# Null Frequencies optSpec.freqNull = freqGap_rps optSpec.freqNullInterp = True # FRF Estimate freq_rps, Txy, Cxy, Sxx, Syy, Sxy, TxyUnc, SxxNull, Snn = FreqTrans.FreqRespFuncEstNoise(rExc, z, optSpec) freq_hz = freq_rps * rps2hz I2 = np.repeat([np.eye(2)], Txy.shape[-1], axis=0).T ToEstNom = Txy # Txy = Sxy / Sxx ToEstUnc = -TxyUnc # TxyUnc = np.abs(Sxn / Sxx) ToEstCoh = Cxy # Cxy = np.abs(Sxy)**2 / (Sxx * Syy) SoEstNom, SoEstUnc, SoEstCoh = FreqTrans.TtoS(ToEstNom, ToEstUnc, ToEstCoh) LoEstNom, LoEstUnc, LoEstCoh = FreqTrans.StoL(SoEstNom, SoEstUnc, SoEstCoh) print(np.sum(SxxNull, axis = -1) / np.sum(Sxx, axis = -1)) print(np.sum(Snn, axis = -1) / np.sum(Syy, axis = -1)) ToEstSNR = np.abs(ToEstNom / ToEstUnc)**2 SoEstSNR = np.abs(SoEstNom / SoEstUnc)**2 LoEstSNR = np.abs(LoEstNom / LoEstUnc)**2 #%% Nyquist Plot - Output Complimentary Sensitivity Function ToLinUncMag = np.abs(ToLinUnc) ToEstUncMag = np.abs(ToEstUnc) numOut, numIn = ToLinNom.shape[0:-1] ioArray = np.array(np.meshgrid(np.arange(numOut), np.arange(numIn))).T.reshape(-1, 2)
# Null Frequencies
optSpec.freqNull = freqGap_rps
optSpec.freqNullInterp = True
# FRF Estimate
freq_rps, Txu, Cxu, Sxx, Syy, Sxy, TxuUnc, SxxNull, Snn = FreqTrans.FreqRespFuncEstNoise(
uExc, uCtrl, optSpec)
freq_hz = freq_rps * rps2hz
I2 = np.repeat([np.eye(2)], Txu.shape[-1], axis=0).T
TiEstNom = -Txu # Si = I - Ti
TiEstUnc = TxuUnc # TxuUnc = np.abs(Sxu / Sxx)
TiEstCoh = Cxu # Cxy = np.abs(Sxu)**2 / (Sxx * Syy)
SiEstNom, SiEstUnc, SiEstCoh = FreqTrans.TtoS(TiEstNom, TiEstUnc, TiEstCoh)
LiEstNom, LiEstUnc, LiEstCoh = FreqTrans.StoL(SiEstNom, SiEstUnc, SiEstCoh)
print(np.sum(SxxNull, axis=-1) / np.sum(Sxx, axis=-1))
TiEstSNR = np.abs(TiEstNom / TiEstUnc)**2
SiEstSNR = np.abs(SiEstNom / SiEstUnc)**2
LiEstSNR = np.abs(LiEstNom / LiEstUnc)**2
#%%
numFreq = len(freqExc_rps)
numTime = len(time_s)
scaleLinUnc = np.sqrt(numFreq / numTime)
TiLinUnc = scaleLinUnc * FreqTrans.FreqResp(
sysTiUnc, freqLin_rps) # Noise STD scaled to Uncertainty by sqrt(numFreq)
I2 = np.repeat([np.eye(2)], TiLinNom.shape[-1], axis=0).T
sysSi = (np.eye(2) - sysTi)
pSigma = [0.0, 0.0]
mSigma = [1.0, 1.0]
pIn = 0.5 * control.ss([], [], [], np.diag(pSigma))
mIn = 0.5 * control.ss([], [], [], np.diag(mSigma))
sysTiUnc = sysSi * sysK * (sysR * pIn - sysN * mIn)
gainTiLinUnc_mag, phaseTiLinUnc_rad, _ = control.freqresp(sysTiUnc,
omega=freqLin_rps)
TiLinUnc = gainTiLinUnc_mag * np.exp(1j * phaseTiLinUnc_rad * deg2rad)
# Ti to Si, Si to Li
SiLinNom, SiLinUnc, _ = FreqTrans.TtoS(TiLinNom, TiLinUnc)
LiLinNom, LiLinUnc, _ = FreqTrans.StoL(SiLinNom, SiLinUnc)
#%% Excitation
numExc = 2
numCycles = 3
ampInit = 1
ampFinal = 1
freqMinDes_rps = 0.1 * hz2rps * np.ones(numExc)
freqMaxDes_rps = 10.1 * hz2rps * np.ones(numExc)
freqStepDes_rps = (10 / freqRate_hz) * hz2rps
methodSW = 'zip' # "zippered" component distribution
# Generate MultiSine Frequencies
freqExc_rps, sigIndx, time_s = GenExcite.MultiSineComponents(
freqMinDes_rps, freqMaxDes_rps, freqRate_hz, numCycles, freqStepDes_rps,
methodSW)
LaEstNomList = []
LaEstUncList = []
LaEstCohList = []
for iSeg, seg in enumerate(oDataSegs):
freq_rps, Txy, Cxy, Sxx, Syy, Sxy, TxyUnc, SxxNull, Snn = FreqTrans.FreqRespFuncEstNoise(
vExcList[iSeg], vFbList[iSeg], optSpec)
freq_hz = freq_rps * rps2hz
TaEstNom = -Txy # Sa = I - Ta
TaEstUnc = TxyUnc # TxuUnc = np.abs(Sxu / Sxx)
TaEstCoh = Cxy # Cxy = np.abs(Sxu)**2 / (Sxx * Suu)
SaEstNom, SaEstUnc, SaEstCoh = FreqTrans.TtoS(TaEstNom, TaEstUnc, TaEstCoh)
LaEstNom, LaEstUnc, LaEstCoh = FreqTrans.StoL(SaEstNom, SaEstUnc, SaEstCoh)
TaEstNomList.append(TaEstNom)
TaEstUncList.append(TaEstUnc)
TaEstCohList.append(TaEstCoh)
SaEstNomList.append(SaEstNom)
SaEstUncList.append(SaEstUnc)
SaEstCohList.append(SaEstCoh)
LaEstNomList.append(LaEstNom)
LaEstUncList.append(LaEstUnc)
LaEstCohList.append(LaEstCoh)
print(np.sum(SxxNull, axis=-1) / np.sum(Sxx, axis=-1))
T_InputNames = sigExcList
T_OutputNames = sigFbList