NONLINEAR STATE ESTIMATION IN THE PRESENCE OF MULTIPLE STEADY-STATES

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.