Boundary identification and control of distributed parameter systems usingsingular functions

Singular functions are fundamental properties that capture the spatial natu re of distributed parameter systems (DPS). This paper presents a framework for the dynamic identification of singular functions of an unknown DPS. The input to a DPS can be spatially distributed or applied at the boundary. Pr evious work [Gay and Ray, Chemical Engineering Science 50 (10) (1995) 1519- 1539] considered the former. The current effort is more concerned with the case of boundary inputs. The concept of boundary topos is also introduced. Both singular functions a nd boundary topos can be identified through simple boundary input response tests and provide alternate bases for a pseudo-modal control scheme. Thus, this work also provides a systematic means for identification and control o f distributed parameter systems through the use of boundary inputs alone. E xamples of self-adjoint and non-self-adjoint systems are considered to demo nstrate the efficacy of the identification and control schemes. (C) 1999 El sevier Science Ltd. All rights reserved.