In this paper, the problem of finite-time tracking for nth-order uncertain nonlinear systems with unmatched uncertainties is addressed. Using a terminal synergetic manifold, a controller is provided to force the tracking error to the origin in finite time in the presence of unmatched uncertainties. With this method, chattering problem is completely removed without defining a new function. Lyapunov theory is used to prove the stability of the proposed method. The proposed controller provides the convergence of finite-time tracking error to zero by suitable performance that is theoretically analysed and proved through simulation.

Purpose -The purpose of this paper is to design a synergetic controller to precisely and quickly track reference signals in robot manipulators. Having smooth control signal this controller enables the nonlinear robot system to track desired references in presence of disturbances in a finite time.Design/methodology/approach -A new synergetic manifold is introduced here, followed by adding a nonlinear exponential term to it have a precise tracking within a finite time of the desired references with disturbances. Previously the nonlinear term was inserted in the main synergetic equation which makes it complicated due to its hard mathematical approach. Using Lyapunov function, the stability of the system in the presence of disturbances is proved. The validity of the resulted system is confirmed by simulating it in Simulink.Findings -Using a terminal synergetic controller with new manifold proposed in this work enables system's state variables to track desired reference signal in the presence of disturbances from any initial condition with proper precision and rate. Simulation results show that compared to similar methods it provides a more proper speed and a finite time convergence with high precision and speed.Originality/value -Providing fast and precise convergence, the proposed controller can be used in robot manipulator systems which need fast response and also have a precise performance such as in printing 3D objects and any industrial process.

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