.PLL.Components.SimpledqPLL .PLL.Components.SimpledqPLLThis block calculates angle and angular velocity of the input
u[2] in α,β-frame.
The used calculation method is based on an angle tracking observer as common in electrical engineering. This implementation is very robust. It determines the angle of the input space phasor.
The angle of a complex space phasor is controlled in such a way
that its imaginary part is equal to zero. The controlled
angle theta is the unwrapped continuous angle.
The output theta approximates the desired angle
by a first order system which time constant is the integral time
constant of the controller:
Im(ej*(u-y)) = sin(u - y)
This expression can be approximated for small differences by
(u - y). Using an integral controller, the transfer
function of the closed loop can, thus, be determined as:
y = u / (1 + s*Ti).
The derivative of the output theta is the
angular velocity w, provided as an output signal
as well.