Numerical validation of order reduction techniques for finite element modeling of a flexible rack feeder system

As shown in previous work, there exist several options for modeling of flexible mechanical systems that are readily applicable for the design of observer-based closed-loop control strategies. Especially, finite element techniques, which are derived by means of an early-lumping approach, provide a good compromise between accurate modeling and real-time capability of the resulting control and estimation procedures. However, an increase of the degrees of (polynomial) ansatz functions for the representation of characteristic quantities such as bending deflections as well as an increase of the number of finite elements lead to rapidly growing system orders. On the one hand, this order increase brings the drawback that an excessive computational effort may be required. In the worst case, this results in a loss of real-time capability. On the other hand, it is also possible that system models are obtained which contain information that is redundant for a feedback control design. The latter holds for cases in which eigenvalues are included in finite-dimensional state-space representations with features of the system dynamics that are sufficiently faster than the available actuators. Hence, order reduction techniques become necessary in practical control tasks. In this paper, suitable modeling and validation approaches are described which allow for limiting the system order to a value that still guarantees sufficient accuracy for the control task at hand. Representative simulation results are discussed in this paper which are the basis for a future experimental validation.