Finite z-Slice Fuzzy Speed Control of a DC Motor Using Hybrid HO-CPO Optimization

Speed control of direct-current (DC) drives requires a balance between tracking performance and electrical demand. This study jointly optimizes controller gains, membership geometry, input uncertainty, three z-levels and their weights, and 25 rule consequents in a finite layered fuzzy controller, labeled T3 in the numerical records. A two-stage evaluation separates optimizer performance from controller-architecture comparisons. Stage I compares study-specific HO, CPO, and Hybrid HO-CPO procedures for the same controller, with 5050 objective evaluations per run. Across 20 matched runs, the hybrid achieves the lowest mean cost (107.5093), followed by CPO (114.8554) and HO (131.1904); rank-based tests identify significant differences. Stage II independently tunes T1, IT2, and finite T3 controllers using the same hybrid and evaluation budget. Their mean costs are 106.2192, 104.6669, and 104.6439, respectively, with no significant architecture difference (Friedman p = 0.7047). Tests with parameter variation, measurement noise, alternative operating conditions, reduced inductance, and perturbed objective weights show that the preferred controller depends on the metric and scenario. The layered controller is competitive in simulation, although its small mean-cost advantage over IT2 is accompanied by a longer optimization time.