Predictive Control of Power Converters and Electrical Drives

4.6 Discrete-Time Model for Prediction

This section describes the discretization process of the load current equation (4.20) for a sampling time T_s. The discrete-time model will be used to predict the future value of load current from voltages and measured currents at the kth sampling instant. Several discretization methods can be used in order to obtain a discrete-time model suitable for the calculation of predictions. Considering that the load can be modeled as a first-order system, the discrete-time model can be obtained by a simple approximation of the derivative. However, for more complex systems this approximation may introduce errors into the model and a more accurate discretization method is required.

The load current derivative di/dt is replaced by a forward Euler approximation. That is, the derivative is approximated as follows:

4.21

which is substituted in (4.20) to obtain an expression that allows prediction of the future load current at time k + 1, for each one of the seven values of voltage vector v(k) generated by the inverter. This expression is

4.22

where denotes the estimated back-emf. The superscript p denotes the predicted variables.

The back-emf can be calculated ...