Accuracy Estimation of the Fractional, Discrete-Continuous Model of the One-Dimensional Heat Transfer Process

摘要

In the paper a new, state space, finite dimensional, non integer order model of a one-dimensional heat transfer process is considered. The proposed model uses a well known finite difference method and fractional Caputo operator to express the time derivative. The second order backward difference describes the derivative along the length. The analytical formula of the step response is given. Accuracy and convergence of the proposed model are numerically analyzed and compared to previously proposed state space model using semigroup approach. Results of simulations point that the good accuracy of the proposed model can be achieved for its relatively low order.