NONLINEAR ADAPTIVE OBSERVATION OF AN EXOTHERMIC STIRRED-TANK REACTOR

Nonlinear control of an exothermic stirred-tank reactor has been previously demonstrated using a number of techniques, including nonlinear static state feedback and output feedback using observers. This paper considers the task of adaptive observation. It is shown that an adaptive observer for concentration can be constructed for an arbitrary order reaction system when only temperature measurements are available. An adaptive observer is constructed to identify the pre-exponential Arrhenius constant and to provide on-line estimation of the unmeasured reactant concentration for a global nonlinear state-feedback controller. The reaction system is transformed into a time-varying adaptive observer canonical form (AOCF) which is linear in the unknown observer states and adaptive parameters. The AOCF was proposed by Bastin and Gevers, who have provided sufficient conditions for its stability. It is shown that the sufficient conditions on the structure of the system and on the signals for global stability of the observer are satisfied by the reaction system, thereby admitting the construction of the adaptive observer for an arbitrary order reaction. Proper choice of observer gains is crucial for an acceptable rate of convergence. Simulations show that the combined observer/controller provides satisfactory closed-loop behavior when the observer time constant is approximately 4 times smaller than the closed-loop time constant. It is also shown why certain transformations result in better adaptive observers.