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Synthesis of strongly stable state-derivative controllers for a time-delay system using constrained non-smooth optimization. (English) Zbl 1206.93038

Summary: The paper presents an optimization-based algorithm for stabilizing retarded systems using a state-derivative feedback controller. It is shown that an application of such a controller results in neutral dynamics of the closed-loop system if small feedback delays occur. Therefore, the strong stability theory of neutral systems needs to be considered in the controller synthesis problem. The stabilization approach is based on minimizing the spectral abscissa of the closed-loop system over the controller parameter space, subject to a strong stability constraint. The constrained optimization problem is first turned into an unconstrained problem by application of a barrier method. Subsequently, the optimization is performed using both Broyden-Fletcher-Goldfarb-Shanno (BFGS) and hybrid algorithms for non-smooth optimization Matlab utilities. In the application example, the theoretical results are applied to regenerative chatter suppression in cutting process.

MSC:

93B50 Synthesis problems
93C05 Linear systems in control theory
93D15 Stabilization of systems by feedback
93D09 Robust stability
93B40 Computational methods in systems theory (MSC2010)
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