Non-linear behavior in wave-based control

This work investigates how geometric non-linear behavior affects the wave-based control strategy, which appears to assume linearity in using superposition of waves. It is found that only non-linearities located at the actuator-system interface (where the wave measurements are made) affect the accuracy, and that, in any case, the resulting errors are small. Even with strong non-linearities in the rest of the flexible system, the wave based control still works perfectly provided the local behavior of the actuator-system interface is linear or close to linear (and the initial and final static deflections of the system are equal). If necessary therefore, one could add a linear, elastic component between it and the remainder of the flexible system to recover "perfect" control. A second option is simply to accept the initial, small error in the non-linear case and to correct it by a further motion of the system. The third solution investigated is to define the "waves" in a less-than-optimal way that is completely insensitive to even the interface non-linearities but which still provides very good motion and vibration control. The paper presents these ideas and illustrates them with numerical simulations and experiments on a single-link flexible robot, made of light carbon fibre, which exhibits pronounced geometrically non-linear behavior.