Parameter and state variation estimation for multi-equilibria nonlinear systems using a "stacked" model structure

To obtain optimal performance in a controlled system, it is important to have accurate knowledge of the system parameters and equilibrium points. For some nonlinear systems, such as a Continuous Stirred Tank Reactor (CSTR), most of the operation of the system is at equilibrium points, and so this paper considers estimation of the parameter variations of a system from their assumed values using steady-state data from selected equilibrium points. It is known that the data from one equilibrium point is not always sufficiently rich to yield information about each parameter variation. This always occurs, for example, if the number of sensors is less than the number of parameters. Hence, this paper shows how the data from several equilibrium points may be fed into an extended Kalman filter based on a "stacked" model to obtain more accurate estimation of the parameter variations of the system. The results are applied to a CSTR, and it is seen that the data from four appropriately chosen equilibrium points is sufficiently rich to accurately estimate the parameter variations