Works considering modal synthesis and using polynomial decomposition of transfer functions of object and controller models are considered mainly for continuous automatic control systems. At the same time, in some cases, it is necessary to consider systems of a discrete type. An example of the synthesis of an automatic control system for an accurate positioning of a table driven by a direct-drive motor is given. Such systems provide accurate positioning in the processes of manufacturing and processing of parts. They are used in various fields of industry: medical, aerospace, automotive and others. In particular, the above model of the precise positioning table is used for packaging semiconductor elements. A feature of this example is the representation of the transfer function of the object model in a discrete form and the presence of four-cycle delay links in it. In addition, this model is unstable due to the presence of poles lying on the stability boundary in it. As a synthesis method, a modal method is used, using a polynomial decomposition of the transfer function of the model of the control object and controller. An approach is also demonstrated that makes it possible to reduce the number of calculations in the synthesis of regulators by reducing the order of the transfer function of the considered object model and reducing the number of unknown parameters of the regulator. At the same time, a regulator is obtained that differs from the original one. Various options for choosing the desired poles of the transfer function of a closed system are analyzed. The choice of the desired poles is carried out in favor of reducing the amount of overshoot of the system relative to the transients of the system with the initial choice of poles.