Experimental flexible beam tip tracking control with a truncated series approximation to uncancelable inverse dynamics

A feedforward design methodology to compensate unstable zeros in linear discrete-time systems with tracking objectives is reviewed. An experimental study for end-point tracking of a flexible beam was performed to validate the effectiveness of the proposed scheme. Results are presented and comparisons with zero-phase error tracking (ZPET) are discussed. The methodology exploits the fact that the noncausal expansion of unstable inverse dynamics is convergent in the region of the complex plane encompassing the unit circle. An approximation to the unstable inverse dynamics that can be implemented follows, by truncating the series and utilizing the necessary preview information. Right-half plane unstable zeros near the unit circle can significantly reduce bandwidth. For such zeros, the series methodology is shown experimentally to yield better performance than ZPET, since both gain as well as phase are compensated.