Phase-based Extremum Seeking Control

Extremum Seeking Control (ESC) is a model-free adaptive control method to locate and track the optimal working point for nonlinear plants. However, as shown recently, traditional ESC methods may not work well for dynamic systems. In this thesis, we consider a novel ESC loop to locate the optimal operating point for both static and dynamic systems. Considering that the phase-lag of the system undergoes a large shift near a steady-state optimum and reaches the value of ⇡/2 at the optimal operating point, the novel ESC applies the phase-lag of the target system to track the optimum. An extended Kalman filter is used to ensure the accuracy of the phase estimation. The structure of a phase locked loop (PLL) is employed in combination with an integral controller to lock the phase near ⇡/2, such that the target system will operate near the optimal working point. The controller is demonstrated by application to optimization of the substrate conversion in a chemical reactor.