An adaptive fast terminal sliding mode control combined with global sliding mode scheme for tracking control of uncertain nonlinear third-order systems

Abstract

In this paper, an adaptive fast terminal sliding mode control technique combined with a global sliding mode control scheme is investigated for the tracking problem of uncertain nonlinear third-order systems. The proposed robust tracking controller is formulated based on the Lyapunov stability theory and guarantees the existence of the sliding mode around the sliding surface in a finite time. Under the uncertainty and nonlinearity effects, the reaching phase is removed and the chattering phenomenon is eliminated. This scheme guarantees robustness against nonlinear functions, parameter uncertainties and external disturbances. The derivative of the state variable is replaced by a delay term in the form of an Euler approximation of the derivative function. Furthermore, the knowledge of upper bounds of the system uncertainties is not required, which is more flexible in the real implementations. Simulation results are presented to show the effectiveness of the suggested method.

Nonsingular fast terminal sliding-mode stabilizer for a class of uncertain nonlinear systems based on disturbance observer

“…are not measurable, one can employ the delayedfeedback control method to model these variables. Specially, the delay term in the form of Euler approximation of the derivative function can be applied for the derivatives of the variables [31]. The variable z is replaced by a delay function, z = 1 h [ _ z(t) _ z(t h)], if the delay h > 0 is su ciently small.…”

“…A disturbance-observer-based recursive TSMC tracker is presented in [30] for the nite-time tracking control of third-order non-holonomic systems with unknown external disturbances. An adaptive FTSMC technique combined with GSM scheme is suggested in [31] for the tracking problem of uncertain nonlinear third-order systems. A Linear Matrix Inequalities (LMI)-based second-order FTSMC method is investigated in [32] for the tracking control of nonlinear uncertain systems with matched and mismatched uncertainties.…”

FTESO‐Based Finite Time Control for Underactuated System Within a Bounded Input

“…This work was supported by National Science Foundation of China (Grant No. In addition, combining with the adaptive control, an adaptive sliding mode controller can improve the performance of closed-loop system [15,16]. manifold which is asymptotically stable, and the latter has more advantages such as faster response and higher precision [9,10].…”

“…Conventional SMC systems adopt linear sliding mode (LSM) and terminal sliding mode (TSM) surfaces based controllers. The former is used to constrain the system motion into a sliding mode Manuscript received June 16, 2016; revised May 5, 2017; accepted June 16,2017.…”

Stability analysis and controller design for the performance improvement of disturbed nonlinear systems using adaptive global sliding mode control approach

“…In GSMC, by using an extra term in the switching curve, the reaching interval of SMC is removed and the states move on the switching curve exactly from the beginning [16,17]. Actually, GSMC has been widely employed into practice since it can guarantee the robustness and acceleration of the system and remove the reaching phase [18,19].…”