This article is representing numerical research and modeling of autonomous unmanned underwater vehicle’s (AUUV) control system for planar motion. A mathematical model of the control system is designed for an underwater vehicle, the structure of which consists of a main thruster and control surfaces. Based on the dynamic AUUV's mathematical model two types of planar motion equations have developed: simple planar motion equations and extended planar motion equations. Both equations types include AUUV’s geometrical characteristics and hydrodynamics coefficients which have determined from computer aided design and CFD simulation. The difference between simplified and extended equations of planar motion consists in the inclusion of an additional planar coordinate and extra hydrodynamic coefficients. For each type of motion equations as input signal typical maneuverers, such as constant value, sin value and Kempf maneuverer (zig-zag maneuverer) have implemented. The system's output signals from external actions in the form of typical maneuverers the estimated of necessity of regulator. As regulator were chosen and used the PID-regulator for velocity and yaw control. The results of this study also demonstrate what the engine thrust required to achieve the desired speed, and identify which equations of motion are appropriate for specific maneuvers performed by the apparatus during its operation and mission execution.