Abstract
A Fractional Order Sliding Mode Control (FOSMC) is proposed in this paper for an integer second order nonlinear system with an unknown additive perturbation term. A sufficient condition is given to assure the attractiveness to a given sliding surface where trajectory tracking is assured, despite the presence of the perturbation term. The control scheme is applied to the model of a quadrotor vehicle in order to have trajectory tracking in the space. Simulation results are presented to evaluate the performance of the control scheme.
Highlights
The design of fractional order controllers has become one of the most exciting topics in control theory leading to interesting applications in the control of physical systems such as suspension systems, permanent magnet synchronous motors, power electronic systems and unmanned aerial vehicles, among others
Numerical simulations show the robustness of the fractional order sliding mode control (FOSMC) with respect to additive uncertainties and the chattering in the control signals is reduced when compared to a integer order sliding mode controller
A perturbation term was introduced at the right hand side of the quadrotor dynamic model (24)–(29) at t = 13 s in order to simulate the effect of weather conditions, such as wind variations
Summary
The design of fractional order controllers has become one of the most exciting topics in control theory leading to interesting applications in the control of physical systems such as suspension systems, permanent magnet synchronous motors, power electronic systems and unmanned aerial vehicles, among others. A sufficient condition is derived to guarantee global attraction to the sliding surface when a fractional order linear system with uncertainties is considered. Motivated by this result, in this paper FOSMC design is proposed to solve a trajectory tracking problem for an integer order nonlinear system where an unknown additive perturbation term is present. Numerical simulations show the robustness of the FOSMC with respect to additive uncertainties (the error tracking is bounded to a small region around zero) and the chattering in the control signals is reduced when compared to a integer order sliding mode controller.
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