全柔性空间机器人运动振动一体化输入受限重复学习控制

AN INPUT LIMITED REPETITIVE LEARNING CONTROL OF FLEXIBLE-BASE TWO-FLEXIBLE-LINK AND TWO-FLEXIBLE-JOINT SPACE ROBOT WITH INTEGRATION OF MOTION AND VIBRATION

探究基座、臂、关节全柔性影响下空间机器人动力学模拟、运动控制及基座、臂、关节三重柔性振动主动抑制的问题,设计了不基于系统模型信息的运动振动一体化输入受限重复学习控制算法.将柔性基座与关节等效为线性弹簧与扭转弹簧,柔性臂视为欧拉-伯努利梁模型,利用拉格朗日方程与假设模态法建立动力学模型,然后,用奇异摄动理论将模型分解为包含刚性变量与臂柔性振动的慢变子系统,包含基座、关节柔性振动的快变子系统,并分别设计相应的子控制器,构成了带关节柔性补偿的一体化控制算法.针对慢变子系统,提出输入受限重复学习控制算法,由双曲正切函数,饱和函数与重复学习项构成,双曲正切函数与饱和函数实现输入力矩受限要求,重复学习项补偿周期性系统误差,以完成对基座姿态、关节铰周期轨迹的渐进稳定追踪.然而,为了同时抑制慢变子系统臂的柔性振动,运用虚拟力的概念,构造同时反映臂柔性振动与系统刚性运动的混合轨迹,提出了基于虚拟力概念的输入受限重复学习控制器,保证基座、关节轨迹精确追踪的同时,对臂的柔性振动主动抑制.针对快变子系统,采用线性二次最优控制算法抑制基座与关节的柔性振动.仿真结果表明:控制器适用于一般柔性非线性系统,满足输入力矩受限要求,实现对周期信号的高精度追踪,有效抑制基座、臂、关节的柔性振动,证实算法的可行性.

In order to analyze the dynamic simulation and movement control of space robot under the influence of full flexible of base,links and joints,as well as the active vibration suppression of base,links and joints,an input limited repetitive learning controller with integration of motion and vibration is proposed.The design of the algorithm is not based on the system model information.The flexible base and the flexible joints are regarded as linear spring and torsion springs.The flexible links are analyzed by the Eulerian Bernoulli model,and the dynamic equation is established by the Lagrange equation and the assumed mode method.Based on the singular perturbation theory,the model is decomposed into a slow subsystem including the system rigid variables and the link flexible vibration,and a fast subsystem including the base and joint flexible vibration.The corresponding sub controllers are designed for the slow and fast subsystems to form the general controller with joint flexible compensation.For the slow subsystem,an input limited repetitive learning controller is proposed,which is composed of hyperbolic tangent function,saturation function and repetitive learning term.The hyperbolic tangent function and saturation function realize the requirement of limited input torque.The repetitive learning term compensates the periodic system error to complete the gradual stable tracking of the expected trajectory of base attitude and joint.However,in order to suppress the flexible vibration of the links of the slow subsystem,a hybrid trajectory reflecting the flexible vibration of the links and the rigid motion of the system is constructed by using virtual force conception,and an input limited repetitive learning controller on virtual force conception is proposed to ensure the accurate tracking of the trajectory of the base and joint,while actively suppressing the flexible vibration of the links.For the fast subsystem,the linear quadratic optimal control algorithm is used to suppress the flexible vibration of the base and joints.The simulation results show that the controller is suitable for general flexible nonlinear system,meets the requirements of limited input torque,realizes high-precision tracking of periodic signal,effectively suppresses the flexible vibration of base,links and joints,and verifies the feasibility of the algorithm.