This is the basic version of the single phase PLL.
Knowing the Amplitude of the input signal u, an adaptive PI-controller can be used
(like in the enhanced version of the single phase PLL.
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].
Problems: especially a double-frequency ripple on the estimated frequency resp. angular velocity ω = 2 π f = w.