Practical Guidelines for $PD$ and $PI$ Delay-Based Controllers.

José-Enrique Hernández-Díez (1, 2) , César-Fernando Méndez-Barrios (2) , Silviu-Iulian Niculescu (3)

1 L2S - Laboratoire des signaux et systèmes
2 UASLP - Universidad Autonoma de San Luis Potosi [México]
3 DISCO - Dynamical Interconnected Systems in COmplex Environments

This paper focuses on the control scheme design of two different control schemes using delays. These two low-complexity controllers are direct alternatives for the $PD$ and $PI$ low-order controllers. More precisely, first, we study a $PD$ controller using the Euler approach for approximating the derivative action. Second, we analyze the implications of imposing a delay in the error signal on the integral action of the $PI$ controller for closed-loop response manipulation purposes. Our main contribution lies in proposing some practical guidelines for the tuning of these delayed control schemes such that the closed-loop system is stable. To this end, the criteria developed in this work makes use of the well-known $D$-partition curves method avoiding crossing direction analysis. Finally, in order to test the effectiveness of the proposed methodology, some numerical examples are presented.

Mots clés: LTI Systems; Delay Control; Stability Crossing Curves; PID controllers; SISO systems

Domaines: Systèmes et contrôle [cs.SY]

José-Enrique Hernández-Díez, César-Fernando Méndez-Barrios, Silviu-Iulian Niculescu. Practical Guidelines for $PD$ and $PI$ Delay-Based Controllers.. 15th IFAC Workshop on Time Delay Systems, Sep 2019, Sinaia, Romania. ⟨10.1016/j.ifacol.2019.12.207⟩. ⟨hal-03171091⟩