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good approx model

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This commit is contained in:
zamofing_t
2018-10-04 15:19:34 +02:00
parent fa00a1ef25
commit c19f588450
2 changed files with 102 additions and 59 deletions
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73
matlab/identifyFxFyStage.m
View File

@@ -14,23 +14,21 @@ function [mot1,mot2]=identifyFxFyStage()
obj.currstep=iddata([zeros(10,1); obj.currstep.data(:,2)],[zeros(10,1); obj.currstep.data(:,3)],50E-6); obj.currstep=iddata([zeros(10,1); obj.currstep.data(:,2)],[zeros(10,1); obj.currstep.data(:,3)],50E-6);
f=load(strcat(path,sprintf('full_bode_mot%d.mat',motid))); f=load(strcat(path,sprintf('full_bode_mot%d.mat',motid)));
obj.frq=f.frq*2*pi; %convert from Hz to rad/s obj.w=f.frq*2*pi; %convert from Hz to rad/s
if motid==2
f.db_mag(1:224)=f.db_mag(225); % reset bad values at low frequencies
end
obj.mag=10.^(f.db_mag/20); %mag not in dB obj.mag=10.^(f.db_mag/20); %mag not in dB
obj.phase=f.deg_phase*pi/180; %phase in rad obj.phase=f.deg_phase*pi/180; %phase in rad
response = obj.mag.*exp(1j*obj.phase); response = obj.mag.*exp(1j*obj.phase);
obj.meas= idfrd(response,obj.frq,0); obj.meas= idfrd(response,obj.w,0);
end end
function tfc=currstep(obj) function tfc=currstep(obj)
opt=tfestOptions; opt=tfestOptions;
opt.Display='off'; opt.Display='off';
tfc = tfest(obj.currstep, 2, 0,opt); tfc = tfest(obj.currstep, 2, 0,opt);
den=tfc.Denominator; s=str2ndOrd(tfc);
num=tfc.Numerator;
k=num(1);
w0=sqrt(num(1));
damp=den(2)/2/w0;
s=sprintf('k:%g w0:%g damp:%g\n',k,w0,damp);
%disp(s); %disp(s);
%h = stepplot(tf1); %h = stepplot(tf1);
%l=obj.currstep.OutputData %l=obj.currstep.OutputData
@@ -45,6 +43,36 @@ function [mot1,mot2]=identifyFxFyStage()
setoptions(h,'FreqUnits','Hz','Grid','on'); setoptions(h,'FreqUnits','Hz','Grid','on');
end end
function s=str2ndOrd(tf)
den=tf.Denominator;
num=tf.Numerator;
k=num(1)/den(3);
w0=sqrt(den(3));
damp=den(2)/2/w0;
s=sprintf('k:%g w0:%g damp:%g\n',k,w0,damp);
end
function tf=fyModel()
num=[ 2.36527033e+11, 1.17108082e+13, 3.62387303e+17];
den=[ 1.00000000e+00, 6.64495206e+03, 2.12777376e+07, ...
1.23728427e+10, 3.07054470e+13, 1.72592127e+15, ...
5.39888656e+17];
tf=idtf(num,den);
end
function tf=fxModel()
num=[ 1.23284092e+11, 4.14791803e+13, 1.18702926e+18, ...
2.96296718e+20, 2.67179357e+24, 4.04662786e+26, ...
1.59131515e+30, 1.02778572e+32, 1.64551888e+35];
den=[ 1.00000000e+00, 6.93892369e+03, 3.17041055e+07, ...
7.66104262e+10, 2.36504992e+14, 2.23054854e+17, ...
5.12578678e+20, 2.04416512e+23, 3.27771400e+26, ...
4.77145416e+28, 3.85452959e+31, 1.28911178e+33, ...
9.52157664e+34];
tf=idtf(num,den);
end
function mot=fyStage() function mot=fyStage()
mot=loadData('/home/zamofing_t/Documents/prj/SwissFEL/epics_ioc_modules/ESB_MX/python/MXTuning/18_10_02/',1); mot=loadData('/home/zamofing_t/Documents/prj/SwissFEL/epics_ioc_modules/ESB_MX/python/MXTuning/18_10_02/',1);
mot.tfc=currstep(mot); mot.tfc=currstep(mot);
@@ -52,12 +80,13 @@ function [mot1,mot2]=identifyFxFyStage()
opt=tfestOptions; opt=tfestOptions;
opt.Display='off'; opt.Display='off';
opt.initializeMethod='iv'; opt.initializeMethod='iv';
opt.WeightingFilter=[1,5;20,670]*(2*pi); % Hz->rad/s conversion opt.WeightingFilter=[1,5;30,670]*(2*pi); % Hz->rad/s conversion
figure(); figure();
mot.tf4_2 = tfest(mot.meas, 4, 2, opt); mot.tf2_0 = tfest(mot.meas, 2, 0, opt);disp(str2ndOrd(mot.tf2_0));
mot.tf6_4 = tfest(mot.meas, 6, 4, opt); mot.tf_mdl= fyModel();
h=bodeplot(mot.meas,'r',mot.tf4_2,'b',mot.tf6_4,'g'); %h=bodeplot(mot.meas,'r',mot.tf4_2,'b',mot.tf6_4,'g');
h=bodeplot(mot.meas,'r',mot.tf2_0,'b',mot.tf_mdl,'g',mot.w);
setoptions(h,'FreqUnits','Hz','Grid','on'); setoptions(h,'FreqUnits','Hz','Grid','on');
end end
@@ -69,16 +98,14 @@ function [mot1,mot2]=identifyFxFyStage()
opt=tfestOptions; opt=tfestOptions;
opt.Display='off'; opt.Display='off';
opt.initializeMethod='iv'; opt.initializeMethod='iv';
opt.WeightingFilter=[1,5;20,670]*(2*pi); % Hz->rad/s conversion opt.WeightingFilter=[1,4;10,670]*(2*pi); % Hz->rad/s conversion
figure(); figure();
mot.tf4_2 = tfest(mot.meas, 4, 2, opt); mot.tf2_0 = tfest(mot.meas, 2, 0, opt);disp(str2ndOrd(mot.tf2_0));
mot.tf6_4 = tfest(mot.meas, 6, 4, opt);
mot.tf13_9 = tfest(mot.meas, 13, 9, opt); mot.tf13_9 = tfest(mot.meas, 13, 9, opt);
num=[5.42637491e-24 1.45926254e-21 5.20861422e-17 9.92527094e-15 1.16707977e-10 1.31240975e-08 7.03191689e-05 3.08626613e-03 7.32824533e+00]; mot.tf_mdl = fxModel();
den=[2.01035570e-35,2.33560078e-31,9.14767135e-28,2.52369732e-24,7.42150891e-21,6.89695386e-18,1.65017156e-14,5.77522779e-12,1.08386286e-08,1.13336206e-06,1.27552247e-03,2.19776479e-02,1.00000000e+00]; %h=bodeplot(mot.meas,'r',mot.tf4_2,'b',mot.tf6_4,'g',mot.tf13_9,'m',mot.tf_py,'b');
mot.tf_py = idtf(num,den); h=bodeplot(mot.meas,'r',mot.tf2_0,'b',mot.tf_mdl,'g',mot.w);
h=bodeplot(mot.meas,'r',mot.tf4_2,'b',mot.tf6_4,'g',mot.tf13_9,'m',mot.tf_py,'b');
setoptions(h,'FreqUnits','Hz','Grid','on'); setoptions(h,'FreqUnits','Hz','Grid','on');
%controlSystemDesigner('bode',1,mot.tf_py); % <<<<<<<<< This opens a transferfiûnction that can be edited %controlSystemDesigner('bode',1,mot.tf_py); % <<<<<<<<< This opens a transferfiûnction that can be edited
@@ -91,10 +118,16 @@ end
function f=SCRATCH() function f=SCRATCH()
[m1,m2]=identifyFxFyStage();
controlSystemDesigner(1,m2.tf_py); % <<<<<<<<< This opens a transferfiûnction that can be edited
%identification toolbox %identification toolbox
systemIdentification systemIdentification
%opt=tfestOptions('Display','off'); %opt=tfestOptions('Display','off');
%opt=tfestOptions('Display','on','initializeMethod','svf'); %opt=tfestOptions('Display','on','initializeMethod','svf');
%opt=tfestOptions('Display','on','initializeMethod','iv','WeightingFilter',[]); %opt=tfestOptions('Display','on','initializeMethod','iv','WeightingFilter',[]);
@@ -183,7 +216,5 @@ function f=SCRATCH()
controlSystemDesigner('bode',mot2); controlSystemDesigner('bode',mot2);
[m1,m2]=identifyFxFyStage();
controlSystemDesigner(1,m2.tf_py); % <<<<<<<<< This opens a transferfiûnction that can be edited
end end

88
python/MXTuning.py
View File

@@ -61,20 +61,25 @@ class MXTuning(Tuning):
def bode_model_plot(self, mot,base): def bode_model_plot(self, mot,base):
self.bode_full_plot(mot,base) self.bode_full_plot(mot,base)
fig=plt.gcf() fig=plt.gcf()
_N=1.#E-3 # normalization factor: -> moves 3 decades to right but has factors around 1
# s -> ms
# Hz -> kHz
# rad/s -> rad/ms
if mot==1: if mot==1:
db_mag1=17.3 #dB #identify matlab: k:0.671226 w0:134.705 damp:0.191004
mag1=10**(db_mag1/20) mag1=0.671226 #10**(db_mag1/20)
f1=6.5 #Hz db_mag1=20*np.log10(mag1)#dB
w1=f1*2*np.pi #rad/sec w1=134.705*_N #rad/sec
f1=w1/2/np.pi; # ca. 6.5Hz
T1=1/w1 T1=1/w1
d1=.7 # daempfung =1 -> keine resonanz -> den1= np.poly1d([T1,1])**2 d1=0.19 # daempfung =1 -> keine resonanz -> den1= np.poly1d([T1,1])**2
num1=np.poly1d([mag1]) num1=np.poly1d([mag1])
den1 = np.poly1d([T1**2,2*T1*d1,1]) den1 = np.poly1d([T1**2,2*T1*d1,1])
#first resonance frequency #first resonance frequency
f2=np.array([197,199]) f2=np.array([197,199])
d2=np.array([.02,.02])#daempfung d2=np.array([.02,.02])#daempfung
w2=f2*2*np.pi #rad/sec w2=f2*2*np.pi*_N #rad/sec
T2=1/w2 T2=1/w2
num2 = np.poly1d([T2[0]**2,2*T2[0]*d2[0],1]) num2 = np.poly1d([T2[0]**2,2*T2[0]*d2[0],1])
den2 = np.poly1d([T2[1]**2,2*T2[1]*d2[1],1]) den2 = np.poly1d([T2[1]**2,2*T2[1]*d2[1],1])
@@ -83,34 +88,36 @@ class MXTuning(Tuning):
#current loop 2nd order approx #current loop 2nd order approx
f4=900. #identification with matlab: k=1, w0=8725, d=0.75
d4=1 # daempfung =1 -> keine resonanz -> den1= np.poly1d([T1,1])**2 dc=.75 # daempfung =1 -> keine resonanz -> den1= np.poly1d([T1,1])**2
w4=f4*2*np.pi #rad/sec wc=8725.*_N # rad/sec
T4=1/w4 #...but phase lag seems to have earlier effect -> reduce wc
num4 = np.poly1d([1.]) wc*=.5 # rad/sec
den4 = np.poly1d([T4**2,2*T4*d4,1]) fc=wc/2/np.pi # ca 1388Hz
#mdl= signal.lti(num4, den4) #num denum Tc=1/wc
#bode(mdl) numc = np.poly1d([1.])
denc = np.poly1d([Tc**2,2*Tc*dc,1])
num=num1*num2*num4#*num3 num=num1*num2*numc#*num3
den=den1*den2*den4#*den3 den=den1*den2*denc#*den3
mdl= signal.lti(num, den) #num denum mdl= signal.lti(num, den) #num denum
print num,den print num
print den
print mdl print mdl
elif mot==2: elif mot==2:
# basic 1/s^2 system with damping an d resonance #identify matlab: k:1.7282 w0:51.069 damp:0.327613
db_mag1=17.3 #dB mag1=1.7282 #10**(db_mag1/20)
mag1=10**(db_mag1/20) db_mag1=20*np.log10(mag1)#dB
f1=4.5 #Hz w1=51.069*_N #rad/sec
w1=f1*2*np.pi #rad/sec f1=w1/2/np.pi; # ca. 6.5Hz
d1=.3 # daempfung =1 -> keine resonanz -> den1= np.poly1d([T1,1])**2
T1=1/w1 T1=1/w1
num1 = np.poly1d([mag1]) d1=0.32 # daempfung =1 -> keine resonanz -> den1= np.poly1d([T1,1])**2
num1=np.poly1d([mag1])
den1 = np.poly1d([T1**2,2*T1*d1,1]) den1 = np.poly1d([T1**2,2*T1*d1,1])
#first resonance frequency #resonance frequency
f2=np.array([57.8,61.8]) f2=np.array([57.8,61.8])
d2=np.array([.05,.055])#daempfung d2=np.array([.08,.095])#daempfung
w2=f2*2*np.pi #rad/sec w2=f2*2*np.pi #rad/sec
T2=1/w2 T2=1/w2
num2 = np.poly1d([T2[0]**2,2*T2[0]*d2[0],1]) num2 = np.poly1d([T2[0]**2,2*T2[0]*d2[0],1])
@@ -118,9 +125,9 @@ class MXTuning(Tuning):
mdl= signal.lti(num2, den2) #num denum mdl= signal.lti(num2, den2) #num denum
#bode(mdl) #bode(mdl)
#second resonance frequency #resonance frequency
f3=np.array([138,151]) f3=np.array([136,148])
d3=np.array([.04,.03])#daempfung d3=np.array([.05,.05])#daempfung
w3=f3*2*np.pi #rad/sec w3=f3*2*np.pi #rad/sec
T3=1/w3 T3=1/w3
num3 = np.poly1d([T3[0]**2,2*T3[0]*d3[0],1]) num3 = np.poly1d([T3[0]**2,2*T3[0]*d3[0],1])
@@ -128,9 +135,9 @@ class MXTuning(Tuning):
#mdl= signal.lti(num3, den3) #num denum #mdl= signal.lti(num3, den3) #num denum
#bode(mdl) #bode(mdl)
#second resonance frequency #resonance frequency
f4=np.array([410,417]) f4=np.array([410,417])
d4=np.array([.015,.02])#daempfung d4=np.array([.015,.015])#daempfung
w4=f4*2*np.pi #rad/sec w4=f4*2*np.pi #rad/sec
T4=1/w4 T4=1/w4
num4 = np.poly1d([T4[0]**2,2*T4[0]*d4[0],1]) num4 = np.poly1d([T4[0]**2,2*T4[0]*d4[0],1])
@@ -138,8 +145,9 @@ class MXTuning(Tuning):
#mdl= signal.lti(num3, den3) #num denum #mdl= signal.lti(num3, den3) #num denum
#bode(mdl) #bode(mdl)
f5=np.array([228,230]) #resonance frequency
d5=np.array([.03,.03])#daempfung f5=np.array([230,233])
d5=np.array([.04,.04])#daempfung
w5=f5*2*np.pi #rad/sec w5=f5*2*np.pi #rad/sec
T5=1/w5 T5=1/w5
num5 = np.poly1d([T5[0]**2,2*T5[0]*d5[0],1]) num5 = np.poly1d([T5[0]**2,2*T5[0]*d5[0],1])
@@ -147,18 +155,22 @@ class MXTuning(Tuning):
#current loop 2nd order approx #current loop 2nd order approx
fc=900. #identification with matlab: k=1, w0=8725, d=0.75
dc=1 # daempfung =1 -> keine resonanz -> den1= np.poly1d([T1,1])**2 dc=.75 # daempfung =1 -> keine resonanz -> den1= np.poly1d([T1,1])**2
wc=fc*2*np.pi #rad/sec wc=8725.*_N # rad/sec
#...but phase lag seems to have earlier effect -> reduce wc
wc*=.5 # rad/sec
fc=wc/2/np.pi # ca 1388Hz
Tc=1/wc Tc=1/wc
numc = np.poly1d([1.]) numc = np.poly1d([1.])
denc = np.poly1d([Tc**2,2*Tc*dc,1]) denc = np.poly1d([Tc**2,2*Tc*dc,1])
#mdl= signal.lti(num4, den4) #num denum
#bode(mdl)
num=num1*num2*num3*num4*num5*numc num=num1*num2*num3*num4*num5*numc
den=den1*den2*den3*den4*den5*denc den=den1*den2*den3*den4*den5*denc
mdl= signal.lti(num, den) #num denum mdl= signal.lti(num, den) #num denum
print num
print den
print mdl
bode(mdl) bode(mdl)
w=np.logspace(0,np.log10(2000),1000)*2*np.pi w=np.logspace(0,np.log10(2000),1000)*2*np.pi
w,mag,phase = signal.bode(mdl,w) w,mag,phase = signal.bode(mdl,w)