Robust Fractional-Order Control with Master–Slave Mechanism for Motor Speed Regulation

Robust controller tuning is essential for the accurate regulation of nonlinear dynamic plants operating under variable conditions. This study proposes an enhanced gradient-based optimizer, termed the quadratic wavelet–enhanced gradient-based optimizer (QWS–GBO), which integrates quadratic interpolation mutation (QIM) and a wavelet mutation strategy (WMS). QIM reinforces population diversity, while WMS mitigates stagnation and strengthens local refinement through adaptive perturbations, yielding a more effective balance between global exploration and local exploitation. QWS–GBO is employed in a reference–follower control framework based on Bode’s ideal response, where the follower is realized by a fractional-order proportional–integral–derivative (FOPID) controller. The FOPID parameters are optimized using QWS–GBO and evaluated in two stages. First, performance is assessed on the CEC2020 benchmark suite under a uniform protocol. Second, the approach is applied to DC motor speed regulation. On the CEC2020 functions, QWS–GBO consistently achieves lower mean objective values and faster convergence than GBO, dwarf mongoose optimization (DMO), the arithmetic optimization algorithm (AOA), and the salp swarm algorithm (SSA) with only minor computational overhead (35.90 s per trial versus 34.00 s for GBO). In the DC motor case, the QWS–GBO–tuned FOPID controller attains a rise time of 0.0216 s, settling time of 0.0350 s, zero overshoot, and peak time of 0.0509 s. Robustness tests under four operating conditions showed limited deviations (maximum 0.0058 s in rise time, 0.0113 s in settling time, 0.465% in overshoot, and 0.0131 s in peak time). Additional analyses confirmed that both QIM and WMS individually contribute measurable gains, validating their joint integration. Implementation details and parameter settings are provided to ensure reproducibility.