Fractional-Order Sliding-Mode Control of a Rail-Mounted Redundant SCARA Under Actuator Degradation and Elbow Locking: Truncated-Memory Analysis and a Reproducible Simulation Benchmark
- 1Electrical Engineering Department, Faculty of Engineering, Universidad de Santiago de Chile, Las Sophoras 165, Estación Central, Santiago 9170124, Chile
Abstract
Kinematic redundancy and fractional-order sliding-mode control (FOSMC) are seldom combined in fault-tolerant manipulation. Here, they are combined on a rail-mounted SCARA arm subject to actuator loss of effectiveness (LOE) and elbow locking. The sliding surface contains a Riemann–Liouville integral of order λ∈(0,1], with λ=1 giving the integral sliding mode (ISMC). Ultimate boundedness is proved under LOE, a post-lock feasibility condition yields a fault-aware redundancy resolution rule, and the short-memory Grünwald–Letnikov implementation is shown to be an exact convolution with a truncated kernel for which the sliding dynamics are stable for any memory length. With jointly tuned gains, a common activity budget, and no added lag or delay, the accuracy-tuned FOSMC-J lowers the tracking error by 49% without faults and by 67% under LOE relative to the best ISMC (20 runs per case; 1.5–2.5 Hz disturbance). However, with an actuator lag of 2 ms, FOSMC-J failed in 9 of 10 lock runs. The moderate-gain FOSMC never failed with 2–4-ms lag, but tolerated less delay than the equal-gain ISMC. Under the lock condition, moderate-gain controllers of both orders always recovered, while high-gain controllers failed in about a third of 100 runs, with a violated margin (integer) or deep saturation (fractional). Moderate gains at reconfiguration removed almost all of the failures.
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BibTeX
@article{urrea2026fractionalorder,
title = {{Fractional-Order Sliding-Mode Control of a Rail-Mounted Redundant SCARA Under Actuator Degradation and Elbow Locking: Truncated-Memory Analysis and a Reproducible Simulation Benchmark}},
author = {Claudio Urrea},
journal = {Fractal and Fractional},
year = {2026},
month = oct,
doi = {10.3390/fractalfract10110748},
url = {https://www.mdpi.com/2504-3110/10/11/748},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Fractional-Order Sliding-Mode Control of a Rail-Mounted Redundant SCARA Under Actuator Degradation and Elbow Locking: Truncated-Memory Analysis and a Reproducible Simulation Benchmark
AU - Claudio Urrea
PY - 2026
DA - 2026/10/27
JO - Fractal and Fractional
DO - 10.3390/fractalfract10110748
UR - https://www.mdpi.com/2504-3110/10/11/748
AB - Kinematic redundancy and fractional-order sliding-mode control (FOSMC) are seldom combined in fault-tolerant manipulation. Here, they are combined on a rail-mounted SCARA arm subject to actuator loss of effectiveness (LOE) and elbow locking. The sliding surface contains a Riemann–Liouville integral of order λ∈(0,1], with λ=1 giving the integral sliding mode (ISMC). Ultimate boundedness is proved under LOE, a post-lock feasibility condition yields a fault-aware redundancy resolution rule, and the short-memory Grünwald–Letnikov implementation is shown to be an exact convolution with a truncated kernel for which the sliding dynamics are stable for any memory length. With jointly tuned gains, a common activity budget, and no added lag or delay, the accuracy-tuned FOSMC-J lowers the tracking error by 49% without faults and by 67% under LOE relative to the best ISMC (20 runs per case; 1.5–2.5 Hz disturbance). However, with an actuator lag of 2 ms, FOSMC-J failed in 9 of 10 lock runs. The moderate-gain FOSMC never failed with 2–4-ms lag, but tolerated less delay than the equal-gain ISMC. Under the lock condition, moderate-gain controllers of both orders always recovered, while high-gain controllers failed in about a third of 100 runs, with a violated margin (integer) or deep saturation (fractional). Moderate gains at reconfiguration removed almost all of the failures.
SN - 2504-3110
ER -