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In this paper, we present a robust control design and analysis for a single axis servo positioning system. A new method that is based on inequalities and bounded constrained optimization technique is developed for tuning the performance weighting function. The effect of parameter changes in the system model are treated as a set of parametric uncertainties. It is shown that the proposed method can simplify the design procedure of H∞ robust controller design. The developed controllers are implemented experimentally; high robustness, precision, and high bandwidth are achieved.