This paper describes a new and straightforward method for controlling spatially distributed plants based on low-order models obtained from spatial discretization techniques. A suitable level of discretization is determined by computing the sequence of v-gaps between weighted models of successively finer spatial resolution, and bounding this by another sequence with an analytic series. It is proved that such a series forms an upper bound on the v-gap between a weighted model in the initial sequence and the spatially distributed weighted plant. This enables the synthesis, on low-order models, of robust controllers that are guaranteed to stabilize the actual plant, a feature not shared by most model reduction methods where the gap between the high-order model and plant is often not known, and where the gap between high-order and reduced models may be too expensive to compute. Since the calculation of the current bound is based on weighted models of small state-dimension, the new method avoids the numerical problems inherent in large-scale model reduction based approaches. The ideas presented in this paper are demonstrated on a disturbance rejection problem for a 1D heat equation. (c) 2010 Elsevier Ltd. All rights reserved.
- Automation & Control Systems
- Engineering, Electrical & Electronic
Jones, B. L., & Kerrigan, E. C. (2010). When is the discretization of a spatially distributed system good enough for control? AUTOMATICA, 46(9), 1462-1468. https://doi.org/10.1016/j.automatica.2010.06.001