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# 141proj - equilibirum =.01 y =.8 x converges to.01 the...

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Part VI x 0 = .0059 - x converges to .01 the desired equilibrium point x 0 = .0058 - x fails to converge to .01 the desired equilibrium point

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x 0 = .0113 - x converges to .01 the desired equilibrium point x 0 = .0014 - x fails to converge to .01 the desired equilibrium point
y 0 = .79 - x converges to .01 the desired equilibrium point y 0 = .80 – x fails to converge to .01 the desired equilibrium point

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y 0 = .55 - x converges to .01 the desired equilibrium point y 0 = .54 - x fails to converge to .01 the desired equilibrium point
Part VIII Previously at x 0 .0114 or at x 0 .0058 the system would not converge to x equilibirum = .01. However, with the nonlinear controller in place of the linear controller we see that: x 0 = .0058 - x converges to .01 the desired equilibrium point x 0 = .0014 - x converges to .01 the desired equilibrium point

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Likewise at y 0 .8 or at y 0 .054 the system would not converge to x equilibirum = .01. Utilizing the nonlinear controller at these points we see that the system still converges to x

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Unformatted text preview: equilibirum = .01 y = .8 - x converges to .01 the desired equilibrium point Despite fluctuation, x is still bounded within a value very close to .01 the desired equilibrium point for both of these graphs at y = .8 and y = .054 y = .054 - x converges to .01 the desired equilibrium point Part X With a sampling interval of 14 x fluctuates once again, but as time progresses it converges to .01 With a sampling interval of 15 x fluctuates and doesn’t necessarily converge to .01 but fluctuates within .0013 and .009. Thus the discrete controller is beginning to fail or has failed at this sampling interval By incrementing the sampling interval to 16, it is evident that the controller has failed as the value of x blows up after a certain time before 12000 . Therefore, a sampling interval of at most 14 is required to ensure that the value of x converges to .01 at equilibrium....
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141proj - equilibirum =.01 y =.8 x converges to.01 the...

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