Comparing method of receptances and optimization-based techniques for pole placement of time-delayed systems

In this paper, two approaches for pole placement in time-delayed systems (TDS) are studied. These include the method of receptances (MoR) and optimization-based technique that explicitly uses the information of the closed-loop poles of the TDS. In MoR, an algebraic system of equations are solved to obtain the closed-loop gains that place the poles of the system at desired locations. However, there is no guarantee that, these poles correspond to the rightmost region of the spectrum. Therefore, the stability of the closed-loop system is not guaranteed. Also, the MoR has only been applied for the case of single delay. In the optimization approach, Galerkin approximations are used to obtain the characteristic roots of the closed-loop system. Further, an objective function containing the information of the rightmost root and desired pole location is minimized using particle swarm optimization (PSO). It is observed that in optimization-based techniques, one can easily handle systems with multiple delays. If the optimization problem converges to the global minimum, pole-placement and stability are guaranteed. However if the optimization problem converges to a local minimum, with the precise information on the rightmost root of the system, the stability can be determined.