Positivity problem for the one dimensional heat transfer process.

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. • The positivity problem for the one dimensional thermal process is addressed. The considered process is described by the fractional order state space model. This problem has not been considered yet. • The positivity is determined by size and location of heater and sensors as well as the size of model. More generally, the positivity of the model can be achieved by choosing the right place for measurement. • The positivity does not depend on non integer orders of the model. This allows to use the proposed results to integer order systems too. • The crucial result is that the external positivity can be achieved without internal positivity by suitable location of heate and sensors. • The proposed external positivity condition is easy in use and it can be employed in real temperature measurements, for example in thermal cameras. [ABSTRACT FROM AUTHOR]