**7. The control system structures**

In Fig. 12 and Fig. 14 the voltage and current multi-scalar control system structure is shown. These structures are based on four PI controllers and contain: the modulator, the speed observer and decouplings blocks .

**Figure 12.** The voltage multi-scalar control system structure

**Figure 13.** The voltage multi-scalar adaptive backstepping control system structure

456 Induction Motors – Modelling and Control

11 x

r\_K ˆ

from 0.1 to -0.1 p.u., the estimated rotor speed \_ ˆ

x12\*

x22\*



x22

<sup>r</sup> ˆ <sup>r</sup> ˆ

**Figure 12.** The voltage multi-scalar control system structure

**7. The control system structures** 

observer and decouplings blocks .


x21\*


x11\*

x11

x21

**Multi-scalar variables**

x12

<sup>r</sup> id ˆ

**Figure 11.** The Speed observer test: the estimated rotor speed x11 in backstepping observer is changed

In Fig. 12 and Fig. 14 the voltage and current multi-scalar control system structure is shown. These structures are based on four PI controllers and contain: the modulator, the speed

m1

m2

**Speed observer backstepping**

*r K* by Krzeminski's speed observer [Krzeminski Z.,

i

**Current Source Inverter**

**~**

ed ud

id

v1

v2

Ld

ua ub ia

ib **IM**

xy abc

xy abc

us us

is is

1999] and the multi-scalar variable: x12, x21, x22 are shown . The load torque m0 is set to -0.1 p.u.

**Figure 14.** The current multi-scalar control system structure.

**Figure 16.** Motor start-up (chapter 4.1- 4.2)

**Figure 17.** Motor reverse (chapter 4.1- 4.2)

**Figure 18.** Motor start-up (chapter 5)

In Fig. 14 the ed\_ref value is determined in ed reference block. The ed reference block can be PI current controller or other controller.

In Fig. 13 the voltage multi-scalar adaptive backstepping control system structure is shown.

In Fig. 15 generalized multi-scalar control system structure is presented. This control structure is divided into two parts: the control system of IM fed by VSI and the control system of IM fed by CSI.
