TY - JOUR
T1 - Observer-Based PID Control Strategy for the Stabilization of Delayed High Order Systems with up to Three Unstable Poles
AU - Cruz-Díaz, César
AU - Del Muro-Cuéllar, Basilio
AU - Duchén-Sánchez, Gonzalo
AU - Márquez-Rubio, Juan Francisco
AU - Velasco-Villa, Martín
N1 - Publisher Copyright:
© 2022 by the authors. Licensee MDPI, Basel, Switzerland.
PY - 2022/5/1
Y1 - 2022/5/1
N2 - In this paper, a new method to manage the stabilization and control problems of n-dimensional linear systems plus dead time, which includes one, two, or three unstable poles, is proposed. The control methodology proposed in this work is an Observer-based Proportional-Integral-Derivative (PID) strategy, where an observer and a PID controller are used to relocate the original unstable open-loop poles to stabilize the resultant closed-loop system. The observer provides an adequate estimation of the delayed-free variables and the PID uses the delay-free variables estimated by the proposed observer. Also, step-tracking is achieved in the overall control scheme. Necessary and sufficient conditions are presented to ensure closed-loop stability based on the open loop parameters of the system. The observer-based PID strategy considers five to seven constant parameters to obtain a stable closed-loop system. A general procedure to implement the proposed control strategy is presented and its performance is evaluated by means of numerical simulations.
AB - In this paper, a new method to manage the stabilization and control problems of n-dimensional linear systems plus dead time, which includes one, two, or three unstable poles, is proposed. The control methodology proposed in this work is an Observer-based Proportional-Integral-Derivative (PID) strategy, where an observer and a PID controller are used to relocate the original unstable open-loop poles to stabilize the resultant closed-loop system. The observer provides an adequate estimation of the delayed-free variables and the PID uses the delay-free variables estimated by the proposed observer. Also, step-tracking is achieved in the overall control scheme. Necessary and sufficient conditions are presented to ensure closed-loop stability based on the open loop parameters of the system. The observer-based PID strategy considers five to seven constant parameters to obtain a stable closed-loop system. A general procedure to implement the proposed control strategy is presented and its performance is evaluated by means of numerical simulations.
KW - PID controller
KW - linear delay systems
KW - observers
KW - stabilization
UR - http://www.scopus.com/inward/record.url?scp=85129319115&partnerID=8YFLogxK
U2 - 10.3390/math10091399
DO - 10.3390/math10091399
M3 - Artículo
AN - SCOPUS:85129319115
SN - 2227-7390
VL - 10
JO - Mathematics
JF - Mathematics
IS - 9
M1 - 1399
ER -