Fractional order PI^λD^μ controller design for satisfying time and frequency domain specifications simultaneously

Area of Science:

• Control Systems Engineering
• Electrical Engineering
• Mechatronics

Background:

• Permanent magnet synchronous motor (PMSM) servo systems require precise control for optimal performance.
• Simultaneously satisfying frequency-domain (stability, robustness) and time-domain (transient response, power consumption) specifications is a significant challenge in controller design.

Purpose of the Study:

• To propose an optimal fractional order proportional integral derivative (PIλDμ) controller design strategy for PMSM servo systems.
• To achieve desired control performance by simultaneously satisfying both frequency-domain and time-domain specifications.
• To demonstrate the superiority of the PIλDμ controller over PIλ and traditional PID controllers.

Main Methods:

• An optimal PIλDμ controller design strategy is developed using analytical calculation and the Differential Evolution algorithm.
• Frequency-domain specifications include gain margin, phase margin, and robustness to loop gain variations.
• Time-domain specifications focus on rapid response, constrained overshoot, and efficient power consumption.

Main Results:

• The PIλDμ controller offers two additional degrees of freedom (fractional orders λ and μ) for enhanced performance.
• Simulations and experiments confirm the PIλDμ controller's ability to meet multiple constraints simultaneously.
• Significant improvements in servo tracking performance for PMSM systems were observed compared to PIλ and PID controllers.

Conclusions:

• The proposed optimal PIλDμ controller provides a robust and high-performance solution for PMSM servo systems.
• Fractional-order control offers distinct advantages over traditional integer-order control for complex system requirements.
• The developed design strategy effectively balances competing control objectives for improved system dynamics.