The solution of the problem of controlling the arc welding process by robotic technological complexes by the quality criterion of the produced products is proposed in this paper. The statement of the problem is given, the criterion of the quality in the form of the goal function is described. The mathematical models based on the principles of J. Forrester's system dynamics is developed. The main indicators that affect the quality of the welding process in RTC and their relationships are identified as system levels. The external factors that depend on the indicators and affect them are also defined. The functional dependencies of the indicators were obtained as a result of approximation of statistical data based on long-term observations of the process. A system of the differential equations that describe the cause-effect relationships between the indicators and the factors is developed. Based on the mathematical model, an algorithm for the search for control actions, the implementation of which minimizes the goal function was developed. The developed models and the control algorithms might significantly improve the quality of the arc welding process. The proposed software is testing as a part of the RTC Kawasaki technical control system at OJSC "Transmash" (Engels, Russia).