Parameter Estimation of RIG Roll Experiments

Setup and descriptions

Without ACM model
Turn on wind tunnel
Only 1DoF for RIG roll movement
Use small-amplitude aileron command of CMP as inputs (in degrees) $$U = \delta_{a,cmp}(t)$$
Consider RIG roll angle and its derivative as States (in radians) $$X = \begin{pmatrix} \phi_{rig} \\ \dot{\phi}_{rig} \end{pmatrix}$$
Observe RIG roll angle and its derivative as Outputs (in degrees) $$Z = \begin{pmatrix} \phi_{rig} \\ \dot{\phi}_{rig} \end{pmatrix}$$
Use output error method based on most-likehood(ML) to estimate $$ \theta = \begin{pmatrix} C_{l,\delta_a,cmp} \\ C_{lp,cmp} \end{pmatrix} $$

Startup computation engines



In [1]:

    
%run matt_startup
%run -i matt_utils

button_qtconsole()

#import other needed modules in all used engines
#with dview.sync_imports():
#   import os









    



importing numpy on engine(s)
importing scipy on engine(s)
importing matplotlib on engine(s)
importing scipy.integrate on engine(s)
importing scipy.interpolate on engine(s)
importing math on engine(s)
importing time on engine(s)
importing itertools on engine(s)
importing random on engine(s)






    



:0: FutureWarning: IPython widgets are experimental and may change in the future.

Data preparation

Load raw data



In [27]:

    
filename = 'FIWT_Exp036_20150605144438.dat.npz'

def loadData():
    # Read and parse raw data
    global exp_data
    exp_data = np.load(filename)

    # Select colums
    global T_cmp, da_cmp
    T_cmp = exp_data['data33'][:,0]
    da_cmp = exp_data['data33'][:,3]

    global T_rig, phi_rig
    T_rig = exp_data['data44'][:,0]
    phi_rig = exp_data['data44'][:,2]

loadData()



In [28]:

    
text_loadData()

Check time sequence and inputs/outputs

Click 'Check data' button to show the raw data.

Click on curves to select time point and push into queue; click 'T/s' text to pop up last point in the queue; and click 'Output' text to print time sequence table.



In [29]:

    
def checkInputOutputData():

    #check inputs/outputs
    fig, ax = plt.subplots(2,1,True)
    ax[1].plot(T_cmp,da1_cmp,'r', picker=2)
    ax[0].plot(T_rig,phi_rig, 'b', picker=2)
    ax[1].set_ylabel('$\delta \/ / \/ ^o$')
    ax[0].set_ylabel('$\phi \/ / \/ ^o/s$')
    ax[1].set_xlabel('$T \/ / \/ s$', picker=True)
    ax[0].set_title('Output', picker=True)
    

    fig.canvas.mpl_connect('pick_event', onPickTime)
    fig.show()
    display(fig)

button_CheckData()

Input $\delta_T$ and focused time ranges



In [30]:

    
# Pick up focused time ranges
time_marks = [
[17.6940178696,117,"ramp u1"],
[118.7,230.395312673,"ramp d1"],
[258.807481992,357.486188688,"ramp u2"],
[359.463122988,459.817499014,"ramp d2"],
[461.067939262,558.784538108,"ramp d3"],
[555.553175853,658.648739191,"ramp u4"],
]

# Decide DT,U,Z and their processing method
DT=0.5
process_set = {
            'Z':[(T_cmp, da_cmp,1),],
            'U':[(T_rig, phi_rig,1),],
            'cutoff_freq': 1 #Hz
           }

U_names = ['$\phi_{a,rig} \, / \, ^o$']
Y_names = Z_names = ['$\delta_{a,cmp} \, / \, ^o$']

display_data_prepare()









    





$$\delta_T=500.0(ms)$$






    




Time ranges






    




Idx Start(s) Spam(s) Description
0 17.69 99.31 ramp u1
1 118.70 111.70 ramp d1
2 258.81 98.68 ramp u2
3 359.46 100.35 ramp d2
4 461.07 97.72 ramp d3
5 555.55 103.10 ramp u4






    




$U$
$\phi_{a,rig} \, / \, ^o$






    




$Z$
$\delta_{a,cmp} \, / \, ^o$

Resample and filter data in sections

For each section,

Select time range and shift it to start from zero;
Resample Time, Inputs, Outputs in unique $\delta_T$;
Smooth Input/Observe data if flag bit0 is set;
Take derivatives of observe data if flag bit1 is set.



In [31]:

    
resample(True);

Define dynamic model to be estimated

$$\left\{\begin{matrix}\begin{align} M_{x,rig} &= M_{x,a} + M_{x,f} + M_{x,cg} = 0 \\ M_{x,a} &= \frac{1}{2} \rho V^2S_cb_c C_{la,cmp}\delta_{a,cmp} \\ M_{x,f} &= -F_c \, sign(\dot{\phi}_{rig}) \\ M_{x,cg} &= -m_T g l_{zT} \sin \left ( \phi - \phi_0 \right ) \end{align}\end{matrix}\right.$$



In [68]:

    
%%px --local
#update common const parameters in all engines

angles = range(-170,171,10)
angles_num = len(angles)

#problem size
Nx = 0
Nu = 1
Ny = 1
Npar = 2*angles_num

#reference
S_c = 0.1254   #S_c(m2) 
b_c = 0.7      #b_c(m)
g = 9.81       #g(m/s2)

#static measurement
m_T = 9.585   #m_T(kg)
l_z_T = 0.0416 #l_z_T(m)
V = 30         #V(m/s)

#previous estimations
F_c = 0.06 #F_c(N*m)

#for short
qbarSb = 0.5*1.225*V*V*S_c*b_c
_m_T_l_z_T_g = -(m_T*l_z_T)*g

angles_cmpx = [-41, -35, -30, -25, -20, -15, -10, -5, 5, 10, 15, 20, 25, 30, 35, 41]
Clda_cmpx = np.array([[ 0.0565249,   0.05387389,  0.04652094,  0.03865756,  0.03113176,  0.02383392,
   0.01576805,  0.00682421, -0.00514735, -0.01570602, -0.02364258, -0.02733501,
  -0.0334053,  -0.03834931, -0.04546589, -0.05275809],
 [ 0.04793643,  0.04133362,  0.03510728,  0.02872704,  0.02349928,  0.01987537,
   0.01354014,  0.00666756, -0.00498937, -0.01074795, -0.01714402, -0.02095374,
  -0.02588346, -0.03155207, -0.03824692, -0.04752196],
 [ 0.04250404,  0.03700739,  0.03057273,  0.02586595,  0.01989991,  0.01626642,
   0.01237347,  0.00642308, -0.00551828, -0.01030141, -0.01654802, -0.02143956,
  -0.0268223,  -0.03110662, -0.03565326, -0.04001201,],
 [ 0.03448653,  0.03160534,  0.02700394,  0.02388641,  0.01988023,  0.01532191,
   0.01052986,  0.00572438, -0.00556645, -0.0101715,  -0.01388348, -0.01619465,
  -0.02044906, -0.02510722, -0.03134562, -0.0355593 ]])

Clda_cmp = np.sum(Clda_cmpx, axis=0)
Lda_cmp = qbarSb*Clda_cmp
Da_cmp = scipy.interpolate.interp1d(Lda_cmp, angles_cmpx)

hdr = int(1/DT)

def obs(Z,T,U,params):
    s = T.size
    
    unk_moment = scipy.interpolate.interp1d(angles, params[0:angles_num])
    col_fric   = scipy.interpolate.interp1d(angles, params[angles_num:angles_num*2])
    
    phi = U[:s,0]

    phi_diff = np.copysign(-1,phi[hdr:]-phi[:-hdr])
    phi_diff = np.concatenate((np.ones(hdr-1)*phi_diff[0], phi_diff, np.ones(hdr-1)*phi_diff[-1]))
    
    Da = Da_cmp(-unk_moment(phi)-col_fric(phi_diff))
  
    return Da.reshape((-1,1))



In [69]:

    
display(HTML('<b>Constant Parameters</b>'))
table = ListTable()
table.append(['Name','Value','unit'])
table.append(['$S_c$',S_c,'$m^2$'])
table.append(['$b_c$',b_c,'$m$'])
table.append(['$g$',g,'$m/s^2$'])
table.append(['$m_T$',m_T,'$kg$'])
table.append(['$l_{zT}$',l_z_T,'$m$'])
table.append(['$V$',V,'$m/s$'])
display(table)









    




Constant Parameters






    




Name Value unit
$S_c$ 0.1254 $m^2$
$b_c$ 0.7 $m$
$g$ 9.81 $m/s^2$
$m_T$ 9.585 $kg$
$l_{zT}$ 0.0416 $m$
$V$ 30 $m/s$

Initial guess

Input default values and ranges for parameters
Select sections for trainning
Adjust parameters based on simulation results
Decide start values of parameters for optimization



In [61]:

    
#initial guess
param0 = [_m_T_l_z_T_g*math.sin(a/57.3) for a in angles]+[F_c]*angles_num

param_name = ['Mu_{}'.format(angles[i]) for i in range(angles_num)] \
           + ['Fc_{}'.format(angles[i]) for i in range(angles_num)]
param_unit = ['Nm']*(2*angles_num)

NparID = Npar
opt_idx = range(Npar)
opt_param0 = [param0[i] for i in opt_idx]
par_del = [0.01]*(2*angles_num)
bounds =  [(-4,4)]*(angles_num) + [(0,0.4)]*(angles_num)
display_default_params()

#select sections for training
section_idx = range(len(time_marks))
display_data_for_train()

#push parameters to engines
push_opt_param()









    




Default Parameters for optimization






    




Idx Description $x_0$ unit opt $\delta_{par}$ min max
0 Mu_-170 0.680084083831 Nm * 0.01 -4 4
1 Mu_-160 1.33860206042 Nm * 0.01 -4 4
2 Mu_-150 1.95645326691 Nm * 0.01 -4 4
3 Mu_-140 2.51486736542 Nm * 0.01 -4 4
4 Mu_-130 2.99687971916 Nm * 0.01 -4 4
5 Mu_-120 3.3878467786 Nm * 0.01 -4 4
6 Mu_-110 3.67589095295 Nm * 0.01 -4 4
7 Mu_-100 3.85226145167 Nm * 0.01 -4 4
8 Mu_-90 3.91160013382 Nm * 0.01 -4 4
9 Mu_-80 3.85210428848 Nm * 0.01 -4 4
10 Mu_-70 3.67558140119 Nm * 0.01 -4 4
11 Mu_-60 3.38739424248 Nm * 0.01 -4 4
12 Mu_-50 2.99629794672 Nm * 0.01 -4 4
13 Mu_-40 2.51417403093 Nm * 0.01 -4 4
14 Mu_-30 1.95566943389 Nm * 0.01 -4 4
15 Mu_-20 1.33775154174 Nm * 0.01 -4 4
16 Mu_-10 0.679192718283 Nm * 0.01 -4 4
17 Mu_0 -0.0 Nm * 0.01 -4 4
18 Mu_10 -0.679192718283 Nm * 0.01 -4 4
19 Mu_20 -1.33775154174 Nm * 0.01 -4 4
20 Mu_30 -1.95566943389 Nm * 0.01 -4 4
21 Mu_40 -2.51417403093 Nm * 0.01 -4 4
22 Mu_50 -2.99629794672 Nm * 0.01 -4 4
23 Mu_60 -3.38739424248 Nm * 0.01 -4 4
24 Mu_70 -3.67558140119 Nm * 0.01 -4 4
25 Mu_80 -3.85210428848 Nm * 0.01 -4 4
26 Mu_90 -3.91160013382 Nm * 0.01 -4 4
27 Mu_100 -3.85226145167 Nm * 0.01 -4 4
28 Mu_110 -3.67589095295 Nm * 0.01 -4 4
29 Mu_120 -3.3878467786 Nm * 0.01 -4 4
30 Mu_130 -2.99687971916 Nm * 0.01 -4 4
31 Mu_140 -2.51486736542 Nm * 0.01 -4 4
32 Mu_150 -1.95645326691 Nm * 0.01 -4 4
33 Mu_160 -1.33860206042 Nm * 0.01 -4 4
34 Mu_170 -0.680084083831 Nm * 0.01 -4 4
35 Fc_-170 0.06 Nm * 0.01 0 0.4
36 Fc_-160 0.06 Nm * 0.01 0 0.4
37 Fc_-150 0.06 Nm * 0.01 0 0.4
38 Fc_-140 0.06 Nm * 0.01 0 0.4
39 Fc_-130 0.06 Nm * 0.01 0 0.4
40 Fc_-120 0.06 Nm * 0.01 0 0.4
41 Fc_-110 0.06 Nm * 0.01 0 0.4
42 Fc_-100 0.06 Nm * 0.01 0 0.4
43 Fc_-90 0.06 Nm * 0.01 0 0.4
44 Fc_-80 0.06 Nm * 0.01 0 0.4
45 Fc_-70 0.06 Nm * 0.01 0 0.4
46 Fc_-60 0.06 Nm * 0.01 0 0.4
47 Fc_-50 0.06 Nm * 0.01 0 0.4
48 Fc_-40 0.06 Nm * 0.01 0 0.4
49 Fc_-30 0.06 Nm * 0.01 0 0.4
50 Fc_-20 0.06 Nm * 0.01 0 0.4
51 Fc_-10 0.06 Nm * 0.01 0 0.4
52 Fc_0 0.06 Nm * 0.01 0 0.4
53 Fc_10 0.06 Nm * 0.01 0 0.4
54 Fc_20 0.06 Nm * 0.01 0 0.4
55 Fc_30 0.06 Nm * 0.01 0 0.4
56 Fc_40 0.06 Nm * 0.01 0 0.4
57 Fc_50 0.06 Nm * 0.01 0 0.4
58 Fc_60 0.06 Nm * 0.01 0 0.4
59 Fc_70 0.06 Nm * 0.01 0 0.4
60 Fc_80 0.06 Nm * 0.01 0 0.4
61 Fc_90 0.06 Nm * 0.01 0 0.4
62 Fc_100 0.06 Nm * 0.01 0 0.4
63 Fc_110 0.06 Nm * 0.01 0 0.4
64 Fc_120 0.06 Nm * 0.01 0 0.4
65 Fc_130 0.06 Nm * 0.01 0 0.4
66 Fc_140 0.06 Nm * 0.01 0 0.4
67 Fc_150 0.06 Nm * 0.01 0 0.4
68 Fc_160 0.06 Nm * 0.01 0 0.4
69 Fc_170 0.06 Nm * 0.01 0 0.4






    




Training Data






    




Idx Start(s) Spam(s) Description
0 17.69 99.31 ramp u1
1 118.70 111.70 ramp d1
2 258.81 98.68 ramp u2
3 359.46 100.35 ramp d2
4 461.07 97.72 ramp d3
5 555.55 103.10 ramp u4



In [62]:

    
# select 4 section from training data
#idx = random.sample(section_idx, 4)
idx = section_idx[:]

# interact_guess();
update_guess();

Optimize using ML



In [63]:

    
display_preopt_params()

if False:
    InfoMat = None
    method = 'trust-ncg'
    def hessian(opt_params, index):
        global InfoMat
        return InfoMat
    dview['enable_infomat']=True
    options={'gtol':1}
    opt_bounds = None
else:
    method = 'L-BFGS-B'
    hessian = None
    dview['enable_infomat']=False
    options={'ftol':1e-6,'maxfun':400}
    opt_bounds = bounds

cnt = 0
tmp_rslt = None
T0 = time.time()
print('#cnt,     Time,      |R|')

%time res =  sp.optimize.minimize(fun=costfunc, x0=opt_param0, \
        args=(opt_idx,), method=method, jac=True, hess=hessian, \
        bounds=opt_bounds, options=options)









    




Parameters for optimization






    




Idx Description $x_0$ unit opt $\delta_{par}$ min max
0 Mu_-170 0.680084083831 Nm * 0.01 -4 4
1 Mu_-160 1.33860206042 Nm * 0.01 -4 4
2 Mu_-150 1.95645326691 Nm * 0.01 -4 4
3 Mu_-140 2.51486736542 Nm * 0.01 -4 4
4 Mu_-130 2.99687971916 Nm * 0.01 -4 4
5 Mu_-120 3.3878467786 Nm * 0.01 -4 4
6 Mu_-110 3.67589095295 Nm * 0.01 -4 4
7 Mu_-100 3.85226145167 Nm * 0.01 -4 4
8 Mu_-90 3.91160013382 Nm * 0.01 -4 4
9 Mu_-80 3.85210428848 Nm * 0.01 -4 4
10 Mu_-70 3.67558140119 Nm * 0.01 -4 4
11 Mu_-60 3.38739424248 Nm * 0.01 -4 4
12 Mu_-50 2.99629794672 Nm * 0.01 -4 4
13 Mu_-40 2.51417403093 Nm * 0.01 -4 4
14 Mu_-30 1.95566943389 Nm * 0.01 -4 4
15 Mu_-20 1.33775154174 Nm * 0.01 -4 4
16 Mu_-10 0.679192718283 Nm * 0.01 -4 4
17 Mu_0 -0.0 Nm * 0.01 -4 4
18 Mu_10 -0.679192718283 Nm * 0.01 -4 4
19 Mu_20 -1.33775154174 Nm * 0.01 -4 4
20 Mu_30 -1.95566943389 Nm * 0.01 -4 4
21 Mu_40 -2.51417403093 Nm * 0.01 -4 4
22 Mu_50 -2.99629794672 Nm * 0.01 -4 4
23 Mu_60 -3.38739424248 Nm * 0.01 -4 4
24 Mu_70 -3.67558140119 Nm * 0.01 -4 4
25 Mu_80 -3.85210428848 Nm * 0.01 -4 4
26 Mu_90 -3.91160013382 Nm * 0.01 -4 4
27 Mu_100 -3.85226145167 Nm * 0.01 -4 4
28 Mu_110 -3.67589095295 Nm * 0.01 -4 4
29 Mu_120 -3.3878467786 Nm * 0.01 -4 4
30 Mu_130 -2.99687971916 Nm * 0.01 -4 4
31 Mu_140 -2.51486736542 Nm * 0.01 -4 4
32 Mu_150 -1.95645326691 Nm * 0.01 -4 4
33 Mu_160 -1.33860206042 Nm * 0.01 -4 4
34 Mu_170 -0.680084083831 Nm * 0.01 -4 4
35 Fc_-170 0.06 Nm * 0.01 0 0.4
36 Fc_-160 0.06 Nm * 0.01 0 0.4
37 Fc_-150 0.06 Nm * 0.01 0 0.4
38 Fc_-140 0.06 Nm * 0.01 0 0.4
39 Fc_-130 0.06 Nm * 0.01 0 0.4
40 Fc_-120 0.06 Nm * 0.01 0 0.4
41 Fc_-110 0.06 Nm * 0.01 0 0.4
42 Fc_-100 0.06 Nm * 0.01 0 0.4
43 Fc_-90 0.06 Nm * 0.01 0 0.4
44 Fc_-80 0.06 Nm * 0.01 0 0.4
45 Fc_-70 0.06 Nm * 0.01 0 0.4
46 Fc_-60 0.06 Nm * 0.01 0 0.4
47 Fc_-50 0.06 Nm * 0.01 0 0.4
48 Fc_-40 0.06 Nm * 0.01 0 0.4
49 Fc_-30 0.06 Nm * 0.01 0 0.4
50 Fc_-20 0.06 Nm * 0.01 0 0.4
51 Fc_-10 0.06 Nm * 0.01 0 0.4
52 Fc_0 0.06 Nm * 0.01 0 0.4
53 Fc_10 0.06 Nm * 0.01 0 0.4
54 Fc_20 0.06 Nm * 0.01 0 0.4
55 Fc_30 0.06 Nm * 0.01 0 0.4
56 Fc_40 0.06 Nm * 0.01 0 0.4
57 Fc_50 0.06 Nm * 0.01 0 0.4
58 Fc_60 0.06 Nm * 0.01 0 0.4
59 Fc_70 0.06 Nm * 0.01 0 0.4
60 Fc_80 0.06 Nm * 0.01 0 0.4
61 Fc_90 0.06 Nm * 0.01 0 0.4
62 Fc_100 0.06 Nm * 0.01 0 0.4
63 Fc_110 0.06 Nm * 0.01 0 0.4
64 Fc_120 0.06 Nm * 0.01 0 0.4
65 Fc_130 0.06 Nm * 0.01 0 0.4
66 Fc_140 0.06 Nm * 0.01 0 0.4
67 Fc_150 0.06 Nm * 0.01 0 0.4
68 Fc_160 0.06 Nm * 0.01 0 0.4
69 Fc_170 0.06 Nm * 0.01 0 0.4






    



#cnt,     Time,      |R|
0001,    0.622,       10.0
0002,    1.006,      594.0
0003,    1.520,        9.2
0004,    2.003,        0.5
0005,    2.583,       14.6
0006,    3.007,        1.2
0007,    3.410,        0.3
0008,    3.716,        1.0
0009,    4.039,        0.4
0010,    4.358,        0.3
0011,    4.710,        0.2
0012,    5.163,        0.3
0013,    5.484,        0.2
0014,    5.826,        0.2
0015,    6.139,        0.2
0016,    6.478,        0.2
0017,    6.805,        0.3
0018,    7.140,        0.2
0019,    7.480,        0.2
0020,    7.803,        0.2
0021,    8.123,        0.2
0022,    8.423,        0.2
0023,    8.729,        0.2
0024,    9.043,        0.2
0025,    9.414,        0.2
0026,    9.820,        0.2
0027,   10.253,        0.2
0028,   10.618,        0.2
0029,   11.113,        0.2
0030,   11.420,        0.2
0031,   11.737,        0.2
0032,   12.057,        0.2
0033,   12.486,        0.2
0034,   12.857,        0.2
0035,   13.159,        0.2
0036,   13.462,        0.2
0037,   13.816,      364.0
0038,   14.119,       21.3
0039,   14.428,        2.8
0040,   14.785,        0.7
0041,   15.101,        0.3
0042,   15.457,        0.2
0043,   15.787,        0.2
0044,   16.092,        0.2
0045,   16.554,        0.2
0046,   16.875,        0.2
0047,   17.172,        0.2
0048,   17.541,        0.2
0049,   17.831,        0.2
0050,   18.136,        0.2
0051,   18.510,        0.2
0052,   18.813,        0.2
0053,   19.116,        0.2
0054,   19.454,        0.2
0055,   19.864,        0.2
0056,   20.197,        0.2
0057,   20.498,        0.2
0058,   20.832,        0.1
0059,   21.214,        0.1
0060,   21.525,        0.1
0061,   21.851,        0.1
0062,   22.268,        0.1
0063,   22.661,        0.1
0064,   23.034,        0.1
0065,   23.346,        0.1
0066,   23.651,        0.1
0067,   23.970,        0.1
0068,   24.359,        0.1
0069,   24.742,        0.1
0070,   25.096,        0.1
0071,   25.413,        0.1
0072,   25.744,        0.1
0073,   26.084,        0.1
0074,   26.500,        0.1
0075,   26.865,        0.1
0076,   27.185,        0.1
0077,   27.498,        0.1
0078,   27.943,        0.1
0079,   28.395,        0.1
0080,   28.695,        0.1
0081,   29.019,        0.1
0082,   29.350,        0.1
0083,   29.638,        0.1
0084,   29.958,        0.1
0085,   30.305,        0.1
0086,   30.646,        0.1
0087,   30.964,        0.1
0088,   31.271,        0.1
0089,   31.627,        0.1
0090,   31.929,        0.1
0091,   32.248,        0.1
0092,   32.612,        0.1
0093,   32.915,        0.1
0094,   33.264,        0.1
0095,   33.590,        0.1
0096,   33.931,        0.1
0097,   34.246,        0.1
0098,   34.704,        0.1
0099,   35.027,        0.1
0100,   35.370,        0.1
0101,   35.661,      163.8
0102,   35.977,       10.5
0103,   36.354,        2.3
0104,   36.643,        0.8
0105,   36.965,        0.3
0106,   37.298,        0.2
0107,   37.597,        0.1
0108,   37.899,        0.1
0109,   38.197,        0.1
0110,   38.513,        0.1
0111,   38.936,        0.1
0112,   39.349,        0.1
0113,   39.697,        0.1
0114,   40.061,        0.1
0115,   40.377,        0.1
0116,   40.676,        0.1
0117,   40.993,        0.1
0118,   41.334,        0.1
0119,   41.636,        0.1
0120,   41.928,        0.1
Wall time: 41.9 s

Show and test results



In [64]:

    
display_opt_params()

# show result
idx = range(len(time_marks))
display_data_for_test();

update_guess();









    




Parameters from optimization






    




Idx Description $x$
0 Mu_-170 0.662927864745
1 Mu_-160 1.02495697393
2 Mu_-150 1.50155537121
3 Mu_-140 2.11479230196
4 Mu_-130 2.62096826149
5 Mu_-120 2.88561124751
6 Mu_-110 3.10052920572
7 Mu_-100 3.17920809804
8 Mu_-90 3.02787759785
9 Mu_-80 2.83733114296
10 Mu_-70 2.64511226392
11 Mu_-60 2.55396114985
12 Mu_-50 2.41080176853
13 Mu_-40 2.08821718749
14 Mu_-30 1.69336983029
15 Mu_-20 1.33704658572
16 Mu_-10 0.786124470153
17 Mu_0 0.139630363921
18 Mu_10 -0.502404303052
19 Mu_20 -1.06067095416
20 Mu_30 -1.55388357326
21 Mu_40 -1.97687800236
22 Mu_50 -2.22694733306
23 Mu_60 -2.40065976571
24 Mu_70 -2.58289702002
25 Mu_80 -2.69317701172
26 Mu_90 -2.84181215556
27 Mu_100 -2.89146634773
28 Mu_110 -2.934887953
29 Mu_120 -2.79056578426
30 Mu_130 -2.55945471641
31 Mu_140 -1.89558536214
32 Mu_150 -1.26825577494
33 Mu_160 -0.713354250566
34 Mu_170 -0.656151848094
35 Fc_-170 0.06
36 Fc_-160 0.06
37 Fc_-150 0.06
38 Fc_-140 0.06
39 Fc_-130 0.06
40 Fc_-120 0.06
41 Fc_-110 0.06
42 Fc_-100 0.06
43 Fc_-90 0.06
44 Fc_-80 0.06
45 Fc_-70 0.06
46 Fc_-60 0.06
47 Fc_-50 0.06
48 Fc_-40 0.06
49 Fc_-30 0.06
50 Fc_-20 0.06
51 Fc_-10 0.294259404074
52 Fc_0 0.00411286437817
53 Fc_10 0.0
54 Fc_20 0.06
55 Fc_30 0.06
56 Fc_40 0.06
57 Fc_50 0.06
58 Fc_60 0.06
59 Fc_70 0.06
60 Fc_80 0.06
61 Fc_90 0.06
62 Fc_100 0.06
63 Fc_110 0.06
64 Fc_120 0.06
65 Fc_130 0.06
66 Fc_140 0.06
67 Fc_150 0.06
68 Fc_160 0.06
69 Fc_170 0.06






    




Test Data






    




Idx Start(s) Spam(s) Description
0 17.69 99.31 ramp u1
1 118.70 111.70 ramp d1
2 258.81 98.68 ramp u2
3 359.46 100.35 ramp d2
4 461.07 97.72 ramp d3
5 555.55 103.10 ramp u4



In [67]:

    
res_params = res['x']
params = param0[:]
for i,j in enumerate(opt_idx):
    params[j] = res_params[i]

k1 = np.array(params[0:angles_num])
k2 = np.array(params[angles_num:angles_num*2])

print('angeles = ')
print(angles)
print('L_unk = ')
print(k1)
print('F_c = ')
print(k2)

%matplotlib inline
plt.figure(figsize=(12,12),dpi=300)
plt.subplot(211)
plt.plot(angles,  k1, 'r')
plt.ylabel('$L_{unk} \, / \, Nm$')
plt.subplot(212)
plt.plot(angles,  k2, 'g')
plt.ylabel('$F_c  \, / \, Nm$')
plt.xlabel('$\phi \, / \, ^o/s$')
plt.show()









    



angeles = 
[-170, -160, -150, -140, -130, -120, -110, -100, -90, -80, -70, -60, -50, -40, -30, -20, -10, 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170]
L_unk = 
[ 0.66292786  1.02495697  1.50155537  2.1147923   2.62096826  2.88561125
  3.10052921  3.1792081   3.0278776   2.83733114  2.64511226  2.55396115
  2.41080177  2.08821719  1.69336983  1.33704659  0.78612447  0.13963036
 -0.5024043  -1.06067095 -1.55388357 -1.976878   -2.22694733 -2.40065977
 -2.58289702 -2.69317701 -2.84181216 -2.89146635 -2.93488795 -2.79056578
 -2.55945472 -1.89558536 -1.26825577 -0.71335425 -0.65615185]
F_c = 
[ 0.06        0.06        0.06        0.06        0.06        0.06        0.06
  0.06        0.06        0.06        0.06        0.06        0.06        0.06
  0.06        0.06        0.2942594   0.00411286  0.          0.06        0.06
  0.06        0.06        0.06        0.06        0.06        0.06        0.06
  0.06        0.06        0.06        0.06        0.06        0.06        0.06      ]



In [14]:

    
toggle_inputs()
button_qtconsole()



In [15]:

    
(-0.05-0.05)/(80/57.3)









    Out[15]:





-0.07162500000000001



In [16]:

    
Clda_cmp/4









    Out[16]:





-0.075975



In [ ]:

Idx	Start(s)	Spam(s)	Description
0	17.69	99.31	ramp u1
1	118.70	111.70	ramp d1
2	258.81	98.68	ramp u2
3	359.46	100.35	ramp d2
4	461.07	97.72	ramp d3
5	555.55	103.10	ramp u4

Name	Value	unit
$S_c$	0.1254	$m^2$
$b_c$	0.7	$m$
$g$	9.81	$m/s^2$
$m_T$	9.585	$kg$
$l_{zT}$	0.0416	$m$
$V$	30	$m/s$

Idx	Description	$x_0$	unit	opt	$\delta_{par}$	min	max
0	Mu_-170	0.680084083831	Nm	*	0.01	-4	4
1	Mu_-160	1.33860206042	Nm	*	0.01	-4	4
2	Mu_-150	1.95645326691	Nm	*	0.01	-4	4
3	Mu_-140	2.51486736542	Nm	*	0.01	-4	4
4	Mu_-130	2.99687971916	Nm	*	0.01	-4	4
5	Mu_-120	3.3878467786	Nm	*	0.01	-4	4
6	Mu_-110	3.67589095295	Nm	*	0.01	-4	4
7	Mu_-100	3.85226145167	Nm	*	0.01	-4	4
8	Mu_-90	3.91160013382	Nm	*	0.01	-4	4
9	Mu_-80	3.85210428848	Nm	*	0.01	-4	4
10	Mu_-70	3.67558140119	Nm	*	0.01	-4	4
11	Mu_-60	3.38739424248	Nm	*	0.01	-4	4
12	Mu_-50	2.99629794672	Nm	*	0.01	-4	4
13	Mu_-40	2.51417403093	Nm	*	0.01	-4	4
14	Mu_-30	1.95566943389	Nm	*	0.01	-4	4
15	Mu_-20	1.33775154174	Nm	*	0.01	-4	4
16	Mu_-10	0.679192718283	Nm	*	0.01	-4	4
17	Mu_0	-0.0	Nm	*	0.01	-4	4
18	Mu_10	-0.679192718283	Nm	*	0.01	-4	4
19	Mu_20	-1.33775154174	Nm	*	0.01	-4	4
20	Mu_30	-1.95566943389	Nm	*	0.01	-4	4
21	Mu_40	-2.51417403093	Nm	*	0.01	-4	4
22	Mu_50	-2.99629794672	Nm	*	0.01	-4	4
23	Mu_60	-3.38739424248	Nm	*	0.01	-4	4
24	Mu_70	-3.67558140119	Nm	*	0.01	-4	4
25	Mu_80	-3.85210428848	Nm	*	0.01	-4	4
26	Mu_90	-3.91160013382	Nm	*	0.01	-4	4
27	Mu_100	-3.85226145167	Nm	*	0.01	-4	4
28	Mu_110	-3.67589095295	Nm	*	0.01	-4	4
29	Mu_120	-3.3878467786	Nm	*	0.01	-4	4
30	Mu_130	-2.99687971916	Nm	*	0.01	-4	4
31	Mu_140	-2.51486736542	Nm	*	0.01	-4	4
32	Mu_150	-1.95645326691	Nm	*	0.01	-4	4
33	Mu_160	-1.33860206042	Nm	*	0.01	-4	4
34	Mu_170	-0.680084083831	Nm	*	0.01	-4	4
35	Fc_-170	0.06	Nm	*	0.01	0	0.4
36	Fc_-160	0.06	Nm	*	0.01	0	0.4
37	Fc_-150	0.06	Nm	*	0.01	0	0.4
38	Fc_-140	0.06	Nm	*	0.01	0	0.4
39	Fc_-130	0.06	Nm	*	0.01	0	0.4
40	Fc_-120	0.06	Nm	*	0.01	0	0.4
41	Fc_-110	0.06	Nm	*	0.01	0	0.4
42	Fc_-100	0.06	Nm	*	0.01	0	0.4
43	Fc_-90	0.06	Nm	*	0.01	0	0.4
44	Fc_-80	0.06	Nm	*	0.01	0	0.4
45	Fc_-70	0.06	Nm	*	0.01	0	0.4
46	Fc_-60	0.06	Nm	*	0.01	0	0.4
47	Fc_-50	0.06	Nm	*	0.01	0	0.4
48	Fc_-40	0.06	Nm	*	0.01	0	0.4
49	Fc_-30	0.06	Nm	*	0.01	0	0.4
50	Fc_-20	0.06	Nm	*	0.01	0	0.4
51	Fc_-10	0.06	Nm	*	0.01	0	0.4
52	Fc_0	0.06	Nm	*	0.01	0	0.4
53	Fc_10	0.06	Nm	*	0.01	0	0.4
54	Fc_20	0.06	Nm	*	0.01	0	0.4
55	Fc_30	0.06	Nm	*	0.01	0	0.4
56	Fc_40	0.06	Nm	*	0.01	0	0.4
57	Fc_50	0.06	Nm	*	0.01	0	0.4
58	Fc_60	0.06	Nm	*	0.01	0	0.4
59	Fc_70	0.06	Nm	*	0.01	0	0.4
60	Fc_80	0.06	Nm	*	0.01	0	0.4
61	Fc_90	0.06	Nm	*	0.01	0	0.4
62	Fc_100	0.06	Nm	*	0.01	0	0.4
63	Fc_110	0.06	Nm	*	0.01	0	0.4
64	Fc_120	0.06	Nm	*	0.01	0	0.4
65	Fc_130	0.06	Nm	*	0.01	0	0.4
66	Fc_140	0.06	Nm	*	0.01	0	0.4
67	Fc_150	0.06	Nm	*	0.01	0	0.4
68	Fc_160	0.06	Nm	*	0.01	0	0.4
69	Fc_170	0.06	Nm	*	0.01	0	0.4

Idx	Description	$x$
0	Mu_-170	0.662927864745
1	Mu_-160	1.02495697393
2	Mu_-150	1.50155537121
3	Mu_-140	2.11479230196
4	Mu_-130	2.62096826149
5	Mu_-120	2.88561124751
6	Mu_-110	3.10052920572
7	Mu_-100	3.17920809804
8	Mu_-90	3.02787759785
9	Mu_-80	2.83733114296
10	Mu_-70	2.64511226392
11	Mu_-60	2.55396114985
12	Mu_-50	2.41080176853
13	Mu_-40	2.08821718749
14	Mu_-30	1.69336983029
15	Mu_-20	1.33704658572
16	Mu_-10	0.786124470153
17	Mu_0	0.139630363921
18	Mu_10	-0.502404303052
19	Mu_20	-1.06067095416
20	Mu_30	-1.55388357326
21	Mu_40	-1.97687800236
22	Mu_50	-2.22694733306
23	Mu_60	-2.40065976571
24	Mu_70	-2.58289702002
25	Mu_80	-2.69317701172
26	Mu_90	-2.84181215556
27	Mu_100	-2.89146634773
28	Mu_110	-2.934887953
29	Mu_120	-2.79056578426
30	Mu_130	-2.55945471641
31	Mu_140	-1.89558536214
32	Mu_150	-1.26825577494
33	Mu_160	-0.713354250566
34	Mu_170	-0.656151848094
35	Fc_-170	0.06
36	Fc_-160	0.06
37	Fc_-150	0.06
38	Fc_-140	0.06
39	Fc_-130	0.06
40	Fc_-120	0.06
41	Fc_-110	0.06
42	Fc_-100	0.06
43	Fc_-90	0.06
44	Fc_-80	0.06
45	Fc_-70	0.06
46	Fc_-60	0.06
47	Fc_-50	0.06
48	Fc_-40	0.06
49	Fc_-30	0.06
50	Fc_-20	0.06
51	Fc_-10	0.294259404074
52	Fc_0	0.00411286437817
53	Fc_10	0.0
54	Fc_20	0.06
55	Fc_30	0.06
56	Fc_40	0.06
57	Fc_50	0.06
58	Fc_60	0.06
59	Fc_70	0.06
60	Fc_80	0.06
61	Fc_90	0.06
62	Fc_100	0.06
63	Fc_110	0.06
64	Fc_120	0.06
65	Fc_130	0.06
66	Fc_140	0.06
67	Fc_150	0.06
68	Fc_160	0.06
69	Fc_170	0.06