Design of a combined quasi-linear distributed state and online parameter estimator for a stratified storage tank

This contribution presents the late lumping design of a combined distributed state and online parameter estimator for a state of the art domestic hot water storage system, a so called stratified storage tank. The discrete- and continuous-time dynamics of the storage tank are described by a hybrid, quasi-linear distributed parameter system, namely a finite state automaton interacting with an underlying diffusion-convection system (DCS), characterized by heat exchange to the ambiance and change of the flow direction. For the development of an advanced process control, the reconstruction of the temperature profile in the storage tank is compulsory. Therefore, a quasi-linear distributed parameter observer with a simultaneously running online estimation algorithm for the determination of the flow velocity are derived. Hereby, the injected correction terms and their tuning parameters are designed based on physical and heuristical considerations. In view of observer convergence, a discussion on the choice of appropriate sensor locations as well as the approximation of the initial temperature profile for the state observer are given. The performance of the distributed state observer and parameter estimator is illustrated by simulation studies and compared to measurement data.