Sun Reflector and tracer

Mansouri

Hello everybody,
I have made a sun reflecting system with sun tracer. I want to reflect sun rays into patio of a building with about 20 meter high. I have installed the system on the roof, opposite the sun and on th edge of the patio.
I have used light sensors and have put them opposit to the mirror. This will cause that mirror moves in up-down or left-right side to adjust itself in such a position which all reflected rays go to patio.
I have to say that I have used a convex mirror, 2 motors for up-down and left-right movement and 1 moto for clock -unter clockwise rotation in the system.

At noon which sun shines directly from the south side,azimuth 180, mirror has zero left-right angel and according to the sun altitude it may have positive, zero or negative angle to up-down.

The problem raises up when azimuth is not about 180. For example when azimuth is 120 and altitude is 30, system adjusts himself with -10 to down and -30 to left side.
In this situation reflected rays do not refect vertically but inclined.

To bring inclined reflected rays vertically I rotate mirror clockwise in the morning and unterclockwise after noons.

Now the question: I do not know how much should I rotate the mirro which everytime all reflected ray be vertically.