(542f) Covariance Based Hardware Selection for Infinite Dimensional Systems

The subject of hardware selection (i.e., selection of sensors and actuators) to be used for the control and monitoring of chemical processes has enjoyed a sustained level of attention within the literature (for extensive reviews please see [1, 2, 3]). As one would expect, a fair amount of these efforts have focused on distributed processes, since the selection of hardware locations for these systems is most pressing. It should also be noted that in the area of finite dimensional systems, a great deal of theoretical progress has been made in recent years, especially with regard to novel and industrially relevant measures of system performance.

The current effort we will focus on a set of recently developed covariance based hardware selection schemes [4, 5, 6], and aim to illustrate how these globally optimal (mixed integer convex programming) schemes can be applied to infinite dimensional processes. The resulting schemes are illustrated through application to an exothermic tubular reactor system. Additionally, an extension of the basic formulation will be presented so as to yield, for the first time, the globally optimal solution to the sensor location problem presented in the 1978 paper by Kumar and Seinfeld [7].

[1] C.Kubrusly and H.Malebranche, ``Sensors and controllers location in distributed systems-a survey,'' Automatica, vol. 21, pp. 117--128, 1985.

[2] S.Padula and R.Kincaid, ``Optimization strategies for sensor and actuator placement,'' NASA/TM-209126, 1999.

[3] M.J. Bagajewicz, Process Plant Instrumentation: Design and Upgrade. Technomic Pub Co, 2000.

[4] D.J. Chmielewski, T.Palmer, and V.Manousiouthakis, ``On the theory of optimal sensor placement,'' AIChE Journal, vol. 48(5), pp. 1001--1012, 2002.

[5] D.J. Chmielewski and J.K. Peng, ``Covariance based hardware selection, part I: Globally optimal actuator selection,'' IEEE Trans. Contr. Syst. Technol., vol. 14, pp 355-361, 2006.

[6] J.K. Peng and D.J. Chmielewski, ``Covariance based hardware selection, part II: Equivalence Results for the Sensor, Actuator and Simultaneous Selection Problems,'' IEEE Trans. Contr. Syst. Technol., vol. 14, pp 362-368, 2006.

[7] S. Kumar and J.H. Seinfeld, “Optimal location of measurements in tubular reactors, Chem. Eng. Sci., Vol. 33, pp 1507-1516, 1978.