This paper designs a servo control system based on sliding mode control for the shape control of elastic objects. In order to solve the effect of non-smooth and asymmetric control saturation, a Gaussian-based continuous differentiable asymmetric saturation function is used for this goal. The proposed detection approach runs in a highly real-time manner. Meanwhile, this paper uses sliding mode control to prove that the estimation stability of the deformation Jacobian matrix and the system stability of the controller are combined, which verifies the control stability of the closed-loop system including estimation. Besides, an integral sliding mode function is designed to avoid the need for second-order derivatives of variables, which enhances the robustness of the system in actual situations. Finally, the Lyapunov theory is used to prove the consistent final boundedness of all variables of the system.

翻译：本文设计了一种基于滑模控制的弹性物体形状伺服控制系统。为解决非光滑及非对称控制饱和的影响，采用了高斯型连续可微非对称饱和函数。所提出的检测方法具有高实时性。同时，本文利用滑模控制证明了变形雅可比矩阵的估计稳定性与控制器系统稳定性的结合，验证了包含估计环节的闭环系统的控制稳定性。此外，设计了积分滑模函数以避免变量二阶导数的需求，增强了系统在实际工况下的鲁棒性。最后，利用李雅普诺夫理论证明了系统所有变量的一致最终有界性。