It has been established that in order to ensure effective filtration and stabilization of the voltage of DC traction substations, it is advisable to use active filters-stabilizers. The dynamic characteristics of an active filter-stabilizer have been analyzed taking into consideration its discrete properties. It has been shown that the voltage converter in an active filter-stabilizer with bilateral pulse-width modulation for small values of control signal increment is an amplitude-pulse modulator of the second kind. In order to improve the efficiency of using an active filter-stabilizer, which is part of the DC traction substation converter, the task was set to synthesize the transfer function of its converter's voltage controller. When analyzing a closed automatic control system, it was established that the transfer function of the voltage controller, which ensures the implementation of processes of finite duration in the closed automatic control system, includes a proportional part, an integral part, and a differential part. To determine the time constants for the transfer function of the PID-controller, as well as its damping coefficient, a closed automatic control system of the active filter-stabilizer voltage converter was investigated using an apparatus of Z-transformation. The result of synthesizing the transfer function of the voltage controller has established the parameters for the controller's transfer function, which ensure that the process of finite duration is executed in a closed system of automatic control over the converter's output voltage. The transition process in the system with a stepwise input effect of the processes of finite duration has been calculated, which confirmed that the transition process in the system ends after three clock intervals of discreteness. Establishing a transition process that ends over the finite number of discrete intervals, which is determined by the order of the characteristic equation, means that the process has been optimized for performance