5.4 SAMPLING FUNCTIONS

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In the last section we looked at a technique for writing equations for discrete variable values. This section will start to relate this to the design of controllers and control algorithms.

Although hinted at earlier, we can now formally define a value `sampled' into the computer. These values are taken in such a short period of time that they are effectively instantaneous. But this means that the value does not include changes between samples, and is particularly prone to noise.

The unit sample has a magnitude of 1 (and can be multiplied by an input magnitude). The subscript can be used to shift it in time. We can relate in the backshift operator, and finally use it to represent input (generating) functions,

As an example develop the expression for the following function assuming a sampling time of 1 s, and then assuming 0.5 s.

Table of sampling functions,

Try the previous example using the lookup table,