TY - GEN

T1 - Nonlinear control of dissipative PDE systems employing adaptive model reduction

AU - Varshney, Amit

AU - Armaou, Antonios

N1 - Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.

PY - 2008

Y1 - 2008

N2 - The problem of feedback control of distributed processes is considered. Typically this problem is addressed through model reduction where finite dimensional approximations to the original infinite dimensional system are derived. The key step in this approach is the computation of basis functions that are subsequently utilized to obtain finite dimensional ODE models using the method of weighted residuals. The most common approach for this task is the Karhunen-Loeve expansion combined with the method of snapshots. However, this approach requires a priori availability of a sufficiently large ensemble of PDE solution data, a requirement which is difficult to satisfy. In this work we focus on the recursive computation of eigenfunctions using a relatively small number of snapshots. The empirical eigenfunctions are continuously modified as additional data from the process becomes available. We use ideas from the recursive projection method to keep track of the dominant invariant eigenspace of the covariance matrix which is subsequently utilized to compute the empirical eigenfunctions required for model reduction. This dominant eigenspace is continuously modified with the addition of each snapshot with possible increase or decrease in its dimensionality, while simultaneously the computational burden is kept relatively small. The proposed approach is applied to control temperature in a jacketed tubular reactor where first order chemical reaction is taking place and the closed-loop system is successfully stabilized at an unstable steady-state.

AB - The problem of feedback control of distributed processes is considered. Typically this problem is addressed through model reduction where finite dimensional approximations to the original infinite dimensional system are derived. The key step in this approach is the computation of basis functions that are subsequently utilized to obtain finite dimensional ODE models using the method of weighted residuals. The most common approach for this task is the Karhunen-Loeve expansion combined with the method of snapshots. However, this approach requires a priori availability of a sufficiently large ensemble of PDE solution data, a requirement which is difficult to satisfy. In this work we focus on the recursive computation of eigenfunctions using a relatively small number of snapshots. The empirical eigenfunctions are continuously modified as additional data from the process becomes available. We use ideas from the recursive projection method to keep track of the dominant invariant eigenspace of the covariance matrix which is subsequently utilized to compute the empirical eigenfunctions required for model reduction. This dominant eigenspace is continuously modified with the addition of each snapshot with possible increase or decrease in its dimensionality, while simultaneously the computational burden is kept relatively small. The proposed approach is applied to control temperature in a jacketed tubular reactor where first order chemical reaction is taking place and the closed-loop system is successfully stabilized at an unstable steady-state.

UR - http://www.scopus.com/inward/record.url?scp=52449103366&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=52449103366&partnerID=8YFLogxK

U2 - 10.1109/ACC.2008.4586613

DO - 10.1109/ACC.2008.4586613

M3 - Conference contribution

AN - SCOPUS:52449103366

SN - 9781424420797

T3 - Proceedings of the American Control Conference

SP - 940

EP - 947

BT - 2008 American Control Conference, ACC

T2 - 2008 American Control Conference, ACC

Y2 - 11 June 2008 through 13 June 2008

ER -