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Both fuzzy logic and sliding mode can compensate the steady-state error of proportional-derivative (PD) control. This paper presents parallel sliding mode compensations for fuzzy PD controllers. The asymptotic stability of fuzzy PD control with first-order sliding mode compensation in the parallel structure is proven. For the parallel structure, the finite time convergence with a super-twisting second-order sliding-mode is guaranteed

Stable Fuzzy PD Control with Parallel Sliding Mode Compensation with Application to Rigid Manipulator