A nonlinear benchmark problem for robust control design

The problem of H_∞ optimal control for the plant consisting from two-mass and non-linear spring is considered in the paper. Till now two mass problem (benchmark problem) was considered for linear cases only. The novelty our work is generalisation of this problem (using the describing function method) for non-linear cases. The H_∞ control theory is firstly adapted to cope with non-linear plants. To this end the theorem is given asserting that the considered non-linear system is optimal in the sense of H_∞ norm criterion if corresponding harmonically linearized system is optimal in the same sense. This fact enables one, by utylization of describing function method, to bring the non-linear two-mass dynamical model to the linear approximation form and thereby to apply H_∞ - type procedures.