Debug scaled up trajectories - getting "resonance"

[avikde]

Been having trouble with large scale up - wing inertia gets so large that inertial terms contribute too much and act force not = drag any more -- see #102

Optimized result there Opt minal=1.6, τ2/1 lim=2.0 => [5.411 18.681 0.866 22.633 12.037 0.0 0.109], fHz=203.8, al[mg]=165.5, u∞=93.1

Related to #88

Conclusions

• using uinfnorm made it use T2 always, and found closer to resonance params
• changing the initial params (two sets of initial trajectories) --> generate output traj resulted in a slight phase shift of the hinge, and the robobee (small) one has a higher hinge amplitude, and (perhaps relatedly) has trouble using the nonlinear transmission at higher amplitudes.
• for now stick to the initial traj where the nonlin transmission helps -> try to show the nonlin benefit

[avikde]

Using the previously-optimized params (good that they are useful!) can get a reasonable initial traj with positive lift with an OL sine traj

With uampl=100

Compare this to the OL-generated robobee-scale traj with uampl=65

Conclusion

• hinge is shifted in phase in the scaled up params
• so may need to shift hinge in output traj to get best use of nonlin transmission?

[avikde]

with uinfnorm

"scaled up" initial traj; higher stiffnesses

6×10 Adjoint{Float64,Array{Float64,2}}:
 1.74783  18.5791  0.293794   1.86264   3.37617  37.1583  0.0555556  12.8695  0.908268  1.35287
 2.33044  18.5791  0.37287    3.38401   5.13494  37.1583  0.06135    19.615   1.0       1.77668
 2.91305  18.5791  0.466087   5.90448   6.95255  37.1583  0.0715692  28.6859  1.0       2.67455
 3.49566  18.5791  0.559305   8.83921   8.48646  37.1583  0.0848421  39.5757  1.0       3.88555
 4.07826  18.5791  0.652522  12.6744   10.5031   37.1583  0.0935684  52.1298  1.0       5.277
 4.66087  18.5791  0.74574   17.4078   12.8704   37.1583  0.101      66.1654  0.994709  6.87455

Opt minal=1.6, τ2/1 lim=2.0 => 1, [4.661 18.579 0.746 17.408 12.87 37.158 0.101], fHz=220.0, al[mg]=162.2, u∞=66.2, J=79.8

robobee-scale initial params; higher stiffnesses

6×10 Adjoint{Float64,Array{Float64,2}}:
 2.0229   17.5765  0.323663   2.55962  3.11022  35.1529  0.0571264  10.9777  0.605469  1.20264
 2.69719  17.5765  0.431551   4.4046   4.2469   35.1529  0.0750447  18.0312  0.530488  2.02821
 3.37149  17.5765  0.539439   7.15449  5.41     35.1529  0.0905757  26.8495  0.975622  3.1574
 4.04579  17.5765  0.647327  10.6293   6.67248  35.1529  0.104403   38.2546  1.0       4.64155
 4.72009  17.6486  0.755214  14.7987   7.98401  32.7479  0.118045   52.5729  1.0       6.50414
 5.39439  18.2524  0.863102  19.8194   9.35743  12.6224  0.130373   70.561   1.0       8.62286

Opt minal=1.6, τ2/1 lim=2.0 => 0, [5.394 18.252 0.863 19.819 9.357 12.622 0.13], fHz=170.5, al[mg]=166.0, u∞=70.6, J=76.7