Calculation of PI controller stable region based on D-partition method

Based on D-partition method, a fast calculation approach for PI controller stable region is introduced. The boundary of the PI stable region is calculated first using D-partition method, and then several sets of equations and inequalities are introduced sequentially to judge which side of the boundary is stable. The approach is simple, and can be applied to any self-stable systems with or without time-delays, while only the process frequency responses are needed. To illustrate its feasibility, some examples are given.