Fractional Order Iterative Learning Control for Fractional Order System with Unknown Initialization

This paper reveals a previously ignored problem for fractional order iterative learning control (FOILC) that the fractional order system may have different behaviors when it is initialized differently. To implement a novel scheme of FOILC for this so-called initialized fractional order system, a D-alpha-type control law is applied, and the convergence condition is derived by using the short memory principle and the system preconditioning, which guarantees the repeatability of initialized fractional order system. Given a permitted error bound, the minimum preconditioning time horizon is calculated from the short memory principle. The relationships of memory and convergent performance are highlighted to show the necessity of preconditioning. A fractional order capacitor model with constant history function is illustrated to support the above conclusions.