Robustness and Performance Parameterization of Smooth Second Order Sliding Mode Control

Novel robustness and performance parameters are established for Smooth Super Twisting Algorithm (SSTA). The stability of SSTA is well established for arbitrary gains using homogeneity approach. The design and tuning of the controller parameters is a major issue and no analytic design method is available so far. A novel Lyapunov function is proposed and by the virtue of stability analysis, the stability bounds for a certain class of uncertainties are determined. In addition, the issue of finite time convergence is also explored, resulting in determination of the settling time as a function of the controller parameters. The proposed settling time formulation suggests a methodical approach to SSTA design in contrast to the available rules of thumb. Unlike the literature available for Higher Order Sliding Mode (HOSM) controllers, the proposed design framework is validated against a challenging problem of the Underground Coal Gasification (UCG) process control. Like the other process control problems the chosen problem is nonlinear and contains significant uncertainties.