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 controlling tension in such continuous webs during the processing operation. Tension is controlled in a dancer control system by connecting a corresponding dancer roll to an actuator apparatus or the like, sensing variables such as position, tension, velocity, and acceleration parameters related to the web and the dancer roll, and providing active force commands, in response to the sensed variables, to cause translational movement, generally including a target acceleration, in the dancer roll to control tension disturbances in the web. In some applications of the invention, the dancer control system is used to attenuate tension disturbances. In other applications of the invention, the dancer control system is used to create tension disturbances.