含弹性索的绳牵引并联机构的动力学和末端轨迹控制

Dynamics and End Trajectory Control of 2-Cable-Driven Parallel Mechanism With Elastic Cable

为了能为实际应用提供更多的机构构型选择及更有效地研究机构动力学和轨迹控制问题,以2索(一索为弹性索;另一索为普通无质量无弹性刚性索)牵引末端执行器实现2个方向平动运动的2T机构为例,研究其动力学和末端轨迹控制问题.首先,在末端执行器运动方程的基础上,推导机构系统的逆动力学公式,给出机构动力学系统的状态空间表示及体现其具有微分平坦性的非正式表达;接着,利用非线性控制理论的线性化过程严格证明该微分平坦性,并获得微分平坦输出量和微分同胚于机构动力学系统的拥有Brunovsky正则形式的线性化和解耦化的等价系统;最后,通过针对该等价系统设计外环线性状态反馈控制器,实现末端执行器的渐近稳定轨迹跟踪,并进行实例控制仿真研究.结果表明:控制仿真可实现末端轨迹渐近稳定跟踪,稳定之后的跟踪误差值为0;但在稳定之前存在轨迹跟踪误差和振荡时间,这可通过优化反馈控制增益或修正反馈控制器来改善.

In order to provide more choices for mechanism types in practical applications as well as more efficiency to solve the problem of dynamics and trajectory control,a kind of 2T cable driven parallel mechanism with one elastic cable and one massless rigid strut was presented which can make the end effector implement 2 directional translations.At first the inverse dynamics formulation was derived based on the motion equations of the end effector,and the state space representation of dynamics system as well as the informal representation of its differential flatness was given.Then the proof of differential flatness was strictly proven by using the linearization of nonlinear control theory and the flat outputs were obtained.The linearized and decoupled system in Brunovsky canconical form diffeomorphic to the previous system was also achieved.An outer linearized feedback controller was designed to implement the asymptotically stable trajectory tracking of the end effector.The results of control simulation have indicated that the asymptotical stability can be realized by control simulation and the tracking error was 0 after stability.However the tracking error and oscillation time before the stability should be improved by optimizing the control feedback gains or correcting feedback controller.