Finite Element Approaches for Real-Time Control and Observer Design of Flexible Rack Feeder Systems

Abstract

The basis for the design of real-time capable control and state estimation strategies for mechanical systems with distributed parameters is the derivation of suitable system models. These models lead to state-space representations that are, on the one hand, sufficiently accurate to capture the dominant features of the system dynamics. On the other hand, the dimensionality of these models has to be limited to a reasonable size to make sure that the resulting control and state estimation approaches can be implemented in real time. Therefore, a huge amount of work has been performed in recent years which is related to early lumping techniques. By using these techniques, the governing partial differential equations are replaced by sets of ordinary differential equations before the control and estimator design is performed. In this paper, both local and global approximations of the system dynamics are compared in simulations. These approximations are determined either by using a finite element representation that is based on the Method of Integrodifferential Relations (MIDR) or, alternatively, by a global Ritz ansatz. Especially the MIDR approach allows for the derivation of system models which exactly fulfill energy conservation laws as well as boundary and inter-element conditions.