Robust Block Control of Fractional-order Systems via Nonlinear Sliding Mode Techniques

This paper presents two novel fast converging robust controllers for Caputo derivative based fractional-order nonlinear systems. These fractional-order systems are high-relative-degree with model uncertainties and external disturbances. First, a new fractional-order model is derived from the original model based on block transformation strategy. Employing the block transformation technique makes the high-relative-degree systems versatile for sliding mode controllers design. In the second step, two different nonlinear sliding manifolds are proposed to reach a short time convergence. Subsequently, appropriate nonlinear sliding mode control laws are developed to assure the robustness and fast converging behaviors. It is worthy to notify that the mentioned sliding manifolds guarantee the fractional-order system last state convergence, and the other states convergence can be assured by control gains of the block transformation. The stability of closed-loop system for both controllers is achieved by the fractional-order stability theorems. Finally, two comprehensive numerical simulations are carried out to indicate the superiority and effectiveness of the suggested robust controllers.