In many cases, the design of a tracking controller can be significantly simplified by the use of a 2-degrees of freedom (DOF) control structure, including a feedforward control (i.e., the inversion of the nominal system dynamics). Unfortunately, the computation of this feedforward control is not easy if the system is nonminimum-phase. Important examples of such systems are flexible multibody systems, such as lightweight manipulators. There are several approaches to the numerical computation of the exact inversion of a flexible multibody system. In this paper, the singularly perturbed form of such mechanical systems is used to give a semianalytic solution to the tracking control design. The control makes the end-effector to even though not exactly, but approximately track a certain trajectory. Thereby, the control signal is computed as a series expansion in terms of an overall flexibility of the bodies of the multibody system. Due to the use of symbolic computations, the main calculations are independent of given parameters (e.g., the desired trajectories), such that the feedforward control can be calculated online. The effectiveness of this approach is shown by the simulation of a two-link flexible manipulator.
Approximate End-Effector Tracking Control of Flexible Multibody Systems Using Singular Perturbations
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received November 2, 2012; final manuscript received October 7, 2013; published online November 19, 2013. Assoc. Editor: Hiroyuki Sugiyama.
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Gorius, T., Seifried, R., and Eberhard, P. (November 19, 2013). "Approximate End-Effector Tracking Control of Flexible Multibody Systems Using Singular Perturbations." ASME. J. Comput. Nonlinear Dynam. January 2014; 9(1): 011017. https://doi.org/10.1115/1.4025635
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