# A new fuzzy indirect rotor field oriented control scheme based speed sensorless induction machine drive feed through an ameliorate three level voltage inverter.

IntroductionInduction motors are widely used in industrial applications because they are less cost, more rugged and reliable than DC motors. Though induction motors have a few advantageous characteristics, they possess nonlinear and time-varying dynamic interactions. Using conventional PI controller, it is very difficult and complex to design a high performance induction motor drive system.

The fuzzy logic controller is attractive approach, which can accommodate the motor parametric variations and difficulty in obtaining an accurate mathematical model of induction motor due to rotor parameter and load time constant variations. In order to have fast transient response, the controller must have the robustness against speed variations and external perturbations. The Fuzzy logic is applied to optimize the PI controller gains which designed to optimize the step response of the system.

In this paper, we describe the speed control strategies of an IRFOC for IM. Next, with help of the Matlab/Simulink, we propose the F-PI controller, which is suitable for speed control of induction motor drives and explain how it works. Finally we compare its simulation results to conventional proportional-plus integral controller. The simulation results validate the robustness and reliable of the proposed F-PI controller for high performance of induction motor drive.

Nomenclature

[v.sub.ds], [v./sub.qs] d-q axis stator applied voltages;

[i.sub.ds], [i.sub.qs] d-q axis stator currents;

[[PHI].sub.dr], [[PHI].sub.qr] d-q rotor flux linkage;

[R.sub.s], [R.sub.r] stator and rotor winding resistances;

[L.sub.s], Lr stator and rotor;

M mutual magnetizing inductances;

[N.sub.p] number of pole pairs;

p Laplace operator;

[[omega].sub.e], [[omega].sub.r], synchronous and electrical angular speed;

[T.sub.e], [T.sub.1] electromagnetic and load torque;

J total inertia;

f friction coefficient;

[[pi].sub.r] rotor time constant;

[sigma] leakage coefficient;

^ denotes the estimated value;

* denotes the reference value;

Three Level Voltage Inverter

As for the two level voltage inverters, we can produce a three-phase three level voltage inverter in complete bridge by assembling three half-bridges using a common capacitive divider (Fig. 1).

[FIGURE 1 OMITTED]

Different PWM strategies to control the three level voltage inverter are given in [1]. ; We use the Sawtooth-Sinusoidal command with two carriers. This strategy is defined by two identical carriers, which one is delay compared to the other by a half period (Fig. 2)

[FIGURE 2 OMITTED]

Field Oriented Control Structure

A block diagram for an IRFOC can be seen on Fig. 3. This design uses a more robust structure known as Indirect Rotor Field Oriented Control, meaning that the rotor angle isn't determined directly by measuring the air gap flux with hall-effect sensors. These sensors are not particularly suited for use in large industrial motors as they can be fragile and sensitive to temperature change [2]. [3].

[FIGURE 3 OMITTED]

The dynamic model of an induction motor can be represented according to usual dq axes components in asynchronous rotating frame as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

Where [sigma] = [M.sup.2]/[L.sub.s][L.sub.r], [[pi].sub.r] = [L.sub.r]/[R.sub.r]

The decoupling control between d and q axes can be achieved by aligning the rotor flux vector to the d-axis and setting the rotor flux linkage to be constant, which means:

[[PHI].sub.qr] = d[[PHI].sub.qr]/dt = 0,

[[PHI].sub.dr] = [[PHI].sub.r] rated flux (2)

Substituting (2) in (1) yields:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

The electromagnetic torque equation and the mechanical speed motor are related by:

J dN/dt + Fn = [T.sub.e] - [T.sub.l] (4)

Where, the electromagnetic torque equation is:

[T.sub.e] = [N.sub.P] M/[L.sub.r] [[PHI].sub.r] [i.sub.qs] (5)

The decoupling control system is given by:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)

Where:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)

Design of F-PI Controller for Induction Motor

The purpose of this paper is to synthesize a controller without the exact knowledge of a model, numerically simple and simulated on Matlab/Simulink allowing good performance in terms of overshoot and fast and accuracy under the speed and load variations. The Fuzzy Logic Toolbox based controller architecture is shown in Fig. 4.

[FIGURE 4 OMITTED]

The fuzzy logic controller employs speed error and change of speed error as inputs, the Ki of PI controller is output.

E(k) = [??] - [??] (8)

[DELTA]e(k) = e(k) - e(k-1) (9)

And it uses following linguistic labels: {NL (Negative Large), NM (Negative Medium), NS (Negative Short), ZE (Zero), PS (Positive Short), PM (Positive Medium), PL (Positive Large)}. Each fuzzy label has an associated membership function. The membership functions as shown in Fig. 5

[FIGURE 5 OMITTED]

The control rules are represented as a set if then rules. The fuzzy rules of proposed controller for speed control of induction motor are presented in Table1. and formulated as follows:

If e (k) is NL and [DELTA]e (k) is N then Ki(k) is ZE.

The present paper uses Mamdani's Max-Min algorithm for inference mechanism. In the defuzzification stage, a crisp value of the output variable is obtained by using the center of gravity method.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (10)

[FIGURE 6 OMITTED]

Sensorless Speed Control Algorithm

Synchronous Angular Speed Estimation [4].

From the row 4 of (3) we obtain

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (11)

Car [[??].sub.r] = 0 in t = 0 s

Where: [??] is the estimate flux, [epsilon] = 0.01.

From the row (3)

[[??].sub.r] M/1 + [[pi].sub.r]P ids (12)

Once we obtain the synchronous angular speed, [[theta].sub.e] is simply equal to:

[[theta].sub.e] = [integral][w.sub.e] (13)

Knowledge of the synchronous angular speed and [[theta].sub.e] is essential for accurately applying the Clarke and Park transforms.

Speed Control

Sensorless control is another extension to the IRFOC algorithm that allows IMs to operate without the need for mechanical speed sensors. These sensors are notoriously prone to breakage, so removing them not only reduces the cost and size of the motor but improves the drive's long term accuracy and reliability [5]. [6]. [7]. [8]; this is particularly important if the motor is being used in a harsh, inaccessible environment such as an oil well.

Instead of physically measuring certain values control engineers can calculate them from a system's state variables. This is known as the state space modeling approach and is a powerful method for analyzing and controlling complex non-linear systems with multiple inputs and outputs. In high performance sensorless motor drives the two main control techniques used are Open Loop Estimators and Closed Loop Observers. In early literature the terms observer and estimator are often used interchangeably however most recent papers [6]. define estimators as devices that use a model to predict the speed using the phase currents and voltages as state variables. Observers also use a model to estimate values however these estimates are improved by an error feedback compensator that measures the difference between the estimated and actual values. The predicted value of speed is then used by the FOC to adjust the PWM waveform in exactly the same way as an actual measured value. [3]. [9]. [10].

From expression (4) we establish the following transfer function

N = 1/Jp + f ([T.sub.e] - [T.sub.l] (14)

In the goal of compare, we study a PI controller for a speed regulation:

N = 1/Jp + f ([K.sub.ps]P+[K.sub.is])([??]-N) - 1/Jp + f [T.sub.l] (15)

Or

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (16)

We obtain the block diagram shows in Fig. 7.

The controller parameters of this 2nd order dynamic characteristic equation are given from:

J/[K.sub.is] = 1/[omega].sup.2.sub.n]; 2[xi].sub.s]/[[omega].sub.n] = [K.sub.ps] + f/[K.sub.is] (17)

[FIGURE 7 OMITTED]

Simulation Results

The SIMULINK model used in this paper, models the induction motor as a continuous system for its dynamic equivalent circuit. The IGBT three level (NPC) inverter is controlled by a PWM with a switching frequency of 18 kHz.

We have tested the robust controller for sensorless speed controlled induction motor drive, with load torque applied as the following way

+ 10 N.m in 1.5 s. - 10 N.m in 2.5 s. + 10 N.m in 6 s. - 10 N.m in 7 s. 0 N.m in 8 s.

For a field reference [[??].sub.r] = 0.8 Wb. ; The speed is fixed at 150, then -150 Rad / s into 3.5 s.

The simulation results show the superiority of the F-PI compared to the traditional PI very used in industry. Therefore, it remains the good choice, it able to reacted positively with an ameliorate three level inverter to control the IM.

[FIGURE 8 OMITTED]

Conclusion

In this paper we presented the states variations in an objective of ameliorate the IM sensorless speed control by an F-PI regulator. A comparison between the F-PI controller and the conventional PI controller reveals the superiority of the first one. The fuzzy controller is less sensitive to the system parameters variation and this proves its robustness.

References

[1] Abed, K., Nabti, K., and Benalla, H., May 08-10 2006, "Ameliorate speed sensorless control of induction machine (IM) by a three level voltage inverter using indirect rotor field oriented control (IRFOC) scheme, simulation and experimentation validation, " Second International Conference on Electrical Systems ICES'06, Oum El Bouaghi, Algeria, pp. 260-265.

[2] Rajashekara, K., Kawamura, A., and Matsuse, K., 1996, "Sensorless control of AC motor drives--speed and position sensorless operation, " IEEE Press, New York.

[3] Abed, K., Nabti, K., and Benalla, H., June 26-28 2006, "A speed sensorless control for triphase induction machine using indirect field-oriented control scheme," Proceedings of the 15th IASTED International Conference APPLIED SIMULATION AND MODELLING, Rhodes, Greece, (522-057) pp. 346-351.

[4] Pinard, M., 2004, Commande electronique des moteurs electriques, Editions DUNOD, Paris.

[5] Chavez, V. S., Palomares, R. A., and Segura, A. N., 16-18 Feb. 2004, " Speed estimation for an induction motor using the extended kalman filter, electronics, communications and computers," CONIELECOMP 2004. 14th International Conference, pp. 63-68.

[6] Lysherski, S., 2000, Electromechanical systems, electric machines and applied mechatronics, CRC Press, Boca Raton.

[7] Shi, K. L., Chan, T. F., Wong, Y. K., and Ho, S. L., Jan. 2000, "Speed Estimation of an induction motor drive using extended kalman filter, power engineering society winter meeting" IEEE, Volume 1, 23-27, pp. 243-248.

[8] Shoudao, H., Yaonan, W., Jian, G., Jiantao, L., and Sihai, Q., 15-19 June 2004, "The Vector Control Based On MRAS Speed Sensorless Induction Motor Drive, Intelligent Control and Automation, " WCICA 2004. Fifth World Congress on Volume 5, pp. 4550-4553.

[9] Hakju, L., Jaedo, L., Sejin, S., 12-16 June 2001, "Approach to Fuzzy control of indirect field-oriented induction motor drives," Industrial Electronics, Proceedings. ISIE 2001. IEEE International Symposium on Volume 2, pp. 1119-1123.

[10] Abed, K., Nabti, K., and Benalla, H., August 29-31, 2007, "A fuzzy IRFOC application in speed sensorless control of IM supplied from an ameliorate inverter, " Proceedings of the 16th IASTED International Conference APPLIED SIMULATION AND MODELLING, Palma de Mallorca, Spain, (581-025).

K. Abed (*), K. Nabti and H. Benalla

(*) Department of Electrical Engineering, Faculty of Engineering Sciences Mentouri University Route d'Ain El Bey, Constantine, 25000, ALGERIA E-mail: Khoudir.abed@Laposte.net

Table : Control Rule Base ECE NL NM NS ZE PS PM PL N ZE S M L M S ZE ZE ZE S M L M S ZE P ZE M L L L M ZE

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Author: | Abed, K.; Nabti, K.; Benalla, H. |
---|---|

Publication: | International Journal of Applied Engineering Research |

Article Type: | Report |

Geographic Code: | 1USA |

Date: | Mar 1, 2008 |

Words: | 1922 |

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