漂浮基柔性空间机械臂的模糊H∞鲁棒控制及柔性振动最优控制

摘要

讨论了存在外界干扰情况下漂浮基柔性空间机械臂的轨迹跟踪和振动抑制问题。结合系统动量守恒关系和拉格朗日方法建立了系统动力学模型。采用奇异摄动法的双时标分解方法，将系统分解描述为关节轨迹跟踪的慢变子系统与描述柔性杆件振动的快变子系统。针对慢变子系统，设计了自适应模糊H∞控制算法，用模糊逻辑系统去逼近系统的不确定项；同时，设计了H∞鲁棒控制项，用它克服模糊逼近误差和外界干扰对输出跟踪误差的影响。针对快变子系统，采用线性二次最优控制方法主动抑制，以保证系统的稳定性。基于 Lyapunov 稳定性理论证明了该算法可确保控制系统是渐近稳定的。系统仿真结果说明了控制器的可靠性和有效性，所设计的控制方案使得系统的跟踪误差及柔性振动快速收敛。%The traj ectory tracking and vibration suppression control for free-floating flexible space manipulator with disturbance were discussed.With the momentum conservation relations,system dy-namics model was set up by the Lagrange method.Using the two-time scale decomposition of singular perturbation method,and the system was decomposed into a slow subsystem which was described joint trajectory tracking and a fast subsystem which was described the vibration of flexible manipula-tor.Then a composite controller consisting of a slow control component and a fast control component was proposed.For the slow subsystem,adaptive fuzzy H∞ control algorithm was designed,the fuzzy logic system was used to approximate the system uncertainty,and a robust H∞ control was used to overcome the fuzzy approximation errors and eliminate the influences of the external disturbance on the output tracking errors.For the fast subsystem,optimal linear quadratic regulator(LQR)was de-signed to damp out the vibration of the flexible links.Based on Lyapunov stability theory,it is proved that this algorithm can ensure the control system is asymptotically stable.Numerical simulation re-sults illustrate that the proposed controller is reliable and effective,this control scheme makes the tracking errors of the system and the flexible vibrations quickly convergence.