The MAMI microtron cascade has been upgraded from 0.855 to 1.5 GeV by a 4th stage. This stage - successfully in operation since Mar 2007 *) for experiments in nuclear physics and delivering a c.w. electron beam of 100uA at 1.558GeV maximum - is a worldwide unique scheme of microtron, a Harmonic Double Sided Microtron (HDSM). In contrast to a Race Track Microtron one turn in the HDSM implies the passage of two different linac lines and accordingly two independent beam focussing schemes. Due to the higher number of tuning parameters it turns out to be much more difficult to understand and describe the actual transverse and longitudinal beam dynamics for all 43 turns in detail. For this reason parameterised models of the beam optics were implemented into the control system, which can be adapted, e.g. by least squares fit, to the measured beam parameters. The models enable analysis and fine tuning of the machine optics as well as very effective correction algorithms for the linac phases or the beam position corrector magnets.