Relationship on Stabilizability of LTI Systems by P and PI Controllers

Authors

  • Zhiping Zhang,

    1. Department of Electrical and Computer Engineering, National University of Singapore, Singapore 119260, Singapore
    Search for more papers by this author
  • Qing-Guo Wang,

    Corresponding author
    1. Department of Electrical and Computer Engineering, National University of Singapore, Singapore 119260, Singapore
    • Department of Electrical and Computer Engineering, National University of Singapore, Singapore 119260, Singapore
    Search for more papers by this author
  • Yong Zhang

    1. GE Water and Process Technologies, 1800 Cailun Road, Zhangjiang High-tech Park, Pudong Shanghai 201203, China
    Search for more papers by this author

Abstract

This paper investigates the relationship on stabilizability of linear time-invariant (LTI) systems by P and PI controllers. Elementary tools such as the Routh stability criterion and Root-Locus method are employed in the analysis. It is found that PI can stabilize all the systems that P stabilizes but in general the converse is not true. The cases with the equivalence of stabilizability by P and PI are established and they are in general low-order systems with few zeros. The cases with non-equivalence are also identified.

Abstract

On étudie dans cet article la relation sur la stabilité des systèmes invariants en temps linéaire (LTI) par des contrôleurs P et PI. Des outils élémentaires tels que le critère de stabilité de Routh et la méthode de Root-Locus sont employés dans l'analyse. On a trouvé que le PI peut stabiliser tous les systèmes que P stabilise, mais en général l'inverse n'est pas vrai. Les cas d'équivalence de stabilité entre P et PI sont établis et s'avèrent en général des systèmes de faible ordre avec peu de zéros. Les cas de non-équivalence sont également déterminés.

Ancillary