Causal inversion of a single-link flexible-link manipulator via output planning

Recently, a method was introduced by Bensoman and Le Vey [1] for the stable inversion of a single-input single-output (SISO) non-minimum phase system through the employment of output planning. The use of a causal input via output planning permits the initial conditions to be freely selected. In the application of this method to a single-link flexible-link manipulator (SFLM), for any initial conditions a polynomial is sought for the end-effector's trajectory that cancels the effects of the internal instability of the inverse system. A drawback of this method, however, is that allows for the development of only one polynomial for any initial conditions imposed on the input and output. An extension of this method is proposed in this paper which does not suffer from this drawback. This extension employs exponential functions to define the end-effector's trajectory, which leads not to just one solution, but to a family of solutions. The results of some simulation studies that verify the proposed extension are included.