# 6Detuning Effects in Induction Motor Vector Control

In vector control described in Chapters 4 and 5, we assumed that the induction machine parameters were known exactly. In practice, the estimated parameters may be off by a significant amount. This is particularly true of the rotor time constant *τ _{r}* (=

*L*/

_{r}*R*), which depends on the rotor resistance that increases significantly as the rotor heats up. In this chapter, we will calculate the steady-state error due to the incorrect estimate of the rotor resistance and also look at its effect on the dynamic response of vector-controlled drives [1,2].

_{r}## 6-1 Effect of Detuning Due to Incorrect Rotor Time Constant *τ*_{r}

_{r}

We will define a detuning factor to be the ratio of the actual and the estimated rotor time constants as

where the estimated quantities are indicated by the subscript “est.” To analytically study the sensitivity of the vector control to *k _{τ}*, we will simplify our system by assuming that the rotor of the induction machine is blocked from turning, that is,

*ω*

_{mech}= 0. Also, we will assume an open-loop system, where the command (reference) currents are and .

As shown in Fig. 6-1 at *t* = 0^{−}, the stator *a*-axis, the rotor *A*-axis, and ...

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