An explicit robust stability condition for uncertain time-varying first-order plus dead-time systems.

Area of Science:

• Process Control
• Control Engineering
• Automotive Systems

Background:

• First-order plus dead-time (FOPDT) models are widely adopted for representing damped dynamic processes with time delays in process control.
• Robust stability and output tracking are critical challenges in systems with time-varying parameters and delays.

Purpose of the Study:

• To derive an explicit condition for parameter- and delay-dependent robust stability of FOPDT systems.
• To propose an internal model control (IMC) approach for parameterizing stabilizing controllers in time-varying FOPDT systems.
• To apply the derived robust stability condition to air-fuel ratio (AFR) control in lean-burn spark ignition (SI) engines.

Main Methods:

• Derivation of an explicit necessary and sufficient parameter-dependent robust stability condition using the small-gain theorem.
• Parameterization of stabilizing controllers via an internal model control (IMC) approach.
• Extraction of an equivalent proportional-integral-derivative (PID) controller for practical implementation.

Main Results:

• An explicit robust stability condition was derived, dependent on nominal system gain, delay, time constant, and uncertainty bounds.
• The IMC approach successfully parameterized stabilizing controllers for time-varying FOPDT systems.
• The proposed method was validated in the context of AFR control for SI engines, addressing significant time-varying transport delays.

Conclusions:

• The derived explicit robust stability condition provides a valuable tool for designing controllers for FOPDT systems with uncertainties.
• The proposed IMC-based robust control strategy effectively handles time-varying parameters and delays, ensuring stable operation.
• The application to AFR control demonstrates the practical relevance and effectiveness of the method in automotive systems.