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WindowTitle->25. Control Systems | Laplace Transforms in Theory and Practice
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One of the central applications of the Laplace transform is the analysis and \
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How about second-order systems? Those systems also can be represented as \
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\>", "Text",
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Cell["\<\
For instance, determine the transfer function of the Integrator. Apply the \
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Cell["\<\
The transfer function is defined as a ratio between the Laplace transforms of \
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For the spring-mass system, one can apply the same steps to derive its \
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\[CloseCurlyQuote]s output behavior with respect to different choices of \
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For other input choices, the situation is more involved. One can try to \
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numerical form.\
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Consider the mass-spring model and its output response for various inputs. If \
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Here, specific values for the parameters have been assigned, but one can keep \
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One of the exercises at the end of this section is to determine this transfer \
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The transfer function has positive poles, which means that under a small \
disturbance the system it moves away from its equilibrium position \
(equilibrium position for the pendulum is a perfectly upright position). One \
concludes that the open-loop system, with no control force applied, is \
unstable. This can be verified by simply looking at the impulse response:\
\>", "Text",
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You can explore tools available in Wolfram Language that allow one to choose \
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Notice that all the poles have a negative real part. Therefore, the inverted \
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Cell["\<\
One may notice that the system oscillates but eventually returns to its \
equilibrium position. One of the exercises, at the end of this section, is to \
determine this state response using the Laplace transform.\
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