Dynamic Phasor Estimates Under the Bellman´s Principle of Optimality: The Taylor-LQG-Fourier Filters

Recently Taylor^K-Kalman-Fourier filters were proposed for estimating dynamic phasors to provide instantaneous estimates and drastically reduce the total vector error by a factor of 10. However, they exhibit resonant frequencies at the edges of the pass band, and high-interharmonic gains. In this paper, the optimal linear quadratic (LQ) control is applied to design feedback filters referred to as Taylor^K-LQG-Fourier filters. This method reduces the interharmonic gains and the resonant frequency at the passband edges of the Taylor^K-Kalman-Fourier filter. The estimates from oscillating signals obtained through this optimal technique are quasi-instantaneous, and provide estimates of the instantaneous frequency, and its rate of change, preserving its synchrony with the signal for control applications. The effectiveness of the proposed algorithm is verified through simulations and experimental results.