Different definitions of "resonance"; confirm param opt in MSD

[avikde]

Related to #91

Try a simpler system than W2D (confusing results in #95)

• change model and H
• pass affine test
• interaction of scaleFactor with the nonlin transmission - is it still a scaling?

[avikde]

Need to now compute H, and check if the same ptilde works (getpt)

[avikde]

affine test passes with τ2 = 0 but not 40

MSD initial traj

[avikde]

This linear approx of the feasible tau region looks pretty good. It seems sufficient for feasibility. TODO PROVE

[avikde]

Bad news - unorm going up as you try to lower tau1, and choose tau2 to stay feasible.

[avikde]

Many problems:

• actf does not match tot 9c28316
• it does not look like it opposes damping

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debugging

• tested the traj, param pair coming into debugComponentsPlot - OK
• using Htil = (y, ynext) -> Hio(y, ynext) + Hia(y, ynext) + Hstiffo(y) + Hstiffa(y) + Hdamp(y) instead of the default also OK

[avikde]

More illuminating without the initial fixTraj* step - u just looks like noise.

[avikde]

Working polytope constraint 74f2e71

Now damping is much higher and u does not just look like noise.

With fixTraj (note this is what causes the stroke to not look symmetric any more since it adds on modifications toward the end of the traj)

Without fixTraj

[avikde]

Debugging actuator force vs damping at resonance

• (note before that the scaling on the last plot was wrong)
• why is damping not exactly in phase and the same magnitude as the drag?

possibilities

• due to the discretization --> is it possible to do the param opt without the discretization? tried fixedδt=0.01 instead of 0.1, but the result is similar
  

• maybe the trajectory is not perfectly sinusoidal--pos/vel in the given trajectory are not exactly in the correct phasing. After 096e9a9

• due to refl act prop shifting resonance assumptions tried m.ma=m.ka=0 but looks the same
• param constraints?

[avikde]

In terms of param constraints:

• fixed the uncertainty about σomax 2c9f0d6
• increased σamax produced this:
  

So it was clearly related to the problem, but I now don't understand this plot... was due to low T and utilizing refl act prop.

With ma=ka=0, σamax = 10000, param = 0.1 144.183 144.183 0.0

With overlaid assumptions of what they should be:

=>

• all the dynamics terms seem correct
• stiffness seems lower than inertial: This following is with "ideal" params (stiffness for resonance)

(ignore actf - "total" is what the force would be with these new params). Now the question is: how do the ideal params take less force than the "optimized" params??

[avikde]

Ideal params

• feasibility: returned g = [9.999581607189612e-9, 0.3000000099972999] gidl =[53.17098179634948, 0.3000000099972999] => infeasible?? fa593e4

Aha, opt was working. With the ideal k, b >= k the polytope constraint on params made bo higher as well, which resulted in a higher cost.

Conclusion:

• with the bo >= ko constraint, the "resonance" i.e. k,m chosen according to k/m = omega^2 is not the solution that leads to the lowest force
• better to pick a lower ko, bo, so that the operating frequency > the "resonance" frequency to take advantage of the correspondingly lower bo.
• this manifests as a "phase shift" such that the act force leads the damping a bit, and is a bit larger than the damping?
• in the following, the actf is greater than the damping <= stiffness and inertial do not cancel each other <= if stiffness were increased to cancel ("resonance def 1") then damping would be even higher due to constraint.

Resonance defs:

1. stiffness = inertial <=> omega^2 = k/m <=> actuator force cancels damping
2. actuator force is smallest

Note that 2 is not the same as 1 when there is a constraint like ko <= bo