https://de.wikipedia.org/wiki/Chirp

#      amp, minFrq, maxFrq, tSec = (10, 10, 300, 30)
import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt
x=np.arange(1,300000)
y=10*np.sin(31.415926535897931*( pow(1.058324104020218,(x*0.000199996614513)) -1) /np.log(1.058324104020218))
plt.show()
plt.plot(x,y)
plt.show()

y=amp*sin( a* (b**(x*c))-1) / log(d) )
  =amp*sin( a/log(d)* (b**(x*c))-1)  )

0.000199996614513=samplingrate in sec. (gatherPeriod==1?)
31.415926535897931 = pi*10 =? 2*pi*f0
1.058324104020218 = k
x*0.000199996614513 =t
1.058324104020218**60 = 30

sin( 2*pi*f0/ln(k)*(k**t-1) )
f(t)=f0*k**t = f0*e**(t*ln(k))

k**t=30 (from 10 to 300 -> 300/10=30)

log(k**t)=log(30)
log(k)*t=log(30)
log(k)=log(30)*(1/t)
log(k)=log(30**(1/t))
k=30**(1/t)
30**(1/60.) = 1.0583241040202176

-----------------------------------------------------------------


  figure();
  h=pzplot(ssc.ss_cl(3),ssc.ss_o(3),ssc.ss_od(3));
  setoptions(h,'FreqUnits','Hz','Grid','on');legend('location','sw');


  %figure();bode(ssc.ss_o(3));
  %figure();tf=tf(ssc.ss_o) pzplot(tf(3));


  h=bodeplot(ssc.ss_cl(3),ssc.ss_o(3),ssc.ss_od(3));
  setoptions(h,'FreqUnits','Hz','Grid','on');

  h=pzplot(ssc.ss_cl(3),ssc.ss_o(3),ssc.ss_od(3));
  setoptions(h,'FreqUnits','Hz','Grid','on');


  h=bodeplot(ssc.ss_cl(3),ssc.ss_o(3),ssc.ss_od(3));
  setoptions(h,'FreqUnits','Hz','Grid','on');
  getoptions(h)




continous to discrete
web(fullfile(docroot, 'control/ref/c2d.html'))


h = tf(10,[1 3 10],'IODelay',0.25); 
hd = c2d(h,0.1)




function f=SCRATCH()
open('stage_closed_loop.slx')


  [m1,m2]=identifyFxFyStage();
  controlSystemDesigner(1,m2.tf_py);    % <<<<<<<<< This opens a transferfiûnction that can be edited

  %identification toolbox
  systemIdentification

  
  
  
  
  %opt=tfestOptions('Display','off');
  %opt=tfestOptions('Display','on','initializeMethod','svf');
  %opt=tfestOptions('Display','on','initializeMethod','iv','WeightingFilter',[]);
  %opt=tfestOptions('Display','on','initializeMethod','iv','WeightingFilter',[1,5;20,570]);
  %tf1 = tfest(mot1frq, 6, 4, opt);
  % Model refinement
  % Options = tf1.Report.OptionsUsed;
  % Options.WeightingFilter = 'prediction';
  % tf1_1 = pem(mot1frq, tf1, Options)





  bodeplot(mot1frq,tf1)
  mag,phase=bode(tf1,frq)
  figure(1)
  subplot(211)


  bodeplot(tf1)

  Opt = n4sidOptions('N4Horizon',[15 15 15]);
  n4s3 = n4sid(mot1frq, 3, Opt)





  %tf([1 2],[1 0 10])
  %specifies the transfer function (s+2)/(s^2+10) while
  sys=tf([1],[1,0,0])
  bode(sys)
  step(sys)

  sys=tf([1],[1,-1,2]) %instable

  sys=tf([1],[1,1,2]) %stable


  %0dB at 12 Hz=12*2*pi rad/s =75.4=k^2 -> k=8.6833

  sys=tf([10],[1,0,0])
  %1/s^2 -> 0dB at 1Hz -40dB/decade
  %10=+20dB


  sys=tf([1],[1,0,2]) %not damped constant sine after step


  sys=zpk([],[1,0,0],100) %stable

  sys=zpk([],[-10,-10],100)


  %parker stage 1 
  %!encoder_sim(enc=1,tbl=9,mot=9,posSf=13000./2048)
  %!encoder_inc(enc=1,tbl=1,mot=1,posSf=13000./650000)
  %!motor_servo(mot=1,ctrl='ServoCtrl',Kp=25,Kvfb=400,Ki=0.02,Kvff=350,Kaff=5000,MaxInt=1000)
  %!motor(mot=1,dirCur=0,contCur=800,peakCur=2400,timeAtPeak=1,IiGain=5,IpfGain=8,IpbGain=8,JogSpeed=10.,numPhase=3,invDir=True,servo=None,PhasePosSf=1./81250,PhaseFindingDac=100,PhaseFindingTime=50,SlipGain=0,AdvGain=0,PwmSf=10000,FatalFeLimit=200,WarnFeLimit=100,InPosBand=2,homing='enc-index')
  Ts=2E-4 % discrete sample time (servo period)
  Kp=25,Kvfb=400,Ki=0.02,Kvff=350,Kaff=5000,MaxInt=1000
  Kp=25,Kvfb=0,Ki=0,Kvff=0,Kaff=0,MaxInt=0


  num=7.32
  den=[5.995e-04 4.897e-02   1.]
  open('stage_closed_loop.slx')
  %sim('stage_closed_loop.slx')

  sys=tf(num,den)
  bode(sys)
  G = tf(1.5,[1 14 40.02]);
  controlSystemDesigner('bode',sys);
  controlSystemDesigner
  linearSystemAnalyzer
  load ltiexamples
  linearSystemAnalyzer(sys_dc)

  controlSystemDesigner('bode',sys);
  controlSystemDesigner(1,sys);    % <<<<<<<<< This opens a transferfiûnction that can be edited
1
  num=[8.32795069e-11, 1.04317228e-08, 6.68431323e-05, 3.31861324e-03, 7.32824533e+00];
  den=[5.26156641e-18, 1.12897840e-14, 7.67853031e-12, 1.03201301e-08, 2.05154780e-06, 1.34279894e-03, 7.19229912e-02, 1.00000000e+00];
  mot2=tf(num,den);
  controlSystemDesigner('bode',mot2);
end


m1=10;        d1=10;             k1=0;
m2=.3;       d2=0.15;            k2=100;
m3=1.2;      d3=.04;            k3=10;

%k2 determines resonance frequency k2 higher -> resfrq higher
%d2 determines the damping d2=0  no damping d2=10 strong damping
%m2 determines how much energy is in the resonance

%m1 is big compared to the other masses
%d1 is the speed dependant friction
%k1 can be set to 0, because these is no position for no force
%-> but this means for 1/s^2 the system is not observable any more

ks=k1+k2+k3;
ds=d1+d2+d3;

A=[  0      1      0      0     0      0      ;
    -ks/m1 -ds/m1  k2/m1  d2/m1 k3/m1  d3/m1  ;
     0      0      0      1     0      0      ;
     k2/m2  d2/m2 -k2/m2 -d2/m2 0      0      ;
     0      0      0      0     0      1      ;
     k3/m1  d3/m1  0      0    -k3/m3 -d3/m3  ];
B=[ 0 1 0 0 0 0]';
C=[ 1 0 0 0 0 0];
D=[0];

ss1=ss(A,B,C,D);
bodeplot(ss1,{.1,1000});
tf(ss1)


%simplified no resonance
A=[  0      1      ;
    -k1/m1 -d1/m1  ];
B=[ 0 1 ]';
C=[ 1 0 ];
D=[0];
ss1=ss(A,B,C,D);
bodeplot(ss1,{.1,1000});
tf(ss1)
chkCtrlObsv(ss1,'')
%but with k1=0 or d1=0 the system is neither controllable nor observable
%-> the 
p = eig(A);
disp(p);

K = place(A,B,[-5 -10]);