Synthesis of feedback systems with large plant ignorance for prescribed time-domain tolerances†

Abstract

There is given a minimum-phase plant transfer function, with prescribed bounds on its parameter values. The plant is imbedded in a two-degree-of-freedom feedback system, which is to be designed such that the system time response to a deterministic input lies within specified boundaries. Subject to the above, the design should be such as to minimize the effect of sensor white noise at the input to the plant. This report presents a design procedure for this purpose, based on frequency response concepts. The time-domain tolerances are translated into equivalent frequency response tolerances. The latter lead to bounds on the loop-transmission function L(jω), in the form of continuous curves on the Nichols chart. Properties of L(jω) which satisfy these bounds with minimum effect of sensor white noise are derived. The design procedure is quite transparent, providing the designer with the insight to make necessary tradeoffs, at every step in the design process. The same design philosophy may be used to attenuate the effect of disturbances on plants with parameter ignorance.