Comparative analysis of fractional-order sliding mode and pole placement control for robotic manipulator

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.