In the control of electrical drives there are two main control schemes that have dominated high-performance applications during the last few decades: field-oriented control (FOC) [5–7] and direct torque control (DTC) [8]. These control strategies will be presented in the next two sections and will be considered for comparison to the predictive control schemes for electrical drives presented later in this book.

The main idea behind FOC is the use of a proper coordinate system that allows decoupled control over the electrical torque *T*_{e} and the magnitude of the rotor flux |**Ψ**_{r}|. This can be achieved by aligning the coordinate system with the rotor flux.

Figure 2.9 shows the relation between the stationary αβ and rotating reference frame *dq*, which is aligned with the rotor flux vector **Ψ**_{r}.

Since the variables are expressed in a rotating coordinates frame, the electromagnetic torque can be controlled via the imaginary component of the stator current *i*_{sq} and the rotor flux magnitude is controlled by its real part *i*_{sd}. These relations are obtained from the machine model expressed in the rotating coordinates frame:

2.7

2.8

where τ_{r} is the time constant of the rotor [7]. ...

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