Tuning of PIλ Controllers for FOPTD Plants via the Stability Boundary Locus

This study intends to present the systematic design procedure of stabilizing fractional order proportional integral controllers for first order plus time delay (FOPTD) plants via the stability boundary locus (SBL) method. Proposed method gives generalized computation equations for tuning related controllers within desired frequency ranges. Besides, equations to compute the real root boundary (RRB) of the SBL are presented. In spite of the classical design technique, this paper proposes to find the starting and ending points and the stability region of the stability boundary of the system by heuristic approach. This method ensures the stability by analytically obtained formulas instead of testing the regions of the SBL with arbitrary selected points. This proves the advantage and the contribution of the proposed procedure. Obtained equations are applied on examples and the results are illustratively given. Comparisons with the literature showed the effectiveness of the proposal.