Saturday , March 2 2024

Stabilizing High-order Delayed Systems with Minimum-phase Zeros Using Simple Controllers*

C. D. Vázquez Rosas1*, J. F. Márquez Rubio1, B. del Muro Cuéllar1, D. F. Novella Rodríguez2, O. Sename3, L. Dugard3
1 Instituto Politécnico Nacional, ESIME Unidad Culhuacán, Av. Santa Ana 1000,
Coyoacán, 04430, CDMX, México (*Corresponding author),,
2 Universidad de Monterrey, Departamento de Ingeniería, Ignacio Morones Prieto 4500,
66238 San Pedro Garza García, N.L., México
3 Univ. Grenoble Alpes, GIPSA-lab, Grenoble, France,

Abstract: This paper analyses the stabilization and control of delayed processes systems containing minimum phase zeros. The high-order delayed process taken into consideration consists of: one unstable pole and m minimum phase zeros. Sufficient conditions are provided in order to guarantee the existence of a stabilizing basic controllers: Proportional (P), Integral (I) and Derivative (D), i.e., P, PI, PD and PID controllers. The frequency domain approach is used to proof the main results. Additionally an optimal H∞ tuning of the controller is proposed. The adequateness of the obtained results are tested by simulation through the implementation of a continuously stirred-tank reactor model.

Keywords: Zeros, Unstable processes, Time-delay, Stabilization.


C. D. Vázquez Rosas, J. F. Márquez Rubio, B. del Muro Cuéllar, D. F. Novella Rodríguez, O. Sename, L. Dugard, Stabilizing High-order Delayed Systems with Minimum-phase Zeros Using Simple Controllers, Studies in Informatics and Control, ISSN 1220-1766, vol. 28(4), pp. 381-390, 2019.


* This paper is an extended version of the work titled “Stability condition for unstable high-order system with minimumphase zeros plus time-delay”, published in the Congreso Nacional de Control Automático (AMCA) 2017 (Vázquez et al. 2017). Employing a different method for the proof, the current paper presents improved sufficient conditions for P/PI controllers in order to stabilize the process taken into consideration. Another novel element is the sufficient condition to guarantee the existence of stabilizing PD/PID controllers. Finally the theory is employed in order to tune the parameters for the PI/PID controllers.