Estimation of inner-domain temperatures for a freezing process

Abstract

Abstract-In this paper a state observer for a distributed parameter system (DPS) with nonconstant parameter functions is presented. The DPS describes the freezing of foodstuff in vertical plate freezers and is a nonlinear heat equation. The observer is based upon the Extended Kalman Filter, meaning that the nonlinear heat equation has been discretized in the spatial domain before designing the observer. We show that the observer is robust with respect to perturbations of parameter functions and noisy measurement signals and that the innerdomain temperatures can be correctly estimated.

Stability properties of a heat equation with state-dependent parameters and asymmetric boundary conditions

“…This is achieved in particular by overestimating c(T ) in the region I ∆T to slow down heat transfer and thus the desired behavior is obtained. We point out that the transitions from c s to c i and from c i to c l have not specifically been introduced in Backi et al (2014a). In this paper, however, the transitions are considered to be functions of the shape c(T ) = p T +q in small neighbourhoods outside I ∆T , where p and q are constants.…”

“…The case considered there, as well as in Backi et al (2014b) and Backi et al (2014a) is also regarded in the present paper, where a parabolic PDE (diffusion equation) is formulated in the state variable T representing temperature, as follows:…”

A heat equation for freezing processes with phase change: stability analysis and applications

“…The subsequent simulations have already been presented in Backi, Bendtsen, Leth, and Gravdahl (2014a). They have been conducted for a non-standard case, where white Gaussian noise was added to the measurements in order to investigate how the observer handles this phenomenon.…”