A fractional adaptation law for sliding mode control

Abstract

This paper presents a novel parameter tuning law that forces the emergence of a sliding motion in the behavior of a multi-input multi-output nonlinear dynamic system. Adaptive linear elements are used as controllers. Standard approach to parameter adjustment employs integer order derivative or integration operators. In this paper, the use of fractional differentiation or integration operators for the performance improvement of adaptive sliding mode control systems is presented. Hitting in finite time is proved and the associated conditions with numerical justifications are given. The proposed technique has been assessed through a set of simulations considering the dynamic model of a two degrees of freedom direct drive robot. It is seen that the control system with the proposed adaptation scheme provides (i) better tracking performance, (ii) suppression of undesired drifts in parameter evolution, (iii) a very high degree of robustness and improved insensitivity to disturbances and (iv) removal of the controller initialization problem.

Combination of Two Nonlinear Techniques Applied to a 3-DOF Helicopter

“…Good references on fractional calculus have been presented in [13,14]. The sliding mode control (SMC) has been also extended in [12,[15][16][17][18][19]. In [15] a PID controller based on sliding mode strategy is designed for linear fractional order systems.…”

“…In [15] a PID controller based on sliding mode strategy is designed for linear fractional order systems. In [17] a single input fractional order model, described by a chain of integrators, is considered for nonlinear systems. In [16][17][18] sliding mode method has been applied to synchronize fractional order nonlinear chaotic systems.…”

“…In [17] a single input fractional order model, described by a chain of integrators, is considered for nonlinear systems. In [16][17][18] sliding mode method has been applied to synchronize fractional order nonlinear chaotic systems. In [12,19] sliding surface has been defined as an expressed manifold with fractional order integral.…”

Analysis and shaping of the self-sustained oscillations in relay controlled fractional-order systems

“…93-108 , DOI: 10.2478/s13540-013-0007-x Discontinuous control approaches were recently suggested in the context of fractional order systems to exploit the underlying useful properties of accuracy and robustness possessed by the discontinuous control methodology (see [11,9,20,10,17]). …”

Pragmatical adaptive synchronization of different orders chaotic systems with all uncertain parameters via nonlinear control

“…Accordingly, following the initial work of Pecora and Carroll [10] in synchronization of identical chaotic systems with different initial conditions, many approaches have been proposed for the synchronization of chaotic and hyperchaotic systems such as linear and nonlinear feedback synchronization methods [11,12], adaptive synchronization methods [13,14], backstepping design methods [15,16], and sliding mode control methods [17,18], etc. However, to our best knowledge, most of the methods mentioned above and many other existing synchronization methods mainly concern the synchronization of two identical chaotic or hyperchaotic systems, the methods of synchronization of two different chaotic or hyperchaotic systems are far from being straightforward because of their different structures and parameter mismatch.…”