The four-tank control problem: Comparison of two disturbance rejection control solutions

Area of Science:

• Control Systems Engineering
• Process Control
• Chemical Engineering

Background:

• The four-tank system is a benchmark for control strategies.
• Real-world systems face challenges like unknown disturbances, parametric uncertainty, measurement errors, and neglected dynamics.

Purpose of the Study:

• To compare and validate two disturbance/uncertainty rejection control laws for the four-tank problem.
• To analyze the dynamic properties influencing control performance.
• To establish conditions for control design applicability and feasibility.

Main Methods:

• Development and comparison of two control laws for disturbance/uncertainty rejection.
• Utilizing Embedded Model Control (EMC) for disturbance rejection.
• Formulating frequency-domain performance and stability inequalities.
• Employing simulation to validate theoretical findings.

Main Results:

• The EMC methodology effectively rejects unknown disturbances and parametric uncertainty.
• Neglected dynamics require filtering, not rejection.
• Frequency-domain inequalities guide closed-loop pole placement and assess feasibility.
• Simulations confirm the effectiveness of the proposed design procedure.

Conclusions:

• The study provides a robust framework for designing controllers for systems with significant uncertainties.
• The presented theorems define the operational range and suggest avenues for extending control design.
• The ability to recover pole placement feasibility is a novel contribution.