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Confused about Pole Zero Compensation of Double Integrator

On Fri, 30 Sep 2005 23:27:51 +0100, Andy wrote (in message ):

Yes, it does behave in a very underdamped way, but only if you make the gain too high or too low. Suppose the compensator consists of a zero at -1 and a pole at -10, then with RootLocs you can easily see that for a minimum damping ratio of 0.7 say, the gain must be not less than 20 and not more than 50 (rounded values). Note: these are the values of K in the open loop transfer function when it is expressed with all coefficients of S as 1, i.e. K(S+A)/S^2(S+B). You can get the same results from the Bode plot by shifting it up/down until the phase margin (at the crossover frequency) drops below a certain value. But its not immediately evident what that value is for a closed loop damping ratio of 0.7

AAR

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AAR
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Aah, good point. I remembered I have a graph of damping ratio versus phase margin for a second order system, 0.7 is achieved with a phase margin of 65degrees. I had forgotten that a root locus diagram shows all values of gain, so by picking that carefully one can keep to a well-damped part of the curve.

cheers,

Andy.

Reply to
Andy

Neither plot is usefull for design unless the frequency tics are included. I guess the reason that I like Nichol's charts is that the closed loop gain and phase are explicitly shown, gain changes are just vertical displacements, it shows exactly what modifications are needed, and gives me an intuitive/visual way to evaluate margin/robustness. In the end though, since I could achieve that same results with any of the techniques, I just like the picture of a open/closed loop map with the storm center; aesthetics.

Enough said by me. Ray

Reply to
RRogers

I think that the more ways one can see a thing, the better one's grasp of it is likely to be. Each representation highlights certain aspects; together they evoke a more complete picture, even if any one of them has all the information.

And by me.

Jerry

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Jerry Avins

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