Systematic Approach to Design a Finite Time Convergent Differentiator in Second Order Sliding Mode Controller

This paper presents a systematic approach to design a Lyapunov based super twisting differentiator. The differentiator will be shown convergent in a finite time whilst the relevant time is accurately estimated.  This differentiator is the main part to establish the sliding surface in higher order sliding mode. The differentiator  is used in the prescribed control structure  to regulate pressures of hydrogen and oxygen of a nonlinear Polymer Electrolyte Membrane Fuel Cells (PEMFCs) to prolong the stack life. The aim of the control strategy is to minimize and keep  the deviation between the pressures of hydrogen and oxygen. The deviation forms a sliding surface, where its appropriate differentiation is required in the control law. It is why to reconstruct finite time derivatives in a closed-loop control.  Finally, simulation result and a comparative study verify the performance of the proposed differentiator and the control structure to provide convergent estimator in finite time.