Extremum seeking control based on phasor estimation

We present an extremum seeking control algorithm based on the estimation of the phasor of the perturbation frequency in the output of the plant. The phasor estimator is based on a continuous time Kalman filter, which is reduced into a variable gain observer by explicitly solving the special case of the Riccati equation. Local stability of the proposed algorithm for general non-linear dynamic systems using averaging and singular perturbations is presented for the single input case. The advantage of the presented algorithm is that it can be used on plants with large and even variable phase lag.