Design of feedback systems with non-minimum-phase unstable plants†

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Abstract
Feedback systems with right half-plane poles and zeros may have inherently very poor sensitivity properties. In the design procedure presented, the closed-loop poles are-restricted to two possible regions in the complex plane. One region is s≤ −σ. σ>0. A second is the interior and boundary of a circle in the left half-plane. The design is optimum in the sense of maximizing the gain factor uncertainty, for which the restriction is satisfied. The design procedure is very simple to execute and results in loop transmission poles and zeros which are symmetrical with respect to the boundary of the forbidden region. The closed-loop poles lie entirely on the boundary, over the range of gain uncertainty.