A Scroll-window Based Non-causal Stable Inversion Approach For Tip Tracking Control Of A Flexible Arm

The flexible manipulator, due to its light weight, low energy consumption and high speed, has increasingly wide application in industrial and aerospace field. This paper mainly deals with the tip tracking control of flexible arm, which consists of tip trajectory tracking and tip path tracking. When the output definition is at the tip level, the dynamic system from the joint torque to the link tip will be non-minimum phase because of the structural flexibility of the link. It is essentially different from the minimum phase system achieved by defining the joint trajectory as system output and limits the control method to non-causal stable inversion theory. This paper presents a new highly accurate tracking approach based on non-causal inversion with scroll-window in time domain, while the difference lies in the requirement only for the desired trajectory within the next window width, compared to the need of the whole future trajectory. In addition to the high-precision performance in output tracking by the standard non-causal stable inversion for non-minimum phase systems, this approach has better practical usability and online tracking performance, which allows achieving on-line tip tracking with high accuracy by planning and control at the moving time according to the local information of the tip trajectory and tip path.The main work of this paper include:(1) The model of planar two-link flexible manipulator is derived in detail. Only the link flexibility is considered, and each link is separately treated as Euler-Bernoulli beam. The flexible offset of each flexible link is approximated through assumed mode shape method and then a fairly accurate theory model of the two-free-degrees and two-links planar flexible manipulators is formulated through the Lagrange energy analysis method. The model provides a reasonable basis for system features analyzing and controller design. (2) Four common control tasks with flexible manipulator are discussed and commonly used control methods corresponding to a specific control task are analyzed. Also the work of characteristics analyzing is completed at different system output defines. First, we conclude that the flexible arm system is a typically affine nonlinear system. Second, we compare the dynamic inversion, relative degree, zero dynamic and non-minimum phase property, external dynamic and internal dynamic at three different output defines that is joint trajectory, tip trajectory and tip path. At last, we emphasize the concept of tip path tracking control task. These characteristics analysis provides a theoretical basis for the control algorithm selection and controller design.(3) As for the task of tip tracking of a flexible arm, this paper details the process of applying the newly proposed scroll-window based non-causal inversion method for the model approximated through a linear processing. We also discussed the convergence of the proposed algorithm and the simulation results show the effectiveness of this new approach in the realization of precise tracking control tasks of tip trajectory tracking and tip path tracking.