Tensor product model transformation based fractional decoupled sliding-mode control for cart-pole system with time-varying sliding surfaces and Dahl friction model

This article proposes a tensor product model transformation based fractional order decoupled sliding mode control (TPFrDSMC) scheme for cart-pole system with friction model. In the design of TPFrDSMC, the fractional order sliding surface is incorporated into the main sliding surface, and the number of tuning the sliding surface slopes is reduced to 5. Based on fuzzy logic, parameters auto-tuning laws for the sliding surface slopes are implemented. Finally, control law of the proposed TPFrDSMC is designed according to Lyapunov stability theorem. The proposal is validated through a simulated cart-pole system with Dahl's friction model. The robustness has been evaluated through simulation in the presence of frictions and disturbances, and comparisons are performed with respect to classical approach show a better performance of the newly proposed method.