TY - JOUR

T1 - Synthesis of H∞ PID controllers

T2 - A parametric approach

AU - Ho, Ming Tzu

N1 - Funding Information:
The author would like to thank the anonymous reviewers for their valuable comments and suggestions. This work was supported by the National Science Council of Taiwan under Grant NSC 89-2218-E-006-034.

PY - 2003/6

Y1 - 2003/6

N2 - This paper considers the problem of synthesizing proportional-integral-derivative (PID) controllers for which the closed-loop system is internally stable and the H∞-norm of a related transfer function is less than a prescribed level for a given single-input single-output plant. It is shown that the problem to be solved can be translated into simultaneous stabilization of the closed-loop characteristic polynomial and a family of complex polynomials. It calls for a generalization of the Hermite-Biehler theorem applicable to complex polynomials. It is shown that the earlier PID stabilization results are a special case of the results developed here. Then a linear programming characterization of all admissible H∞ PID controllers for a given plant is obtained. This characterization besides being computationally efficient reveals important structural properties of H∞ PID controllers. For example, it is shown that for a fixed proportional gain, the set of admissible integral and derivative gains lie in a union of convex sets.

AB - This paper considers the problem of synthesizing proportional-integral-derivative (PID) controllers for which the closed-loop system is internally stable and the H∞-norm of a related transfer function is less than a prescribed level for a given single-input single-output plant. It is shown that the problem to be solved can be translated into simultaneous stabilization of the closed-loop characteristic polynomial and a family of complex polynomials. It calls for a generalization of the Hermite-Biehler theorem applicable to complex polynomials. It is shown that the earlier PID stabilization results are a special case of the results developed here. Then a linear programming characterization of all admissible H∞ PID controllers for a given plant is obtained. This characterization besides being computationally efficient reveals important structural properties of H∞ PID controllers. For example, it is shown that for a fixed proportional gain, the set of admissible integral and derivative gains lie in a union of convex sets.

UR - http://www.scopus.com/inward/record.url?scp=0038034165&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0038034165&partnerID=8YFLogxK

U2 - 10.1016/S0005-1098(03)00078-5

DO - 10.1016/S0005-1098(03)00078-5

M3 - Article

AN - SCOPUS:0038034165

SN - 0005-1098

VL - 39

SP - 1069

EP - 1075

JO - Automatica

JF - Automatica

IS - 6

ER -