Closed‐form minimax time‐delay filters for underdamped systems

This paper derives closed‐form solutions for the parameters of a time‐delay filter designed to be robust to uncertainties in frequencies to be cancelled. It is shown that the slope of the magnitude plot of the two time‐delay filter is zero at the nominal frequency indicating that it is a local maximum. This information is used for deriving the solution of the parameters of the time‐delay filter in closed form. Three time‐delay filters are also designed which force a zero of the filter to be located at the nominal frequency of the system. Uniform and non‐uniform distributions of the penalty over the uncertain regions are permitted in this formulation. The applicability of the proposed technique for the control of multi‐mode systems is also illustrated.