Fast integral terminal synchronous sliding mode control for pantograph robots

In this paper, a fast integral terminal synchronous sliding mode control (FITSSMC) is newly proposed for a 2-degree-of-freedom (2-DOF) pantograph robot (PR). Firstly, the mathematical modeling of the PR is established using inverse kinematics, forward kinematics, and servo motor dynamics. Secondly, the FITSSMC is developed based on the norm-normalized sign function (NNSF) to guarantee the fast synchronous convergence of the position tracking errors of the two servo motors that the PR consists of. Based on the novel exponential piecewise functions, the sliding surface and the reaching law of the proposed FITSSMC are constructed for fast tracking error convergence. Moreover, an integral term is utilized in the proposed FITSSMC to ensure singularity avoidance and strong robustness towards external disturbances. To estimate the unmeasurable states of both servo motors in the PR, two finite-time state observers (FTSOs) are designed. Thirdly, the synchronous and finite-time stability of the PR control system under the FITSSMC is analyzed using the Lyapunov method. Thus, the proposed control scheme is able to achieve the fast synchronous convergence and minimize the synchronous position tracking errors of both motors of the PR. Finally, the comparative simulation and experimental results on the PR demonstrate the superior performance of the proposed control with the fast synchronous convergence and better tracking accuracy in the presence of uncertainties and external disturbances.