Fractional-calculus-based control scheme for dynamical systems with input uncertainty

Abstract

Since the existence of unwanted oscillations should be avoided in practical systems, this article investigates active vibration and oscillation suppression of two-degree-of-freedom dynamical systems using a novel variable structure control methodology. Owing to high stability and generality of the fractional-calculus-based differential equations, a non-integer-order sliding surface is proposed. Afterward, the occurrence of the sliding motion is ensured using a switching control rule. The effects of the input nonlinearities, which are usually existed in mechanical actuators, are fully dealt with using the introduced fractional sliding modes. In addition, unknown lumped uncertainties are considered to disturb the system dynamics. As a result, the proposed controller is robust against system and control fluctuations and can handle bounded external perturbations. Moreover, careful stability synthesis is developed to theoretically confirm the control designs. Finally, two numerical case studies, which include oscillation control of a magnetic bearing system and a gyroscope device, are provided to demonstrate the superior performance of the suggested control technology.