Dynamic Responses of Electrical Hair Clippers with Fractional Damping and Its Robust Stabilization Design

Purpose Our primarily objective is to investigate the properties of the hair clipper with the fractional model damping and proposed a robust control method to keep this device in the relevant operation zone. First, an appropriate strategy is applied to study the amplitude-frequency response of the hair clipper system with the fractional derivative. Secondly, under the consideration of constraints such as uncertainties and unmolded dynamics, a robust stabilization method is proposed to control the motion of the mobile part of the magnetic circuit of the hair clipper with a time delay. Study design/methodology/approach With the help of fractional models, some technical specifications about the hair clipper parameters are proposed and cannot be obtained by the classical integer ones. The ultimate stabilized properties is used to derive the Ricatti equation which the solution ensures the convergence of the systems states. Findings The majors’ results obtained of this paper are threefold Perfect knowledge of the dynamics behavior of the hair clippers with the effects of fractional damping. Improvement of the design of the hair clippers devices from a technological point of view Establishment of a robust controller for the air-gap position to avoid a collision. Originality/value This work is unique in the literature notably the control proposed. This analysis allows disclosing some novel and interesting nonlinear phenomena were disclosed. It’s important to note that the technic developed in this paper enable not only to overcome the disturbances and delays but also to achieve the objective with accuracy and faster. This strategy can be efficiently implemented for the hair clippers systems and also for different types of real physical systems such as mechanical systems, electrical systems and electromechanical systems.