In this paper, the combination of a nonlinear system and a robust sliding-mode controller with sliding integral surface is studied. This controller is composed of a linear part and a nonlinear part defined by a non-smooth function. Calculating the frequency response curve of such a system can be time-consuming and difficult using time integration methods. An original algorithm based on the harmonic balance method and capable of directly calculating the periodic solutions of a robust sliding-mode controller with sliding integral surface is proposed. In addition, the classical numerical methods for continuation of nonlinear frequency response curves and stability calculation of periodic solutions have been adapted to take into account the integral component of the control law. Finally, experimental validations on a non-linear structure have been carried out, attesting to the efficiency of the proposed controller and the robustness of the proposed numerical tools.