The simultaneous optimization problem for sensitivity and gain margin

• Published in: IEEE transactions on automatic control Vol. 35; no. 5; pp. 558 - 563
• Main Authors: Yan, W., Anderson, B.D.O.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.05.1990; Institute of Electrical and Electronics Engineers
• Subjects: Applied sciences; Computer science; control theory; systems; Control systems; Control theory. Systems; Exact sciences and technology; Feedback; Gain measurement; Interpolation; Linear systems; Optimal control; Particle measurements; Robust control; Robustness; Systems engineering and theory; Linear system; Feedback system; Compensator; Control synthesis; Robustness; SISO system; Simultaneity; Non minimum phase system; Optimization; Constrained optimization
• ISSN: 0018-9286
• DOI: 10.1109/9.53522

The combined sensitivity and gain margin problem for single-input single-output linear systems is formulated and solved using a complex function interpolation technique. It is proved that this problem always has a real rational solution provided it is solvable in the complex irrational sense. The sensitivity minimization problem subject to a gain margin constraint and its dual problem are also considered. The range of the gain margin constraint is given subject to which the optimal constrained sensitivity is identical with the optimal unconstrained sensitivity. It is shown that, not unexpectedly, the gain margin maximization conflicts with the sensitivity minimization for a nonminimum phase plant.< >