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Minimization of \(\ell_{2}\) norm of the error signal in posicast input command shaping: a polynomial approach. (English) Zbl 1266.93052

Summary: In this paper, design of a posicast input command shaper is formulated in discrete-time domain as minimization of \(\ell_2\) norm of the error sequence. This optimization task is solved by simple algebraic manipulation with polynomials, namely, solving two-sided linear equations with polynomials and modular shift of a polynomial. Numerical examples are given to demonstrate properties of the optimal design in contrast with the classical Smith’s design technique achieving complete cancellation of residual vibrations.

MSC:

93B51 Design techniques (robust design, computer-aided design, etc.)
93C05 Linear systems in control theory

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PolyX
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References:

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