Design of Proportional-Integral-Retarded (PIR) Controllers for Second-Order LTI Systems.

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 d while achieving the PIR tuning as an explicit function of d and system parameters.