Nonlinear fractional PI control of a class of fractional-order systems

This paper deals with the design of nonlinear PI control techniques for regulating a class of fractional-order dynamics governed by a commensurate-order model, possibly nonlinear, perturbed by an external disturbance. The suggested control algorithm is the combination between a fractional-order PI controller and a nonlinear robust version of it, namely a second-order sliding mode control algorithm called "super-twisting" controller in the literature. A key feature of the approach is the use of ad-hoc sliding manifolds whose construction involves fractional order derivatives. A constructive Lyapunov based synthesis is illustrated, which leads to simple tuning rules for the controller parameters guaranteeing the asymptotic rejection of the external disturbance under appropriate smoothness restrictions. Computer simulations illustrate the effectiveness of the proposed technique.