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In general, to control industrial processes that show an inverse response output is difficult. This difficulty arises because achievable performance and robustness levels are competing factors that the designer has to deal with. In this paper we focus on proportional integral derivative (PID) control of inverse response processes, in particular with the Direct Synthesis design for disturbance rejection DS-d tuning method of Chen and Seborg. The paper presents equations that link the control system design performance parameter (closed-loop control system speed) with its minimum robustness level, measured with the maximum sensitivity M_S, for the mentioned tuning method. In this way, the proposed result allows to obtain robust PID control systems with M_S ≤ 2 for inverse response processes. The examples show the effectiveness of the proposed design parameter lower limit estimation for the DS-d tuning method.