On the Misunderstanding of the Ziegler-Nichols's Formulae Usage

In the Ziegler-Nichols's method of reaction curve, the proportional gain should be calculated as an inverse relation of the plant steady-state gain. One of the reasons behind this is to avoid an excessively high loop gain, which can jeopardize many required characteristics of the closed loop. However, many reports, scientific papers and books have been neglecting such gain compensation in the tuning formulae. This brief presents a comprehensive discussion about such uncompensated tuning rules. The main paper finding is that either the stability margin or the disturbance rejection is reduced in this case. A theoretical analysis is performed to obtain the main result. Moreover, a consistent simulation study is also performed to show the impact of the lack of compensation on performance.