A novel PID control with fractional nonlinear integral

Nonlinear Dynamics - A nonlinear PID controller for robust tracking of second-order nonlinear systems is proposed, which consists in a classical PD structure plus a fractional-order nonlinear...     

Fractional integral sliding modes for robust tracking of nonlinear systems

Memory and heritage of differintegral operators require knowledge of the error manifold derivative at the initial time to sustain a sliding motion for any initial condition. Moreover, when the system is subject to (unknown) disturbances, such initial condition is unknown; thus, the enforcement of an integral sliding motion has been elusive with a chatter-less controller. In this paper, a novel fractional-order integral sliding mode (FISM) is proposed to maintain an invariant sliding mode due to an exact estimation of disturbances at first step. Our scheme is continuous after initial condition, avoiding chattering effects thanks to the topological properties of differintegral operators. In contrast to other FISM approaches, the proposed scheme induces a fractional-order reaching dynamics of order \((1+\nu )\in (1,2)\) to enforce an integral sliding mode for any initial condition, even in the presence of Hölder (continuous but not necessarily differentiable) disturbances and model uncertainties. Simulations show the reliability of the proposed scheme.