Optimization of Robustness Index in Robust Control Systems Based on Integral Square Error

The concept of a robustness index in robust control theory was first introduced by Trung Do Cao and Manh Nguyen Van for general industrial processes and specifically for thermal processes. This index enables the preselection of the desired robustness level for a system. Theoretically, the robustness index can be arbitrarily selected within the range (0, +∞), with larger values indicating greater robustness of the control system. However, the robustness index must also ensure that the output signal closely tracks the input signal. In process control, two common criteria for evaluating control performance are the integral square error (ISE) and the integral absolute error (IAE). This study presents a method to determine the appropriate range of robustness index values such that the system’s ISE is optimized. Specifically, it identifies the robustness index value that minimizes the ISE and characterizes the range of robustness index values for which the ISE remains near its minimum. The proposed approach provides a systematic basis for selecting the robustness index in control system design, particularly for thermal process applications.