Backlash compensation for plants with saturating actuators

A compensation scheme is proposed for plants subject to both saturation and backlash in series at the actuator. It is shown that the series connection of a backlash inverse, saturation and the backlash itself is equivalent to a saturation function at a different level to the original saturation, and we call this the saturation equivalence'. Therefore, it is proposed to include such a backlash inverse in the compensator. This is shown to be optimal in a sense defined in the article. It is then straightforward to devise a compensator scheme based on traditional anti-windup. This is illustrated in both simulation and on a laboratory scale rig with severe backlash. A correction for the chattering observed in the control signal due to the discontinuous nature of the nonlinearity inverse is also presented.