Robustness Test of Controlled Property Indirectly Measured from State Estimation: Application to a Solidification Process

In state estimation, a model of the system behaviour combined with sensors is used to estimate unmeasurable properties. However, most models are uncertain due to unmodeled dynamics, time-varying parameters, and linearization. In order to yield good performance, the overall system has to be robust with respect to measurement error and model uncertainties. In this paper, state estimation and control in a solidification process is considered. The objective is to estimate and control the solidification rate, defined as the time derivative of the interface position. Most often, the interface position can not be measured directly, and an online estimate must be calculated in order to allow for feedback control. The solidification model has a variable structure where the state definitions depend on the interface position. An observer based on a linearized model of the solidification process is developed. Uncertainty is introduced in order to compensate for nonlinearities, parameter uncertainties, and neglected dynamics. A gain-scheduled Pi-controller is used to control the estimated interface position, and the robustness properties for the system are illustrated in simulations with various sources of model uncertainties.