**8. Experimental verification of the control systems**

The tests were carried out in a 5.5 kW drive system. The motor parameters are given in Table 2 and the main per unit values in Table 3. In Fig. 16, 17 motor start-up and reverse for control system presented in chapter 4.1-4.2 are shown. In Fig. 18, 19 motor start-up and reverse for control system presented in chapter 5 are shown. Fig. 20,21 presents the same steady state like previous but for adaptive backstepping control system (chapter 4.3). Fig. 22 presents diagram of stator currents and voltages when motor is starting up for voltage control system (chapter 4.3). In Fig. 23 load torque setting to 0.7 p.u. for current control is presented. In Fig. 24, 25 the id current and the sinusoidal stator voltage and stator current are presented.

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

current controller or other controller.

system of IM fed by CSI.

are presented.

shown.

**Figure 15.** Generalized Multi-scalar Control System of Induction Machine supplied by CSI or VSI.

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

\* usβ

\* usα

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

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

The tests were carried out in a 5.5 kW drive system. The motor parameters are given in Table 2 and the main per unit values in Table 3. In Fig. 16, 17 motor start-up and reverse for control system presented in chapter 4.1-4.2 are shown. In Fig. 18, 19 motor start-up and reverse for control system presented in chapter 5 are shown. Fig. 20,21 presents the same steady state like previous but for adaptive backstepping control system (chapter 4.3). Fig. 22 presents diagram of stator currents and voltages when motor is starting up for voltage control system (chapter 4.3). In Fig. 23 load torque setting to 0.7 p.u. for current control is presented. In Fig. 24, 25 the id current and the sinusoidal stator voltage and stator current

**8. Experimental verification of the control systems** 

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

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

**Figure 22.** The currents and voltages

**Figure 23.** Load torque is set to 0.7 p.u. (chapter 5)

**Figure 24.** id current and the stator voltage

**Figure 19.** Motor reverse (chapter 5)

**Figure 20.** Motor start-up (chapter 4.3)

**Figure 21.** Motor reverse (chapter 4.3)

**Figure 22.** The currents and voltages

**Figure 19.** Motor reverse (chapter 5)

**Figure 20.** Motor start-up (chapter 4.3)

**Figure 21.** Motor reverse (chapter 4.3)

x22

x12

x11


0 1


0,8


Time [ms] KTL

0,9 x21

200 1000 1800 2600

**Figure 23.** Load torque is set to 0.7 p.u. (chapter 5)

**Figure 24.** id current and the stator voltage

PARAMETER VALUE Pn (motor power) 5.5 kW Un (phase to phase voltage) 400 V In (current) 10.9 A J (interia) 0.0045 kgm2 nn (rotor speed) 1500 rpm

Rs (stator resist.) Rr (rotor resist.)

**Table 2.** The motor drive system parameters

**Table 3.** Definition of per unit values

*Electronics and Applications, IEEE 2005.* 

**Author details** 

Marcin Morawiec

**10. References** 

Lm (mutual-flux induct.) Ls (stator induct.) Lr (rotor induct.)

Current Source Converter C (capacitor in dc-link) Rd (inductor resist.) CM,L (input-output caps)

PARAMETER PER UNIT VALUES

DEFINITION DESCRIPTION <sup>3</sup> *U U b n* base voltage *b n I I* base current *b bb z UI* base impedance

*Gdansk University of Technology, Faculty of Electrical and Control Engineering, Poland* 

Adamowicz M.; Guzinski J.; Minimum-time minimum-loss speed sensorless control of induction motors under nonlinear control, *Compatibility in Power Electronics 2005*. Bassi E.; Benzi F.P.; Bolognani S.; Buja G.S., A field orientation scheme for current-fed induction motor drives based on the torque angle closed-loop control, *IEEE Transactions* 

*on Industry Applications, Volume 28, Issue 5, Sept.-Oct. 1992 Pages: 1038 – 1044.* Glab (Morawiec) M.; Krzeminski Z. & Włas M., The PWM current source inverter with IGBT transistors and multiscalar model control system, *11th European Conference on Power* 

0.045 0.055 1.95 2.05 2.05

0.1 0.002 0.2

**Figure 25.** The stator current in stationary state.

where:

x11 is the rotor speed, x12 is the variable proportional to electromagnetic torque, x21 is the square of rotor flux and x22 is the additional variables, id is the dc-link current, usα,β are the capacitor voltage components, KTL is correction element (load torque), isα,β are the stator current components.
