S. Valluri et M. Soroush, NONLINEAR STATE ESTIMATION IN THE PRESENCE OF MULTIPLE STEADY-STATES, Industrial & engineering chemistry research, 35(8), 1996, pp. 2645-2659
This paper concerns the problem of state estimation in nonlinear deter
ministic processes. For moderately nonlinear deterministic processes,
the inadequacy of full-order Luenberger observer and extended Luenberg
er observer with constant gain is shown analytically and through numer
ical simulation of a chemical reactor. The results indicate that the c
onvergence of an extended Luenberger observer with constant gain may b
e poorer than that of a simple linear Luenberger observer. A nonlinear
observer design method with varying gain is applied to a classical ex
othermic stirred-tank reactor with multiple steady states. Under signi
ficant observer-initialization errors and several observer gains, the
global asymptotic convergence of the nonlinear observer is demonstrate
d through numerical simulations. In the presence of the multiple stead
y states, the nonlinear observer converges to the same steady-state op
erating point at which the reactor operates, irrespective of the obser
ver initial conditions.