Non-linear design for cost of feedback reduction in systems with large parameter uncertainty †

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Abstract
Feedback systems containing linear, minimum-phase plants with large parameter uncertainty may be designed to achieve specified performance tolerances over the entire range of parameter uncertainty. The principal ‘cost of feedback’ is in the feedback loop bandwidth, which is generally much larger than that of the system as a whole. This makes the system very sensitive to sensor noise and high-frequency parasitics. It is shown how a non-linear ‘first-order reset element’ (FORE) may be used to drastically decrease the feedback loop transmission bandwidth. One is logically led to FORE by simple, linear feedback frequency response concepts. The paper assumes that the primary design problem is to satisfy quantitative response tolerances to command inputs. However, disturbances at the plant are not neglected, but the specification on such disturbances is in the damping of the step response. An important feature of the non-linear design is that the system response to command inputs is almost exactly that of a linear system designed for the same specifications, permitting linear superposition for such inputs. The disturbance response is nonlinear.