Evaluation of a Fuzzy-Supervised PID Controller for a Parallel Rehabilitation Mechanism

Accurate actuator-space tracking is an important engineering requirement for repeatable motion delivery by parallel rehabilitation mechanisms, but controller performance should also be assessed under configuration-dependent dynamics and modeling uncertainty. This study evaluates a bounded fuzzy-supervised proportional-integral-derivative (FSPID) controller for a three-chain 3STC+S parallel rehabilitation mechanism. CAD-derived inverse kinematics generated the three prismatic-joint reference trajectories, while closed-loop behavior was simulated using a Simscape Multibody model including rigid-body mass and inertia properties, gravity, closed-loop constraints, and external force/moment loading. Three fixed-gain PID loops formed the baseline. The FSPID supervisor used zero-order Sugeno inference to adjust proportional and derivative gains within prescribed bounds, while the integral action remained fixed and was implemented with a leaky integrator. Under the nominal 1° trajectory at 0.2 Hz, FSPID reduced mean root-mean-square error (RMSE), maximum absolute error, and integral absolute error (IAE) by 0.25%, 0.37%, and 0.21%, respectively. Under sustained external loading, maximum-error reductions reached 9.33-10.20%, with mean actuator-wise peak-force changes within approximately ±2%. Additional simulations examined trajectory amplitude, synthetic measurement noise, viscous damping, and combined nonidealities. The results support FSPID as a conservative simulation-level refinement of fixed-gain PID; experimental validation remains necessary.