This is the enhanced version of the single phase PLL, based on the basic version of the single phase PLL, avoiding the mentioned double-frequency ripple on the estimated frequency.
The output y[1] is a cosine signal in phase with the input u,
the output y[2] is a sine signal 90° phase shifted to y[1].
The output y[3] is a cosine signal in phase with the input u and the estimated amplitude, i.e. the fundamental harmonic.