As a classical and effective method for solving various time-varying problems, the zeroing neural network (ZNN) is widely applied in the scientific and industrial realms. In plentiful studies on the ZNN model, its robustness and convergence have been two essential criteria to evaluate the quality of the model. Improvements in the ZNN model have been focused on its convergence speed; however, the adjustability of its convergence speed has been neglected in most prior works, which restricts its extensive promotion in practical application. Considering the above-mentioned issue, a well-designed activation function (WDAF) is designed. Based on the WDAF, a robust predefined-time convergence ZNN (RPTCZNN) model with adjustable convergence speed is proposed to solve the dynamic matrix inversion problem. In addition, the upper bound of the RPTCZNN model's convergence time is theoretically validated by strict mathematical analysis in a noiseless and noisy environment. Finally, several simulation experiments of the proposed model are conducted to find solutions of dynamic matrix inversion with different dimensions. Moreover, the realization of the tracking control of the robotic manipulator further illustrates the model's superior convergence and robustness.