Transport delay compensation is the actual problem of the modern control theory. In this paper the case of a linear time-invariant control system with a constant transport delay of the control signal is considered. Predictor state feedback which is able to provide stability of the transport delay system is synthesized and the details of its realization as a dynamic regulator are described. The example of the dynamic model of the unicycle mobile robot is considered. The results of the computer modelling in the MATLAB-Simulink environment are presented. The influence of the constant transport delay of the control signal on the stability of the system and the efficiency of the described dynamic regulator is shown.