The fractional, multi-order, reduced model of the one-dimensional heat transfer process

Abstract

In the paper a new, fractional, reduced, multi-order model of a one-dimensional heat transfer process is addressed. The proposed model is the generalization of state space models using single fractional order. The use of various orders for each mode of state equation allows to better describe a behaviour of a thermal system. In addition, the analysis of controllability and observability allows to reduce the dimension of the model without loss of its accuracy. Such a model has not been proposed yet. Theoretical considerations are validated using experimental data obtained from the real laboratory system. Results of analysis supported by experiments show that the use of various orders together with eliminating of non-controllable and non-observable modes of the model allows to obtain the accurate and relatively low order model.