Block pulse-based techniques for modelling and synthesis of non-integer systems

Abstract

In this article, generalised operational matrices of the orthogonal block pulse basis, approximating the Riemann–Liouville formula accurately, are exploited for the modelling and control synthesis of fractional dynamic systems. The main advantage of using this tool is that it allows us to transform the analytical fractional differential calculus into an algebraic one relatively easier to solve. The developments presented have led to the formulation of two optimisation problems. In fact, in the first part, the solution of a least square algorithm could provide a reduced integer transfer function approximating the considered fractional system. While in the second part, the proposed non-linear function to be minimised may be helpful for the state space parameters setting of PI λ D μ controllers. Simulations in both cases are exhibited to show the effectiveness of the detailed techniques.