Robust parametric classical control design

This paper extends well-known graphical design tools such as the Nyquist plot, Bode plot, and Nichols charts to the domain of control systems containing parameter uncertainty. We have specifically considered linear interval control systems, namely those where the uncertain parameters appear linearly in the characteristic polynomial and vary in intervals, because in these cases exact construction of frequency envelopes is possible. Using these developments, we calculate various extremal stability margins for such systems, and these are used with standard classical control design techniques to deal with robustness with respect to parametric uncertainty. In addition, we give an effective technique to iteratively select values of the design parameters within given ranges so that the closed loop system produces improved gain or phase margin