A SimpleFourierAnalysisTechniquefor MeasuringtheDynamic Responseof Manual ControlSystems

From apractical standpoint mostdynamic response analysis techniques arecomplicated, expensive, andtimeconsuming tomechanize andoperate. Thesetechniques usually require digital orspecial-purpose analog equipment, andthecomputations areoften performed sometime after dataarecollected. Adaptive paramater tracking techniques partially overcome these faults: buttheyeither haveprescribed forms, which isan undesirable restriction forbasic research, orinthecaseoffree-form methods thecomputational requirements becomeexcessive. To over- comethese drawbacks, anon-line Fourier analysis technique hasbeen developed whichdeals onlywiththeinput anderror signals inamanual feedback control system. Several sine wavesareusedfortheinput, and theon-line datameasurement includes theerror variance andasimple meansforobtaining thesineandcosine transforms oftheerror signal ateachoftheinput frequencies. Fromthis relatively small amountof data, weshowsimple waystocompute theopen- andclosed-loop dynamic response atinput frequencies andtherelative amountoflinearly corre- lated powerintheerror signal. Thispaperdescribes therationale and theory forthetechnique anddiscusses twomethods formechanizing it; oneinvolving standard analog computer components andonebasedon conventional electromechanical components. Finally, atypical application ofthis method ispresented.