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Sensitivity of a class of distributed parameter control systems
Author(s) -
Seinfeld John H.
Publication year - 1969
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.690150116
Subject(s) - sensitivity (control systems) , control theory (sociology) , trajectory , mathematics , measure (data warehouse) , nonlinear system , open loop controller , matrix (chemical analysis) , limiting , boundary (topology) , mathematical optimization , closed loop , mathematical analysis , computer science , control (management) , physics , engineering , materials science , control engineering , mechanical engineering , quantum mechanics , astronomy , artificial intelligence , electronic engineering , database , composite material
A sensitivity matrix is defined as a measure of trajectory deviations to small parameter variations of both open and closed loop controlled nonlinear parabolic and first‐order hyperbolic systems. In general the parameters may enter through the system equations or the boundary conditions and may be time or spatially dependent. The introduction of a positive measure of the sensitivity, the norm of the sensitivity matrix, into the performance index is shown to be effective in limiting the trajectory deviations due to the parameter variations. The open and closed loop control of a double pipe heat exchanger is analyzed with the open loop problem solved by an approximate procedure. The sensitivity reformulation is successful in reducing trajectory sensitivity, however at the cost of decreased overall performance.