Quantitative synthesis of uncertain cascade feedback systems with plant modification

Abstract

Consider the constrained part (denoted as the plant) of a control system, consisting of n cascaded sections, each of whose outputs can be sensed for feedback purposes. Feedback from these points is to be used to achieve a priori specified tolerances on the system response, despite great uncertainty in plant parameter values. In this first quantitative work of its kind, the feedback is permitted to proceed directly to internal plant variables, constituting ‘ plant modification ’. The reason is that the internal plant signal levels needed to achieve a specific output are now affected by the feedback loops. This is in contrast to previous quantitative research in which the feedback was confined to the plant input. The plant signal levels needed to achieve a specific output were then not influenced by the feedback. Plant modification feedback permits greater reduction in the ‘ cost of feedback ’, in terms of feedback loop bandwidths and effect of sensor noise, at the cost of increase in plant internal signal levels. In this work, the maximum permitted increase γ in signal level, is part of the design specifications. A step by step design proceduro is presonted for satisfying this γ requirement and the system response tolerances over the given rango of plant uncertainty, and doing so at sensibly minimum ‘ cost of feedback ’. This permits the designer to achieve desired trade-off between increased plant signal level and cost of feedback.