeasurable system states. Finally, through a co-design of the observer and fuzzy controller, an anti-disturbance closed-loop system is constructed, and convex optimization is used to solve controller parameters that satisfy the H∞ performance index, thereby guaranteeing dynamic stability under disturbances. Simulations show that the TNL function observer has better performance than the conventional types. The proposed architecture can effectively address the challenges of nonlinear state estimation and robust control, providing an innovative solution for wave compensation in marine engineering equipment, which is of great practical value for enhancing the performance of operations such as ship-to-ship transfer and maritime rescue.