Shaping structure dynamics with truncation-error bounded reduced-order models for integrated mechanism/control design

Abstract

A method for shaping the structure dynamics of mechatronic systems using truncation-error bounded reduced-order models is developed and applied to a heavy-duty robot with noncollocated sensors and actuators. Modeling is a critical issue in the integrated approach to design and control. The model required for mechanical design is different from that for control design. The former is geometric and parametric with respect to the dimensions of the parts. Dynamic models derived from such geometric models are in general of high order. The model for control design must be an explicit I/O causal form with an appropriate system order. As the mechanical structure is altered during integrated design, dynamic model validity is difficult to preserve due to the strong influence of design parameter changes on model truncation error. Even the model order may change. A method is presented for improving structural performance while maintaining validity of reduced-order models by upper-bounding truncation error. This uses Hankel singular values and sensitivity Jacobians. Changes to dynamics are obtained by altering design parameters within the subspace where the Hankel singular values corresponding to unmodeled dynamics may be kept lower than a certain limit, preserving the validity of the reduced-order model. The method is then applied to the design of a heavy-duty robot with noncollocated sensors and actuators. With this method, since the truncation-error of the structural model is upper-bounded, a controller can be designed so as to guarantee robustness.