In this paper, a sliding mode control scheme is developed to stabilise a class of nonlinear perturbed underactuated system with a non-integral momentum. In this scheme, by initially maintaining a subset of actuated variables on sliding manifolds, the underactuated system with the non-integrable momentum can be approximated by one with the integrable momentum in finite time. During sliding, a subset of the actuated variables converge to zero and a physically meaningful diffeomorphism is systematically calculated to transform the reduced order sliding motion into one in a strict feedback normal form in which the control signals are decoupled from the underactuated subsystem. Furthermore, based on the perturbed strict feedback form, it is possible to find a sliding mode control law to ensure the asymptotic stability of the remaining actuated and unactuated variables. The design efficacy is verified via a multi-link planar robot case study.

本文提出了一种滑模控制方案，以稳定一类具有非积分动量的非线性摄动欠驱动系统。在此方案中，通过最初在滑动歧管上保留一组致动变量，可以在有限时间内将动量不可积分的欠驱动系统近似为动量不可积分的系统。在滑动过程中，被致动变量的子集收敛到零，并且系统地计算出物理上有意义的微分同构，以将降阶滑动运动转换为严格反馈正态形式，其中控制信号与欠驱动子系统分离。此外，根据受干扰的严格反馈表，可以找到一种滑模控制定律，以确保其余已激活和未激活变量的渐近稳定性。通过多链接平面机器人案例研究验证了设计效果。