Design of fractional order predictive functional control for fractional industrial processes

• The fractional order predictive functional control (FPFC) method is designed.
• The Oustaloup approximation is employed to derive the approximate model of fractional order system.
• The Grünwald–Letnikov (GL) definition and the fractional calculus operator are used in its cost function for optimal control.

Many phenomena in practical processes cannot be accurately described by conventional differential equations, while fractional order differential equations can describe the characteristics of such processes more accurately. In this paper, the fractional order predictive functional control (FPFC) method is designed for a class of single-input single-output (SISO) fractional order linear systems. The Oustaloup approximation is employed to derive the approximate model of fractional order system. Meanwhile, the Grünwald–Letnikov (GL) definition and the fractional calculus operator are used in its cost function, which further extend the applications of fractional order calculus to the predictive functional control algorithm. And then the optimal control is obtained. Compared with traditional predictive functional control based on integer reduced order model, simulation results reveal that the fractional order controller yields improved control performance.