Presented contribution describes a seismically balanced machine tool axis with advantages and disadvantages of that kind of concept. After an introductory survey on the seismically balanced machine tool, a system simulation is presented. This system simulation includes a model of the mechanical parts, a model of a synchronous linear motor, and a model of the control circuits. The control algorithm of relative distance (with simulation of relative distance control of two masses) and centre of gravity movement control (absolutisation) is presented. The LQ control algorithm was compared to the heavily used PID control algorithm. The results are shown in the last section of this paper. With these results, optimal design of controller can be achieved.