Synthesis of inverse filters with projected dynamical systems

The present paper describes a procedure for synthesising an inverse filter for a complex hysteretic nonlinearity as it occurs in active materials such as piezoelectric ceramics, magne-tostrictive materials and shape memory alloys using the so-called modified Prandtl-Ishlinskii approach. In this synthesis procedure the parameters of an appropriate linear error model have to be optimised in a convex polyhedron to ensure the existence of the corresponding inverse filter. As in future work concerned with iterative and adaptive compensation strategies the determination of the parameters should be performed on-line, the solution of the underlying convex quadratic programming problem is formulated as the global exponentially stable equilibrium point of a properly projected dynamical system.