Determination of all feasible robust PID controllers for open-loop unstable plus time delay processes with gain...

Area of Science:

• Control Systems Engineering
• Robust Control Theory
• Process Automation

Background:

• Open-loop unstable processes with time delays (OLUPTD) present significant control challenges.
• Ensuring robustness against gain variations and achieving desired stability margins is critical.
• Existing methods may have limitations in applicability or generality for OLUPTD systems.

Purpose of the Study:

• To propose a novel graphical method for computing robust Proportional-Integral-Derivative (PID) controllers.
• To address gain and phase margin specifications for general OLUPTD processes.
• To simultaneously guarantee robustness and optimize performance criteria like Integral Absolute Error (IAE) or Integral Squared Error (ISE).

Main Methods:

• Utilizing a virtual gain-phase margin tester compensator to ensure robust safety margins.
• Employing stability equation and parameter plane methods to define stability and gain/phase margin boundaries.
• Graphically determining the overlapping region (GPMSOR) of these boundaries to identify feasible robust PID controllers.

Main Results:

• The Gain and Phase Margin Specifications-Oriented Region (GPMSOR) is identified, characterizing all feasible robust PID controllers.
• Controller gains within the GPMSOR are optimized to minimize IAE or ISE performance criteria.
• The proposed method successfully finds optimal PID controller gains, ensuring pre-specified gain/phase margins and performance.

Conclusions:

• The developed graphical method provides a systematic approach for designing robust PID controllers for OLUPTD processes.
• Simultaneous assurance of robustness (gain/phase margins) and performance (IAE/ISE) is achieved.
• An algorithm is presented for rapid identification of the GPMSOR and optimal PID gain set selection.