发表机构
School of Astronautics, Northwestern Polytechnical University; Ningbo Institute of Northwestern Polytechnical University（西北工业大学航天学院; 西北工业大学宁波研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过相平面分析揭示连续滑模控制中二阶系统渐近收敛方向存在分岔，其阈值与临界阻尼边界一致，为运动控制设计提供预测框架。
AI 中文摘要
对于连续滑模控制（SMC）下的二阶系统，文献中长期依赖相平面图例，隐含假设相平面轨迹沿与设计滑模面相切的方向趋近平衡点。本文通过对受标准线性SMC作用的双积分器系统进行严格的相平面分析，研究了这一切向收敛假设。我们揭示了渐近状态比并非唯一，而是表现出依赖于控制增益、滑模面参数和初始条件的分岔现象。关键发现是系统可能沿隐式次曲面而非与设计滑模面对齐的方向收敛，这意味着平滑进入并非全局保证。我们推导了收敛比的闭式表达式，并建立了一个分类框架，精确刻画了平滑进入假设何时成立、何时失效。该分析进一步扩展到经典PD控制，并表明分岔阈值与区分两种收敛区域的临界阻尼边界重合。这些发现连接了终端几何与收敛平滑性，为高性能运动控制设计提供了预测框架。仿真结果验证了所提出的收敛区域分类。
英文摘要
For second-order systems under continuous sliding mode control (SMC), the literature has long relied, largely through phase-portrait illustrations, on the implicit convention that the phase-plane trajectory approaches the equilibrium along a direction tangential to the designed sliding surface. This paper investigates this tangential convergence assumption through a rigorous phase-plane analysis of the double-integrator system subject to standard linear SMC. We reveal that the asymptotic state ratio is not unique but instead exhibits a bifurcation that depends on the control gains, the sliding surface parameter, and the initial conditions. The key finding is that the system may converge along an implicit secondary manifold rather than aligning with the designed sliding surface, implying that smooth entry is not globally guaranteed. We derive closed-form expressions for the convergence ratios and establish a classification framework that precisely characterizes when the smooth-entry assumption holds and when it fails. The analysis is further extended to classical PD control, and we show that the bifurcation threshold coincides with the critical damping boundary that separates the two convergence regimes. These findings bridge terminal geometry and convergence smoothness, providing a predictive framework for high-performance motion control design. Simulation results validate the proposed classification of convergence regimes.
Comments13 pages, 5 figures
