A discrete pole-placement-based and multiestimation-based adaptive control scheme involving a relative adaptation dead zone is presented for a plant with known poles and unknown zeros. The basic usefulness of the proposed multiestimation scheme is related to the use of a set of models of reduced order associated with the multiestimation scheme instead of a high-order one. Depending on the frequency spectrum characteristics of the input and on the estimates evolution, the multiestimation scheme selects on-line the most appropriate model and its related estimation scheme in order to improve the identification and control performances. Robust closed-loop stability is proved even in the presence of unmodeled dynamics of sufficiently small sizes as it has been confirmed by simulation results. The scheme chooses in real time the estimator/controller associated with a particular reduced model possessing the best performance according to an identification performance index by implementing a switching rule between estimators. The switching rule is subject to a minimum residence time at each identifier/adaptive controller parameterization for closed-loop stabilization purposes. A conceptually simple higher-level supervisor, based on heuristic updating rules which estimate on-line the weights of the switching rule between estimation schemes, is discussed.

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In waterjet and laser milling, material is removed from a solid surface in a succession of layers to create a new shape, in a depth-controlled manner. The inverse problem consists of defining the control parameters, in particular, the two-dimensional beam path, to arrive at a prescribed freeform surface. Waterjet milling (WJM) and pulsed laser ablation (PLA) are studied in this paper, since a generic nonlinear material removal model is appropriate for both of these processes. The inverse problem is usually solved for this kind of process by simply controlling dwell time in proportion to the required depth of milling at a sequence of pixels on the surface. However, this approach is only valid when shallow surfaces are etched, since it does not take into account either the footprint of the beam or its overlapping on successive passes. A discrete adjoint algorithm is proposed in this paper to improve the solution. Nonlinear effects and non-straight passes are included in the optimization, while the calculation of the Jacobian matrix does not require large computation times. Several tests are performed to validate the proposed method and the results show that tracking error is reduced typically by a factor of two in comparison to the pixel-by-pixel approach and the classical raster path strategy with straight passes. The tracking error can be as low as 2–5% and 1–2% for WJM and PLA, respectively, depending on the complexity of the target surface.

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