Quantitative feedback theory for active vibration control synthesis

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Abstract
Quantitative feedback theory emphasizes that the major reason for using feedback in control is plant parameter and disturbance uncertainty. The parameter uncertainty is quantitatively expressed by a set of possible plants, and the quantitative formulation of system closed-loop performance by a set of acceptable command-response and disturbance response functions. The latter is treated, the design problem being to find a compensation which guarantees that the actual disturbance transfer function satisfies the closed-loop performance. The case of uncertain highly underdamped poles is examined, and it is shown how quantitative feedback theory handles this case. Two examples are given, one of which is with non-minimum phase compensation. The compensators are of a relatively low order, satisfy gain and phase margin specification, and have low sensitivity to parameter uncertainty.