<p>Proportional-integral and proportional-integral-derivative controllers are widely used in industrial process control due to their simple structure. One challenge during controller design is ensuring the robustness of the closed-loop system in the presence of uncertainty in the process model. In the frequency domain, robustness can be assessed using disk margins. Disk margins extend the classical gain and phase margins by representing a family of complex perturbations that account for simultaneous gain and phase variations in the frequency response. In this paper, a frequency-based proportional-integral-derivative controller design procedure is presented to guarantee robust stability using disk margins specifications. The problem is formulated using convex optimization with constraints represented as linear matrix inequalities. The frequency response of the nominal loop transfer function is shaped so that its Nyquist curve avoid the exclusion region given by the disk margins. A method for determining the disk margin parameters from a set of models with uncertainties is also presented. Simulation results shown the application of this method in comparison with controllers designed using the classical stability margins and the linear margins approaches. In the examples, the proposed method results in controllers that meet the disk margins specification and guarantee stable closed-loops for all models in the set.</p>