This paper proposes a universal guaranteed active fault diagnosis framework for systems with zonotopic, polytopic, or ellipsoidal uncertainties. Based on the notion of the second-order cone, a novel set representation that unifies the above set forms for set-membership estimation in fault diagnosis is derived. The principle of fault diagnosis within a specified time horizon is to design an input sequence to separate the output sets of all fault scenarios. In our framework, the input design problem is formulated as a mathematical program with complementarity constraints. To reduce computational complexity, a smoothing approach is applied such that gradient-based methods can be utilized to search for solutions efficiently. The effectiveness of the proposed method is demonstrated by a numerical example.