Quantitative feedback synthesis of sampled-data systems with time-delay by approximate Z-transform

Area of Science:

• Control Engineering
• Systems Theory
• Digital Control Systems

Background:

• Sampled-data systems with time delays present challenges in control design due to non-minimum phase zeros.
• Traditional methods struggle with plant parameter uncertainty and the transformation from analog to digital controllers.

Purpose of the Study:

• To propose an Equivalent Disturbance Rejection (EDR) technique within the Quantitative Feedback Theory (QFT) framework.
• To address the design of controllers for sampled-data systems affected by time delays and parameter uncertainty.
• To provide a systematic and transparent design methodology for physical controller realization.

Main Methods:

• Utilizing the Equivalent Disturbance Rejection (EDR) concept to manage non-minimum phase zeros from time-delay approximations.
• Employing approximate Z-transform to convert analog controllers and plants to their digital equivalents.
• Treating sampling time as a design parameter to stabilize uncertain sampled-data systems.

Main Results:

• The proposed EDR method effectively overcomes non-minimum phase zeros introduced by time-delay approximations.
• Adjusting the sampling time allows for the stabilization of uncertain sampled-data systems.
• The design framework is demonstrated to be systematic, relying on algebraic manipulations.

Conclusions:

• The EDR approach offers a robust and transparent method for designing controllers for time-delayed sampled-data systems.
• This methodology facilitates the direct realization of physical controllers within specified parameter bounds.
• The QFT-based design framework provides a significant improvement over existing approaches for this class of systems.