Disturbance rejection performance analyses of closed loop control systems by reference to disturbance ratio

Area of Science:

• Control Systems Engineering
• Signal Processing
• System Analysis

Background:

• Evaluating disturbance rejection capacity is crucial for closed-loop control systems.
• Existing methods may not fully account for communication channel limitations.
• Quantitative analysis is needed for comparing and improving disturbance rejection.

Purpose of the Study:

• To introduce and analyze the reference to disturbance ratio (RDR) for assessing disturbance rejection.
• To provide a quantitative method for evaluating control system performance regarding disturbances.
• To derive design criteria for PID and fractional order PID (FOPID) controllers based on RDR.

Main Methods:

• Calculating the ratio of reference signal energy to disturbance signal energy at the system output.
• Theoretical analysis of RDR based on controller transfer function energy spectral density.
• Deriving design criteria for PID and FOPID controllers.
• Spectral RDR analysis to investigate frequency dependence.

Main Results:

• RDR provides a quantitative measure of disturbance rejection capacity.
• RDR of negative feedback systems is determined by controller's energy spectral density.
• Design criteria for PID and FOPID controllers were established.
• Frequency-dependent disturbance rejection capabilities were analyzed.

Conclusions:

• RDR offers a straightforward analytical method for disturbance rejection evaluation.
• The study provides a basis for designing controllers with improved disturbance rejection.
• RDR analysis is effective for both PID and FOPID controllers.