Multiplicity-Induced-Dominancy Extended to Neutral Delay Equations: Towards a Systematic PID Tuning Based on Rightmost Root Assignment

Recently, the conditions on a multiple spectral value to be dominant for retarded time-delay system with a single delay were deeply explored. Such a property was called Multiplicity-Induced-Dominancy. It was then exploited in the design of delayed stabilizing controllers. As a matter of fact, the approach is merely a delayed-output-feedback where the delay and gain candidates result from the manifold defining the maximal multiplicity of a real spectral value. This can also be seen as a “partial” pole-placement method, which, unlike the methods based on finite spectrum assignment, does not render the closed -oop system finite-dimensional but consists in appropriately controlling its rightmost spectral value. This work aims to extend such a design approach to time-delay systems of neutral type occurring in the classical problem of PID stabilizing design for SISO delayed plants. More precisely, the controller’s gains (k_i, k_p, k_d ) are tuned using the intentional multiplicity’s algebraic constraints allowing to the stabilization of unstable delayed plants. Among others, one of the specificity of such a design method is related to the analytical assignment of the closed-loop solution’s decay rate.