Motion Control of Underactuated Cart-Double-Pendulum System Via Fractional-Order Sliding Mode Controller

In this paper, the motion control problem of an underactuated cart-double-pendulum system is addressed. These systems are very complicated nonlinear and underactuated systems with 3-degrees of freedom and two control inputs. By analyzing the dynamic properties of the system, a fractional-order sliding surface is presented. Based on presented sliding surface, a fractional-order sliding mode motion control approach is presented to handle the dynamic system in a robust manner. The nonlinearities of the dynamic system are approximated using a radial basis function neural network. Using an adaptive compensator, the neural network reconstruction error and upper limits on disturbances are compensated. The stability of the presented approach is assessed using Barbalat’s lemma and the Lyapunov stability criteria. As a result of the proposed controller, an asymptotic error convergence is achieved, and the efficiency of the controller is enhanced. Furthermore, numerical simulation studies are used to validate the efficiency of the designed control approach.