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PD–PID controller for delayed systems with two unstable poles: a frequency domain approach |
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| Authors: | David Fernando Novella-Rodríguez Basilio del Muro Cuéllar Juan Francisco Márquez-Rubio Miguel Ángel Hernández-Pérez Martin Velasco-Villa |
| Affiliation: | 1. Tecnologico de Monterrey, Escuela de Ingeniería y Ciencias , Ciudad de México, Mexico;2. Instituto Politécnico Nacional (IPN), ESIME Culhuacan , Santa Ana 1000, C.P. 04430, Coyoacan, Ciudad de México, México;3. Sección de Mecatrónica, Departamento de Ingeniería Eléctrica, Cinvestav-IPN, Av. Instituto Politécnico Nacional 2508 , Ciudad de México, Mexico |
| Abstract: | This paper deals with the stability problem of linear delayed systems containing two unstable real poles by means of PD controllers. The analysis presented is based on frequency domain techniques. Necessary and sufficient conditions for the existence of stabilising controllers are given in terms of the parameters of the system and the time delay size. The main result is extended to delayed systems with two unstable poles and n stable real poles. PID controllers are also considered in order to control the studied systems, obtaining similar stability conditions. Numerical examples are presented in order to illustrate the control performance. |
| Keywords: | Time delays unstable system PID controller high order system |