Delay Margin Computation and Controller Design of Time-delayed AGC System Based on Root Locus Analysis

To investigate the small-signal stability of automatic generation control (AGC) system with constant communication delay, this paper establishes its state-space based on Padé approximation and conducts eigenvalue calculation. Then, by tracking the change of eigenvalues with time delay, the time-delay margin can be confirmed. Different controller parameters have complex influence on time delay margin and damping performance, so this paper utilizes particle swarm optimization (PSO) to obtain the optimal PI controller parameters to derive delay margin largest and an ideal damping performance. Finally, the simulation studies verify the correctness of time-delay margin calculation and indicate the AGC system has an ideal damping performance with optimal PI controller parameters

Root-Locus Analysis of Delayed First and Second Order Systems

For finite dimensional linear system the root-locus method is well established however for the case of delayed systems the method has some problems due to the transcendental term involved. This work intends to illustrate the problems that arises when a root-locus diagram is performed as well as to develop a Matlab function that provides the root-locus diagram for delayed low order systems. In this way, some comments about the problems that should be tackled to obtain a generalization of the computational method for delayed systems with real m poles and n zeros