Revisiting the Reaction Curve Based Tuning Method for Continuous Sliding Mode Controllers: Frequency Domain Analysis

Sliding mode control (SMC) provides strong robustness against matched disturbances. Among SMC schemes, the super-twisting algorithm (STA) provides continuous control action and finite-time convergence for systems of relative degree one. However, in real applications, actuator imperfections and unmodeled dynamics prevent true finite-time convergence and cause high-frequency oscillations called chattering. The chattering effect can be mitigated by tuning control parameters, for instance, through frequency-domain analysis. Yet, most existing methods rely on simplified system models, limiting their applicability to complex systems. This work proposes a generalized frequency-domain framework for STA gain tuning based on a first-order plus dead time (FOPDT) model. The method identifies FOPDT parameters from the reaction curve and employs describing function and harmonic balance analysis to predict analytically the chattering amplitude, average energy, and frequency. The resulting relations provide explicit guidelines for tuning STA gains to minimize chattering while maintaining robust performance. Validation through both simulations and experiments on a DC motor position control system confirms that the proposed approach achieves improved robustness and accuracy compared with standard STA and PI tuning methods.