Fractional-Order-Based System Identification for Heat Exchangers

Abstract

In this paper, we present a system identification (SI) procedure to build linear time-dependent fractional-order differential equation (FDE) models, that are able to describe time-dependent behavior of heat exchangers. The SI operation is carried out via global regression of an error-cost function by a simulated annealing optimization algorithm. The parameters in the models are: the order of the equation, the coefficients in it and-when necessary-the derivative of the initial condition. The Caputo definition of the fractional derivative, and the Mittag-Leffler function, are used to obtain the corresponding solutions. To test the SI approach, we consider a number of time-dependent analytical problems and experimental data from a shell-and-tube heat exchanger. In all cases, the resulting fractional-order model represents behavior of the system more accurately than typical integer-order models.