This note presents a design technique for the delay-based controller called proportional integral retarded (PIR), which solves the regulation problem of a general class of stable second-order LTI systems. Using spectral analysis, the technique yields a tuning strategy for the PIR by placing a triple real dominant root for the closed-loop system. This result ultimately guarantees a desired exponential decay rate σdwhile achieving the PIR tuning as an explicit function of σdand system parameters.
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Ramírez et al. (2015) studied this question.
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