TMHMATOΣ XHMIKΩN MHXANIKΩN
ΠANEΠIΣTHMIOY ΠATPΩN
ΟΜΙΛΗΤΗΣ:ΑντώνιοςΑρμάου, Assoc. Professor, Pennsylvania State University, USA – ΕπισκέπτηςΚαθηγητήςΠανεπιστημίουΠατρών
ΘΕΜΑ:Recent progress on advanced model order reduction and control structure synthesis of complex chemical processes – Part 1: Distributed parameter systems
ΤΟΠΟΣ:Αίθουσα Συνεδριάσεων ΤΧΜ
ΗΜΕΡ/ΝΙΑ:Πέμπτη 28 Νοεμβρίου 2013
ΩΡΑ:15:00
ΠΕΡΙΛΗΨΗ:
In recent years the interest in control of spatially distributed systems has significantly increased due to the need to synthesize model-based controllers for complex transport-reaction processes that are characterized by the coupling of chemical reaction with significant convection, diffusion, and dispersion phenomena. Such processes as exemplified by catalytic reactions, polymerization processes, plasma etching and semiconductor manufacturing, exhibit spatial variations that need to be explicitly accounted by the controller.
Typically, this problem is addressed through model reduction, where finite dimensional ordinary differential equation (ODE) approximations to the original partial differential equation (PDE) process models are derived and used for controller design. The key step in this approach is the computation of basis functions that are subsequently utilized to obtain the ODEs using the method of weighted residuals. A common approach to this task is the proper orthogonal decomposition method (POD).
The successful application of POD requires the a priori availability of a sufficiently large ensemble of PDE solution data. During closed-loop simulation, situations may arise when the POD basis functions fail to accurately represent the dynamics of the PDE system. Since additional data from the process become available during operation, we focused our attention on the recursive computation of the basis functions, which we coin Adaptive POD (APOD). Subsequently, we derive low-order models specifically tailored for the design of feedback controllers and observers for distributed processes. Following the derivation, we present the synthesis of robust output feedback controllers. An important requirement of APOD is to keep the computational burden relatively small, to ensure on-line implementation. The performance of the controller structure hinges on the frequency of the sampling, which must be of the same order as the frequency of the appearance of new trends.
One of the prerequisites of APOD is obtaining snapshots frequently enough. In this talk, we will address the question how infrequent can these measurements. We address this issue in a two-fold approach. We first introduce a refined ensembling approach focusing on maximizing retained information that is received from the infrequent distributed sensor measurements. We subsequently identify criteria for minimizing communication bandwidth from the periodic measurement sensors to the controller based on closed-loop stability. To determine the smallest frequency at which the controller must be updated, a Lyapunov function evolution is monitored. When the Lyapunov function begins to violate a stability threshold, the ensemble updating continues for as long as the value of Lyapunov function satisfies the stability criteria and the controller is restructured.
We evaluate the effectiveness of the proposed approaches numerically through (a) representative examples of diffusion-reaction processes and (b) the Kuramoto Sivashinsky equations. The original and the modified ensemble construction approaches for APOD are compared in different conditions and the robustness of modified APOD with respect to uncertainty, number of snapshots and number of continuous point sensors and their locations is illustrated.