Predicting servomechanism dynamic errors from frequency response measurements

A theory is presented for analytically relating frequency domain criteria to time domain performance criteria. Third-order models are shown to adequately predict dynamic errors in a wide variety of high order physical systems with bandwidths differing by more than 100 to 1. Model coefficients lie in a relatively small region of the coefficient plane, suggesting that check-out spot frequencies and tolerances previously established empirically may be of general use. Good agreement is observed between predictions based on design data and experimental frequency response results obtained under field conditions on tolerancing an electro-hydraulic servo to satisfy dynamic error constraints on time domain inputs. When used in reverse, the technique predicts system filter properties from time domain measurements. Results are applicable to both manual and automatic test procedures. The general form of low-order model permits a reasonable approximation to frequency domain tolerances by inspection, reducing costly development and field tests.