Feedforward control design for finite-time transition problems of non-linear MIMO systems under input constraints

Abstract

A new approach is presented for the feedforward control design of non-linear systems with the application to finite-time setpoint transitions under input constraints. This contribution extends recently presented results for the SISO case to non-linear quadratic MIMO systems. The inversion-based design treats the transition task as a two-point boundary value problem (BVP) defined in the input–output coordinates of the considered system. For its solvability, free parameters are provided in ansatz functions for the highest output derivatives. This concept allows the direct incorporation of input constraints within the formulation of the BVP. The resulting BVP with free parameters can be solved, e.g., with a standard MATLAB function. The load transport of an overhead crane serves as an example to illustrate the concept.

Acknowledgements

The article was written when K. Graichen was with Institut für Systemdynamik, Universität Stuttgart, Germany. Currently he is with Centre Automatique et Systèmes, Ecole Nationale Supérieure des Mines de Paris, 75272 Paris, Cedex O6, France. The authors dedicate this paper to Michael Fliess on the occasion of his 60th birthday to acknowledge his ideas and works which have initiated many research and PhD projects at Universität Stuttgart.