Sliding mode control with perturbation estimation (SMCPE): a new approach

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Abstract
Sliding mode control (SMC) of a general class of nonlinear control systems is considered in this work. The conventional SMC technique requires knowledge of the upperbounds of disturbances and modelling uncertainties to assure robustness. However, this may not be easy to obtain. As a remedy, an estimation process for these dynamic perturbations is employed jointly with the SMC technique. This new methodology, sliding mode control with perturbation estimation (SMCPE), offers a robust feedback control with much lower gains than its conventional counterparts against slowly varying perturbations. This resolves one of the problematic issues which has caused concern over the years of development of SMC applications. An interesting perspective of selecting the cut-off frequency for s dynamics is presented with a novel upperbound argument. Much desirable tracking fidelity is arrived through SMCPE in the computer simulation studies for a two-link manipulator. A companion approach to SMCPE, the discrete equivalent of it, is also studied in this paper. A discrete SMC controller is developed for the same class of systems and perturbations using the discrete attractivity condition. This method is shown to possess properties similar to the continuous SMCPE.