Neural control is paramount in maintaining upright stance of a human; however, the associated time delay affects stability. In the design and control of wearable robots to augment human stance, the neural delay dynamics are often overly simplified or ignored leading to over specified systems. In this letter, the neural delay dynamics of human stance are modelled and embedded in the control of a supernumerary robotic tail to augment human balance. The actuation, geometric and inertial parameters of the tail are examined. Through simulations it was shown that by incorporating the delay dynamics, the tail specification can be greatly reduced. Further, it is shown that robustness of stance is significantly enhanced with a supernumerary tail and that there is positive impact on muscle fatigue.