A Self-Guided Fractional-Order Fuzzy PD Controller for MEMS Gyroscope

This article explores an application of a self-guided fractional-order fuzzy proportional–derivative (SGFOFPD) controller for a microelectromechanical system (MEMS) gyroscope. The SGFOFPD is an intelligent, adaptive, and formula-based fuzzy logic controller (FBFLC). Based on the current error and its rate of change, it can dynamically adjust its gains. Overall, it is a Takagi–Sugeno model-based fuzzy adaptive controller that employs noninteger-order differentiation operators in its design, thereby enhancing the robustness of the FBFLC. The performance of the SGFOFPD is evaluated against its integer-order counterpart, the self-guided integer-order fuzzy proportional–derivative (SGIOFPD) controller. For tuning, the scaling factors of both controllers were optimized using the gray wolf optimization technique for a customized cost function. The presented simulation study demonstrated that the SGFOFPD controller reduced the cost function by a factor of 1.51 compared to the SGIOFPD controller, highlighting a notable enhancement in trajectory-tracking performance. To assess performance under model uncertainties, the damping coefficients and spring constants were allowed to vary individually, then in combination (all three damping coefficients or all three spring constants). The simulation results revealed that the SGFOFPD controller outperformed the SGIOFPD controller across all combinations. To assess the combined effect, all six parameters were also varied simultaneously, and the statistical analysis was performed on the resulting cost function. The SGFOFPD controller had a median cost of 0.3031—about 1.475 times lower than the SGIOFPD’s median of 0.4471—indicating a tighter distribution. To further evaluate the disturbance-rejection performance, sinusoidal external disturbances were applied along thex- andy-axes with varied amplitudes and frequencies, and the resulting cost function values were recorded. The results revealed that the SGFOFPD controller recorded a median cost of 0.5326, which is 2.2189 times lower than the SGIOFPD controller’s median cost of 1.1818. Based on these results, it is safe to conclude that the SGFOFPD controller is a more consistent, stable, and effective control solution for a MEMS gyroscope.