Adaptive Chattering-Free PID Sliding Mode Control for Tracking Problem of Uncertain Dynamical Systems

Aiming at the trajectory tracking problem with unknown uncertainties, a novel controller composed of proportional-integral-differential sliding mode surface (PIDSM) and variable gain hyperbolic reaching law is proposed. A PID-type sliding mode surface with an inverse hyperbolic integral terminal sliding mode term is proposed, which has the advantages of global convergence of integral sliding mode (ISM) and finite time convergence of terminal sliding mode (TSM), and the control effect is significantly improved. Then, a variable gain hyperbolic approach law is proposed to solve the sliding mode approaching velocity problem. The variable gain term can guarantee different approaching velocities at different distances from the sliding mode surface, and the chattering problem is eliminated by using a hyperbolic function instead of the switching function. The redesign of the sliding mode surface and the reaching law ensures the robustness and tracking accuracy of the uncertain system. Adaptive estimation can compensate for uncertain disturbance terms in nonlinear systems, and the combination with sliding mode control further improves the tracking accuracy and robustness of the system. Finally, the Lyapunov stability principle is used for stability analysis, and the simulation study verifies that the proposed control scheme has the advantages of fast response, strong robustness, and high tracking accuracy.

Automated summary

This paper proposes a novel controller for the trajectory tracking problem with unknown uncertainties utilizing PIDSM and a variable gain hyperbolic reaching law. The control effect is significantly improved by introducing a PID-type sliding mode surface and a variable gain hyperbolic approach law. The simultaneous redesign of the sliding mode surface and reaching law ensures the robustness and tracking accuracy of the uncertain system. The combination of adaptive estimation and sliding mode control further enhances the tracking accuracy and robustness of the system.