In the predictive control strategies presented throughout this book, the cost function is based on the future error, that is, the error between the predicted variable and the reference at the next sampling instant. This means that future references need to be known.

In general, future references are not known, so they need to be estimated. A very simple approach, based on the assumption that the sampling frequency is much higher than the frequency of the reference signal, considers that the future value of the reference is approximately equal to the present value of the reference.

For the predictive current control example it can be assumed that **i**^{*}(*k* + 1) = **i**^{*}(*k*), and the cost function can be rewritten as

12.5

This approximation will lead to a one-sample delay in the reference tracking of the reference currents.

If compensation of the calculation time delay, presented in the previous section, is considered, the reference **i**^{*}(*k* + 2) is required. Using the same idea, the future reference can be assumed to be **i**^{*}(*k* + 2) = **i**^{*}(*k*), resulting in the cost function

12.6

and the reference tracking will present a two-sample delay.

The effect of the delay introduced by this approximation of future references is shown in Figure 12.8. It can be seen that this ...

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