Proper orthogonal decomposition (POD) is a basis reduction technique that allows simulations of complicated
systems to be calculated at faster speeds with minimal loss of accuracy. The reduced order basis is created from
a set of system data called snapshots. The speed and information retention of POD make it an attractive
method to implement reduced-order models of smart material systems. This can allow for the modeling of
larger systems and the implementation of real time control, which may be impossible when using the full-order
system. There are times when the dynamics of a system can change during a simulation, and the addition of
more information to the set of snapshots would be beneficial. The implementation of control on a system is a
time when adding new snapshots to the collection can increase the accuracy of the model. Using updates allows
more flexibility when trying to balance the accuracy and the speed of the simulation. By updating the POD
basis at specific times throughout the interval, we can increase the accuracy of the model and control by using
a greater amount of the information given by the snapshots, while we can increase the speed of the simulation
during times when using less information will still result in sufficient accuracy.
The use of finite element or finite difference techniques to discretize nonlinear smart material system models can yield full-order numerical models that accurately characterize the system dynamics but do so at significant computational cost. This can preclude the use of these full-order models for uncertainty analysis, sensitivity analysis, system design, or real-time control implementation. In this paper, we discuss the construction of reduced-order system models using proper orthogonal decompositions (POD) with updates. Through the use of snapshots constructed from the full-order models, fundamental physics is retained while significantly improving efficiency for high-speed implementation.