Loop shaping for robust performance using Rbode plot

H_∞ and μ-synthesis have been widely used to design controllers to achieve robust performance. However, these automated tools often do not provide much insight into the relationship between the open loop frequency response and the performance in the presence of model uncertainties. This paper presents a method for translating the robust performance criterion into contours on the open loop Rbode plot of a compensated SISO system so that robust controllers can be directly synthesized with classical loop shaping. The design concept is to shape the open loop response to avoid intersections between the contours and magnitude and phase graphs. In contrast to the asymptotic criteria in the literature, these contours incorporate both phase and magnitude information, and provide precise bounds in the vicinity of the 0 dB crossover frequency. An application of this concept to the design of the controller for an lateral tape motion compensation system shows its utility.