机械臂分数阶滑模控制与极点配置控制的对比分析

摘要

本文以非线性两连杆机械臂为对象，在相同轨迹与10 N·m方波扰动条件下，将分数阶滑模控制（FOSMC）与极点配置控制（PPC）进行基准比较。目前针对工业界常用的PPC开展定量正面比较的证据仍很稀缺，工程师因而难以判断分数阶设计所增加的复杂度何时是值得的。本文用拉格朗日动力学推导被控对象，在Python中实现两种控制器，并借助基于SciPy的仿真评估跟踪精度与力矩开销。在所采用的分数阶导数近似下，FOSMC的均方根误差（RMSE）为0.458 rad（q1）与0.453 rad（q2），而PPC把误差限制在0.365 rad与0.337 rad。不过，分数阶设计所需的平均力矩更低，为69.2/29.0 N·m，低于PPC的86.1/41.4 N·m，从而揭示出一种精度—能耗折中：在精度上PPC占优，在驱动开销上FOSMC占优。该基准提供了可用于工程决策的证据——即使跟踪性能落后，分数阶滑模面仍会改变力矩需求；同时也促使人们开展硬件在环验证，以弥合已识别的精度差距。

Abstract

Fractional-order sliding mode control (FOSMC) is benchmarked against pole placement control (PPC) on a nonlinear two-link manipulator subjected to identical trajectories and 10 N·m square disturbances. Quantitative head-to-head evidence against industrial PPC is scarce, leaving engineers uncertain when fractional designs justify their added complexity. We derive the plant via Lagrange dynamics, implement both controllers in Python, and evaluate tracking and torque effort using SciPy-based simulations. Under the adopted fractional derivative approximation, FOSMC attains RMSEs of 0.458 rad (q1) and 0.453 rad (q2) whereas PPC limits the errors to 0.365 rad and 0.337 rad. The fractional design, however, requires lower mean torques of 69.2/29.0 N·m compared to PPC's 86.1/41.4 N·m, exposing a precision-energy trade-off that now favours PPC on accuracy and FOSMC on actuation effort. The benchmark delivers deployable evidence that fractional sliding surfaces shift torque demand even when their tracking performance lags, and it motivates hardware-in-the-loop validation to close the identified accuracy gap.