**5. Experimental results**

The DTC strategy were implemented using a Texas Instruments DSP TMS320F2812 platform. The system consists of a three-phase voltage source inverter with insulated-gate bipolar transistors (IGBTs) and the three-phase induction motor parameters are shown in the appendix. The stator voltage commands are modulated by using symmetrical space vector PWM, with switching frequency equal to 2.5 kHz. The DC bus voltage of the inverter is 226 V. The stator voltages and currents are sampled in the frequency of 2.5 kHz. A conventional PI regulators generates a torque reference by using the speed error. The flux and torque estimation, and the flux and torque PIs regulators and speed controller have the same sampling frequency of 2.5 kHz. The encoder resolution is 1500 pulses per revolution. The algorithm of the DTC strategy was programmed on the Event Manager 1 of the Texas Instruments DSP TMS320F2812 platform and its flowchart is presented in Figure 11 and the schematic of implemention is presented in Figure 12.

**Figure 12.** Schematic of implemention.

motor speed operation at 2 Hz and 6 Hz.

measurements of currents, voltages and parameters variations.

Five no-load induction motor tests were made. The first one was the response to a torque step of 12.2 Nm which is shown in Figure 13. It can be seen the satisfactory response of torque although it has oscillation. This oscillation occurs due to the natural lack of accuracy in the

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Tuning PI Regulators for Three-Phase Induction Motor Space

Vector Modulation Direct Torque Control Using Complex Transfer Function Concept

Figure 14 shows when the speed varies from 6.28 rad/s to 18.85 rad/s in 200 ms. This result confirms the satisfactory performance of the controller due to the fact that the the speed reaches the reference in several conditions although the gains of PI are designed for induction

In the third test the speed varies in forward and reversal operation and the result are presented in Figures 15(a) and 15(b). The speed changes from 13 rad/s to -13 rad/s in 1 s and the gains of PI regulator are not changed during the test. This result confirms the satisfactory performance of the controller due to the fact that the the speed reaches the reference in several conditions and the PI regulator was designed for induction motor speed operation at 4.15 Hz. The small

Figure 16 presents the speed response when the speed varies from 6.28 rad/s to -6.28 rad/s. The result confirms the satisfactory performance of the PI regulator again due to the fact that

error occurs due the natural lack of accuracy in the measurement of the speed.

**Figure 11.** The flowchart of the DSP program.

**Figure 12.** Schematic of implemention.

10 Will-be-set-by-IN-TECH

The DTC strategy were implemented using a Texas Instruments DSP TMS320F2812 platform. The system consists of a three-phase voltage source inverter with insulated-gate bipolar transistors (IGBTs) and the three-phase induction motor parameters are shown in the appendix. The stator voltage commands are modulated by using symmetrical space vector PWM, with switching frequency equal to 2.5 kHz. The DC bus voltage of the inverter is 226 V. The stator voltages and currents are sampled in the frequency of 2.5 kHz. A conventional PI regulators generates a torque reference by using the speed error. The flux and torque estimation, and the flux and torque PIs regulators and speed controller have the same sampling frequency of 2.5 kHz. The encoder resolution is 1500 pulses per revolution. The algorithm of the DTC strategy was programmed on the Event Manager 1 of the Texas Instruments DSP TMS320F2812 platform and its flowchart is presented in Figure 11 and the

**5. Experimental results**

schematic of implemention is presented in Figure 12.

**Figure 11.** The flowchart of the DSP program.

Five no-load induction motor tests were made. The first one was the response to a torque step of 12.2 Nm which is shown in Figure 13. It can be seen the satisfactory response of torque although it has oscillation. This oscillation occurs due to the natural lack of accuracy in the measurements of currents, voltages and parameters variations.

Figure 14 shows when the speed varies from 6.28 rad/s to 18.85 rad/s in 200 ms. This result confirms the satisfactory performance of the controller due to the fact that the the speed reaches the reference in several conditions although the gains of PI are designed for induction motor speed operation at 2 Hz and 6 Hz.

In the third test the speed varies in forward and reversal operation and the result are presented in Figures 15(a) and 15(b). The speed changes from 13 rad/s to -13 rad/s in 1 s and the gains of PI regulator are not changed during the test. This result confirms the satisfactory performance of the controller due to the fact that the the speed reaches the reference in several conditions and the PI regulator was designed for induction motor speed operation at 4.15 Hz. The small error occurs due the natural lack of accuracy in the measurement of the speed.

Figure 16 presents the speed response when the speed varies from 6.28 rad/s to -6.28 rad/s. The result confirms the satisfactory performance of the PI regulator again due to the fact that

(a) Speed reversal operation (12.57 rad/s.div).

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Tuning PI Regulators for Three-Phase Induction Motor Space

Vector Modulation Direct Torque Control Using Complex Transfer Function Concept

(b) Speed forward and reversal (13 rad/s.div).

**Figure 15.** Speed forward and reversal operation and *a* phase current (10 A/div)

**Figure 16.** Speed response to step operation (12.57 rad/s.div) and *a* phase current (10 A/div).

**Figure 13.** Responses to step torque operation (9 Nm/div).

**Figure 14.** Speed forward and reversal operation (15.7 ras/s.div) and *a* phase current (10 A/div).

the speed reaches the reference value and the gains of PI are designed for induction motor speed operation at 2 Hz.

In load test the speed reference was 36.6 rad/s and a load torque of 11.25N.m was applied to the motor. In this test a dc generator is coupled to the rotor of induction motor. So the generated voltage of the DC generator is conected to the load with variable resistance. The test is shown in Figure 17 and the steady state error is 4.5%.

336 Induction Motors – Modelling and Control Tuning PI Regulators for Three-Phase Induction Motor Space Vector Modulation Direct Torque Control Using Complex Transfer Function Concept <sup>13</sup> 337 Tuning PI Regulators for Three-Phase Induction Motor Space Vector Modulation Direct Torque Control Using Complex Transfer Function Concept

12 Will-be-set-by-IN-TECH

**Figure 14.** Speed forward and reversal operation (15.7 ras/s.div) and *a* phase current (10 A/div).

test is shown in Figure 17 and the steady state error is 4.5%.

the speed reaches the reference value and the gains of PI are designed for induction motor

In load test the speed reference was 36.6 rad/s and a load torque of 11.25N.m was applied to the motor. In this test a dc generator is coupled to the rotor of induction motor. So the generated voltage of the DC generator is conected to the load with variable resistance. The

**Figure 13.** Responses to step torque operation (9 Nm/div).

speed operation at 2 Hz.

(b) Speed forward and reversal (13 rad/s.div).

**Figure 15.** Speed forward and reversal operation and *a* phase current (10 A/div)

**Figure 16.** Speed response to step operation (12.57 rad/s.div) and *a* phase current (10 A/div).

**Author details**

**7. References**

39(5): 217–220.

*Engineering Society* .

*Trans. Power Electronics* 3(4): 420–429.

graphs, *IEEE Trans. Ind. Electron.* 42: 263–271.

*IEEE Trans. Ind. Applications* 40: 1388–1397.

The Netherlands: Elsevier.

*Applications* 43(6): 1639–1649.

16(6): 846–851.

Alfeu J. Sguarezi Filho

*Universidade Federal do ABC, Brazil*

José Luis Azcue and Ernesto Ruppert

*School of Electrical and Computer Engineering, University of Campinas, Brazil*

using complex vectors, *IEEE Trans. Ind. Applicat.* 32: 817–825.

motor direct torque control, *Sba Controle e Automação* 20(2).

of stator flux, *Electric Power Systems Research* 78: 1712–1718.

complex transfer functions, *IEEE Trans. Ind. Electron.* 42: 263–271.

[1] Blaschke, F. [1977]. The principle of field orientation control as applied to the new transvector closed loop control system for rotating machines, *Siemens Review*

Tuning PI Regulators for Three-Phase Induction Motor Space

Vector Modulation Direct Torque Control Using Complex Transfer Function Concept

339

[2] Briz, F., degener, M. W. & Lorenz, R. D. [2000]. Analysis and design of current regulators

[3] Buja, G. & Kazmierkowski, M. [2004]. Direct torque control of pwm inverter-fed ac

[4] Cad, M. M. & de Aguiar, M. L. [2000]. The concept of complex transfer functions applied to the modeling of induction motors, *IEEE Winter Meeting 2000 of the IEEE Power*

[5] Casadei, D., Serra, G. & Tani, A. [2001]. Steady-state and transient performance evaluation of a dtc scheme in the low speed range, *IEEE Trans. on Power Electronics*

[6] Depenbrock, M. [1988]. Direct self-control(dsc) of inverter-fed induction machine, *IEEE*

[7] Filho, A. J. S. & Filho, E. R. [2008]. The complex controller applied to the induction motor control, *IEEE Applied Power Electronics Conference and Exposition - APEC* pp. 1791–1795. [8] Filho, A. J. S. & Filho, E. R. [2009]. The complex controller for three-phase induction

[9] Gataric, S. & Garrigan, N. R. [1999]. Modeling and design of three-phase systems using

[10] Holtz, J. [1995]. The representation of ac machine dynamics by complex signal flow

[11] Holtz, J., Quan, J., Pontt, J., Rodríguez, J., newman, P. & Miranda, H. [2004]. Design of fast and robust current regulators for high-power drives based on complex state variables,

[12] Kenny, B. H. & Lorenz, R. D. [2001]. Stator and rotor flux based deadbeat direct torque control ofinduction machines, *IEEE Industry Applications Conference* 1: 133–139. [13] Kovács, P. K. & Rácz, E. [1984]. *Transient Phenomena in Electrical Machines*, Amsterdam,

[14] Kumsuwana, Y., Premrudeepreechacharna, S. & Toliyat, H. A. [2008]. Modified direct torque control method for induction motor drives based on amplitude and angle control

[15] Lee, K.-B., Blaabjerg, F. & Yoon, T.-W. [2007]. Speed-sensorless dtc-svm for matrix converter drives with simple nonlinearity compensation, *IEEE Transactions on Industry*

motors - a survey, *Industrial Electronics, IEEE Transactions on* 51(4): 744–757.

**Figure 17.** Load test (18,3 rad/s.div) and *a* phase current (20 A/div).
