Both neural network and sliding mode can compensate the steady-state error of proportional-derivative (PD) control. PD control with neural compensation is smooth, but it is not asymptotically stable. PD control with sliding mode is asymptotically stable, but the chattering is big. This paper first analyzes the asymptotic stability of PD control with parallel neural networks and the first-order sliding mode compensation. Then a serial compensation structure is proposed. In the serial compensation, a dead-zone neural PD control assures that the regulation error is bounded. And a super-twisting second-order sliding-mode is used to guarantee finite time convergence of the sliding mode PD control.