Generalized Proportional-Integral-Derivative Interpretation of a Class of Improved Two-Degree-of-Freedom Controllers

Area of Science:

• Control Engineering
• Systems Science
• Electrical Engineering

Background:

• Traditional active disturbance rejection controller (ADRC) uses estimated states, potentially causing phase lag.
• Improved linear ADRC utilizes plant output for feedback, aiming to mitigate phase lag issues.
• Limited research exists on the mathematical relationship between traditional and improved linear ADRC.

Purpose of the Study:

• To establish the mathematical relationship between traditional linear ADRC and improved linear ADRC.
• To analyze their distinctions in the frequency domain from a generalized PID control perspective.
• To evaluate the control performance improvements of the improved ADRC.

Main Methods:

• Mathematical derivation of the relationship between traditional and improved linear ADRC.
• Generalized PID control interpretation for both controller types.
• Numerical simulations for time-domain analysis and disturbance rejection tests in a DC-DC converter.

Main Results:

• The improved ADRC provides a novel, three-parameter approach to generalized PID control, with fewer parameters than standard generalized PID.
• Time-domain simulations show the improved ADRC eliminates overshoot during set-value tracking.
• Disturbance rejection in a DC-DC converter demonstrates significantly better performance for the improved ADRC, with a 7.44x reduction in maximum voltage drop and negligible voltage rise.

Conclusions:

• The improved linear ADRC offers enhanced control performance, faster tracking, and superior disturbance rejection compared to the traditional ADRC.
• The study provides a clear mathematical link between traditional and improved ADRC through generalized PID control.
• The improved ADRC presents a more efficient method for achieving generalized PID control with fewer tuning parameters.