Chapter8FrequencyResponseMethod

Afeedbacksystemhasalooptransferfunction

Determinethecornerfrequencies(breakfrequencies)fortheBodeplot.

Determinetheslopeoftheasymptoticplotatverylowfrequenciesandathighfrequencies.

SketchtheBodemagnitudeplot.

2.Theasymptoticlog-magnitudecurvesfortwotransferfunctionsaregiveninFigure8.2.Sketchthecorrespondingasymptoticphaseshiftcurvesforeachsystem.Determinethetransferfunctionforeachsystem.Assumethatthesystemshaveminimumphasetransferfunctions.

Figure8.2

Chapter9StabilityintheFrequencyDomain

1.TheNyquistplotofaconditionallystablesystemisshowninFigure9.1foraspecificgainK.

(a)Determinewhetherthesystemisstable,andfindthenumberofroots(ifany)intheright-hands-plane.ThesystemhasnopolesofGc(s)G(s)intherighthalf-plane.

(b)Determinewhetherthesystemisstableifthe-1pointliesatthedotontheaxis.

Figure9.1

Adirect-drivearmisaninnovativemechanicalarminwhichnoreducersareusedbetweenmotorsandtheirloads.Becausethemotorrotorsaredirectlycoupledtotheloads,thedrivesystemshavenobacklash,smallfriction,andhighmechanicalstiffness,whichareallimportantfeaturesforfastandaccuratepositioninganddexteroushandlingusingsophisticatedtorquecontrol.

ThegoaloftheMITdirect-drivearmprojectistoachievearmspeedsof10m/s[15].Thearmhastorquesofupto660Nm(475ftlb).Feedbackandasetofpositionandvelocitysensorsareusedwitheachmotor.ThefrequencyresponseofonejointofthearmisshowninFigure9.2(a).Thetwopolesappearat3.7Hzand68Hz.Figure9.2(b)showsthestepresponsewithpositionandvelocityfeedbackused.Thetimeconstantoftheclosed-loopsystemis82ms.Developtheblockdiagr