Gain Space Stability Analysis of Nonlinear Systems under PI Control

This study examines the nonlinear stability of general systems under single-loop PI control. The analysis focuses on the positive feedback region of the gain space which is important, for instance, when the system is open-loop unstable. By analyzing the normal form equation about a critical gain setting, the nonlinear stability and dynamics are classified for such systems. Criteria for global stability and sensitivity of system stability to set-point change and/or error are derived based on the derivatives of the nonlinear gain curve. Some of the results are demonstrated experimentally.