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Entry  Wed Nov 22 17:52:25 2017, gautam, Update, Optimal Control, Visualizing cost functions globalCosts.pdf
    Reply  Tue Jan 2 16:37:26 2018, gautam, Update, Optimal Control, Oplev loop tuning loopOpt_180102_1706.pdfglobalCosts.pdf
       Reply  Wed Jan 3 12:33:16 2018, rana, Update, Optimal Control, Oplev loop tuning 
          Reply  Wed Jan 3 16:25:32 2018, awade, Update, Optimal Control, Oplev loop tuning 
       Reply  Tue Jan 9 21:57:29 2018, gautam, Update, Optimal Control, Oplev loop tuning loopOpt_180108_2232.pdf
Message ID: 13450     Entry time: Wed Nov 22 17:52:25 2017     Reply to this: 13497
Author: gautam 
Type: Update 
Category: Optimal Control 
Subject: Visualizing cost functions 

I've attempted to visualize the various components of the cost function in the way I've defined it for the current iteration of the Oplev optimal control loop design code. For each term in the cost function, the way the cost is computed depends on the ratio of the abscissa value to some threshold value (set by hand for now) - if this ratio is >1, the cost is the logarithm of the ratio, whereas if the ratio is <1, the cost is the square of the ratio. Continuity is enforced at the point at which this transition happens. I've plotted the cost function for some of the terms entering the code right now - indicated in dashed red lines are the approximate value of each of these costs for our current Oplev loop - the weights were chosen so that each of the costs were O(10) for the current controller, and the idea was that the optimizer could drive these down to hopefully O(1), but I've not yet gotten that to happen.

Based on the meeting yesterday, some possible ideas:

  1. For minimizing the control noise injection - we know the transfer function from the Oplev control signal coupling to MICH from measurements, and we also have a model for the seismic noise. So one term could be a weighted integral of (coupling - seismic) - the weight can give more importance to f>30Hz, and even more importance to f>100Hz. Right now, I don't have any suc frequency dependant requirement on the control signal.
  2. Try a simpler problem first - pendulum local damping. The position damping controller for example has fewer roots in the complex plane. Although it too has some B/R notches, which account for 16 complex roots, and hence, 32 parameters, so maybe this isn't really a simpler problem?
  3. How do we pick the number of excess poles compared to zeros in the overall transfer function? The OL loop low-pass filters are elliptic filters, which achieve the fastest transition between the passband and stopband, but for the Oplev loop roll-off, perhaps its better to have a just have some poles to roll off the HF response?
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