Finite-time disturbance observer via continuous fractional sliding modes

Recently, a great deal of effort has been devoted to the design of robust control techniques that compensate for lumped disturbances in mechanical robots and general electromechanical systems through disturbance observers. In this paper, assuming the Hamiltonian structure of Euler–Lagrange systems subject to a wider class of disturbances, and by exploiting some essential properties of fractional-order integro-differential operators, such as heritage and memory, a disturbance observer that is theoretically exact is proposed based on continuous fractional sliding modes, where exactness is understood in the sense of equality, in contrast to simple equivalence. The novelty of the proposal arises from the fact that the continuous fractional sliding-mode disturbance observer is exact, assuring finite-time disturbance estimation, in contrast with a classical integer-order sliding motion that is equivalent. Consequently, there arises a disturbance observer in finite time, including exact observation of continuous but not necessarily differentiable Hölder disturbances, as well as a clear compromise between regularity and robustness, which stands for a quite important issue overlooked in the conventional integer-order case. Representative simulations are discussed to highlight the reliability of the proposed method.