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

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.