On dynamic sliding mode control of nonlinear fractional-order systems using sliding observer

In this study, a new fractional-order dynamic sliding mode control (FDSMC) for a class of nonlinear systems is presented. In FDSMC, an integrator is placed before the input control signal of the plant, in order to remove the chattering. However, in FDSMC method, the dimension of the resulted system (integrator plus the system) is bigger than the primary system. As a result, the model of the plant is needed to be known completely, in order to stabilize the system. Then, a sliding observer is proposed to extract an appropriate model for the unknown nonlinear system. Then, the chattering free controller can be obtained such that the closed-loop system has the desired properties. Lyapunov theory is used to verify the stability problem of the presented both observer and controller. For practical applications consideration, we have not applied the upper bound of the system dynamic either in controller or in observer. The effectiveness of the proposed method in comparison to the conventional fractional sliding mode control (FSMC) method is addressed. We have utilized a same observer in both control approach, in order to have a valid comparison. The simplicity of the proposed FDSMC method in concept and also in realization can be seen with comparison of the relevant equations. In addition, it is clear that the FDSMC can remove chattering completely, while chattering is the main challenge of the conventional FSMC. Finally, the validity of the proposed method is shown by some simulation examples based on the Arneodo chaotic system.