Nonlinear Control of Non-Observable Non-Flat MIMO State Space Systems Using Flat Inputs

Abstract

Despite a large popularity of flatness based methods for nonlinear open and closed loop control, fundamental questions have not been answered and remain open. One of the most elementary of these questions is a systematic computation of flat outputs. Motivated by the problem of actuator placement the dual concept of flat inputs has been introduced which have then shown to be useful quantities for the control of non-flat systems regardless of physical realization as pure computational quantities. For observable systems flat inputs can be derived algebraically, but it has been shown that they exist for (certain) non-observable systems as well. The computation in the general non-observable case, however, remains an open problem.In this contribution we propose a control method based on flat inputs by combining two existing SISO approaches, generalizing it to the MIMO case and circumventing some of its drawbacks, in particular the unsolved flat input computation for non-observable systems. Our method can then be applied to nonlinear non-observable non-flat MIMO systems with stable internal dynamics. We illustrate this approach by an academic example.