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Message ID: 9454     Entry time: Tue Dec 10 17:27:47 2013
Author: Jenne 
Type: Update 
Category: Treasure 
Subject: Baby oplev LQR designed loop 

I *finally* figured out how to bend Matlab to my will, and close a very simple oplev loop using LQR technology. 

This is super, super simple, but it's a step in the right direction.  There is no noise, just a simple pendulum with a resonant frequency of 0.75Hz, and a Q of 10.  The LQR tries to keep the position of the pendulum at a minimum, and does not care at all about the velocity.  You cannot (with Matlab's LQR, at least that I can find) make it care "0" about the control output, so it cares about the control output a factor of 1e-4 as much as the position.

Here are some plots:

The first plot has the open loop system (just the pendulum, no control at all), as well as the closed loop system (the pendulum under control).

NoControlVsClosedLoop_BabyOplev.png

Plot 2 is the open loop gain of the controller that the LQR designed.

OpenLoopGain_BabyOplev.png

Plots 3 and 4 are the step and impulse responses of the open loop (pendulum with no control), and closed loop (pendulum with feedback) systems.

StepResp_BabyOplev.png

ImpResp_BabyOplev.png

The conclusion from the plots (if this were an interesting system) is that it doesn't take much to damp an ideal pendulum.  The real conclusion here is that I think I now know how to use the Matlab LQR function, and can make a loop with some noise now.

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