Extremum seeking control based on phasor estimation

Phasor extremum seeking control with adaptive perturbation amplitude

“…Remark 1: It is important to note that the proposed approach is slightly different from the original phasor ESC presented in [4], [14]. Here, the state vector z = β 0 α 1 β 1 T does not depend on the perturbation amplitude a p .…”

“…For the demonstration of the proposed approach, and without loss of generality, we will approximate our system as a Wiener-Hammerstein model, that is, linear input and output dynamics with a non-linearity in between [3], [4], [9] as illustrated in Fig. 1.…”

“…where w(t) and v(t) are mutually independent disturbances with Q = qI and R = r as their respective covariances [4] while A is a 3 × 3 matrix of zeros and C(ωt) is given by…”

“…where ζ can be derived by finding the steady-state periodic solution of the continuous-time Kalman filter similar to the work in [4] or it can be left as a tuning parameter of the time-varying state observer. Remark 1: It is important to note that the proposed approach is slightly different from the original phasor ESC presented in [4], [14].…”

“…Another approach, based on NewtonRaphson optimization, tries to drive the system into optimum by estimating both the gradient and Hessian [3]. Recently, a phasor-based ESC approach was proposed in [4], [5]. Here, the phasor, which is proportional to the gradient, is estimated using a Kalman filter and then used to drive the system into optimality.…”