Comparative Fuzzy Reconstruction Frameworks for Multivalued Control-Valve Stiction Hysteresis In Process Control Systems

Control-valve stiction is a persistent source of nonlinear oscillation, degraded regulation, and excessive actuator activity in process-control systems because identical controller-demand values can correspond to different stem positions depending on motion direction and sticking history. This study develops a path-parameterized data-driven framework for reconstructing the resulting multivalued controller-output–valve-position trajectory using four first-order Takagi–Sugeno fuzzy architectures: fuzzy C-means, 16-rule and nine-rule subtractive-clustering models, and an adaptive neuro-fuzzy inference system. A normalized path coordinate converts the multivalued trajectory into synchronized single-valued representations suitable for fuzzy reconstruction. Validation uses an 801-sample literature-grounded Choudhury valve-stiction benchmark with 3% deadband-plus-stickband and 1% slip jump. To avoid artificial statistical replication, one 201-point, 50-s cycle is used for quantitative identification, while the remaining deterministic cycles are retained only for repeatability visualization. Across ten repeated 70/30 train–test partitions, the adaptive neuro-fuzzy model achieved the lowest mean held-out NRMSE (0.001652), followed by the 16-rule (0.001894), nine-rule (0.002490), and fuzzy C-means (0.008684) models. In the full-cycle descriptive fit, the adaptive neuro-fuzzy model achieved the lowest NRMSE (0.001431), whereas the 16-rule model yielded the smallest loop-area error (0.0106%). Under 5% training-noise contamination, the compact fuzzy C-means model produced the lowest clean-test NRMSE, revealing an accuracy–robustness trade-off. The results demonstrate that path-parameterized fuzzy inference can provide an interpretable surrogate for valve-stiction-loop reconstruction, soft sensing, digital-twin visualization, and control-performance monitoring. Because the benchmark is model-generated rather than a raw plant acquisition, the results establish reconstruction fidelity and within-trajectory generalization rather than independent experimental prediction.