3.7 ContinuousTime Models of DiscreteTime Systems
The function ToContinuousTime, when applied to discretetime objects, converts them to the continuoustime domain. In many respects ToContinuousTime behaves as an inverse function to ToDiscreteTime and applies inverse algorithms to those described previously in Section 3.5. Again, the methods can be chosen through the Method option, which accepts the same values. The conversion attempts to find the slowest possible continuoustime model the outputs of which would match the ones of the discretetime model at the sample time.
Finding continuoustime equivalents of discretetime systems.
Here a continuoustime system from an earlier example is converted to the discretetime domain.
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This brings the system back to continuous time.
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As our sampling period T is realvalued, we can simplify the result and see that the system is the same as the one we started with.
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Here is the lag system used earlier.
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This converts the system to the discretetime domain using the bilinear transformation with frequency prewarping.
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This brings the system back to continuous time.
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This is the discretetime approximation of the lag system obtained with the firstorder hold.
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This converts the result back to continuous time.
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Note that in the case of the FirstOrderHold method, ToContinuousTime cannot use the inverse of the statespace algorithm implemented in ToDiscreteTime and, as an exception, resorts to the conversion using transfer functions, which is less efficient.
