Calculating the real-time constraints
=====================================

1a.
psi2 - psi1 = (720°/4 * ((i + 4) - 1) + phi2) - (720°/4 * (i - 1) + phi1)
            = 720°/4 * i + 720°/4 * 3 - 720°/4 * i + 720°/4 * 1 + phi2 - phi1
            = 720°/4 * 4 (for phi2 = phi1)
            = 720°

--(750rpm)-->  x = 720° * min / (750 * 360°)
                 = 2 / 750 * 60 sec
                 = 0.16 sec
                 = 160 msec                    (maximal)
                   ~~~~~~~~

--(6500rpm)--> x = 720° * min / (6500 * 360°)
                 = 2 / 6500 * 60 sec
                 = 0.01846 sec
                 = 18.46 msec                  (minimal)
                   ~~~~~~~~~~

1b.
psi2 - psi1 = (720°/4 * ((i + 1) - 1) + phi2) - (720°/4 * (i - 1) + phi1)
            = 720°/4 * i + phi2 - 720°/4 * (i - 1) - phi1
            = 720°/4 (for phi2 = phi1)
            = 180°

--(750rpm)-->  x = 180° * min / (750 * 360°)
                 = 1 / (750 * 2) * 60 sec
                 = 0.04 sec
                 = 40 msec                    (maximal)
                   ~~~~~~~

--(6500rpm)--> x = 180° * min / (6500 * 360°)
                 = 1 / (6500 * 2) * 60 sec
                 = 0.004615 sec
                 = 4.615 msec                 (minimal)
                   ~~~~~~~~~~


2.
psi_max - psi_min = (720°/4 * (i - 1) + phi_max) - (720°/4 * (i - 1) + phi_min)
                  = phi_max - phi_min
                  = 1° (Def., because of +-0.5°, 2 * 0.5° = 1°)

--(750rpm)-->  x = 1° * min / (750 * 360°)
                 = 1° * 60 sec / (750 * 360°)
                 = 0.0002222 sec
                 = 222.2 usec
                   ~~~~~~~~~~

--(6500rpm)--> x = 1° * min / (6500 * 360°)
                 = 1° * 60 sec / (6500 * 360°)
                 = 0.00002564 sec
                 = 25.64 usec
                   ~~~~~~~~~~


3.
delta_t = 2 * 5 usec = 10 usec

--(750rpm)-->  delta_psi_max = 10 usec *  750 * 360° / 60 sec = 0.045° ---> +-0.0225° (maximal)
                                                                ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
--(6500rpm)--> delta_psi_min = 10 usec * 6500 * 360° / 60 sec = 0.39°  ---> +-0.195°  (minimal)
                                                                ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

4.
delta_psi = 360° / 60 = 6°

--(750rpm)-->  x = 6° * min / ( 750 * 360°) = 6° * 60 sec / ( 750 * 360°) = 0.001333 sec = 1333 usec
                                                                            ~~~~~~~~~~~~~~~~~~~~~~~~
--(6500rpm)--> x = 6° * min / (6500 * 360°) = 6° * 60 sec / (6500 * 360°) = 0.0001358 sec = 153.8 usec
                                                                            ~~~~~~~~~~~~~~~~~~~~~~~~~~
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