Composite non-linear feedback control using Mittag-Leffler function

Abstract

Transient performance of any physical system is very important concern for the controller design of that system. Composite non-linear feedback control (CNF) is one of such controls with which optimum transient performance can be achieved. It has a combination of linear feedback law and non-linear feedback law. In the conventional CNF control, non-linear feedback law uses a decaying exponential function as a non-linear function. In the proposed modified CNF, this exponential function is replaced with Mittag-Leffler function (MLF) for the non-linear control law. Mittag-Leffler function which is one of the special functions from fractional calculus and it is the generalization of exponential function. By fine tuning the parameters in MLF, better control over damping ratio can be achieved. This improves the performance of the system further, giving lesser rise time, settling time and the percentage overshoot. The modern flight control application is used to demonstrate the effectiveness of CNF controller using MLF.