This invention pertains to processing continuous webs such as paper, film, composites, and the like, in dynamic continuous processing operations. More particularly, it relates to accumulating limited lengths of such continuous webs and to controlling tension in such continuous webs during the processing operation. Both tension control and limited accumulations are achieved in a festoon system by connecting a corresponding festoon to actuator or the like, sensing variables such as position, tension, velocity, and acceleration parameters related to the web and the festoon, and providing active force commands, in response to the sensed variables, to cause translational movement, generally including a target acceleration, in the upper festoon rolls to control tension disturbances in the web while providing limited accumulation of a length of the web. In some applications of the invention, the festoon control system is used to attenuate tension disturbances. In other applications of the invention, the festoon control system is used to create controlled tension disturbances.