Preferred embodiments of the invention implement techniques for modifying the command trajectory, the architecture of a servomechanism control system, or both, to reduce the servo error during and/or after the command trajectory. An iterative refinement procedure generates for use by the servomechanism control system a corrective input, du, which significantly reduces the error between the desired and actual servomechanism control system outputs. In one embodiment, a uniquely identified plant model is employed in the iterative refinement procedure to compute an approximate gradient that improves the performance and reliability of the refinement procedure. In another embodiment, the actual plant response is used in place of the identified model in the iterative refinement procedure. This is accomplished by time-reversing the stored error signal from a training run, before applying it to the plant to generate an update to the corrective input signal du.