Positivity problem for the one dimensional heat transfer process

Abstract

In the paper the positivity problem of the model of an one dimensional heat transfer process is addressed. Such a problem has not been considered yet. The considered thermal process is described by the fractional order state equation, derived from parabolic heat equation with homogenous Neumann boundary conditions and distributed control and observation. The internal and external positivity of the model depend on heater and sensor location as well as the size of the model. It is proved that the external positivity of the considered system can be achieved without internal positivity. Conditions of the internal and external positivity are proposed and proved. Theoretical considerations are supported by experiments. Experiments were done using the real system containing typical industrial components. The proposed results can be applied in real temperature measurements, for example in thermal cameras.