Nonsingular Fast Terminal Sliding Mode Control with Extended State Observer and Tracking Differentiator for Uncertain Nonlinear Systems

A continuous nonsingular fast terminal sliding mode (NFTSM) control scheme with the extended state observer (ESO) and the tracking differentiator (TD) is proposed for second-order uncertain SISO nonlinear systems. The system's disturbances and states can be estimated by introducing the ESO, then the disturbances are compensated effectively, and the ideal transient process of the system can be arranged based on TD to provide the target tracking signal and its high-order derivatives. The proposed controller obtains finite-time convergence property and keeps good robustness of sliding mode control (SMC) for disturbances. Moreover, compared with conventional SMC, the proposed control law is continuous and no chattering phenomenon exists. The property of system stability is guaranteed by Lyapunov stability theory. The simulation results show that the proposed method can be employed to shorten the system reaching time, improve the system tracking precision, and suppress the system chattering and the input noise. The proposed control method is finally applied for the rotating control problem of theodolite servo system.