# Speed sensorless direct torque control and stator resistance estimator of induction motor based MRAS method.

IntroductionAdvanced control of electrical machines requires an independent control of magnetic flux and torque. For that reason it was not surprising, that the DC-machine played an important role in the early days of high performance electrical drive systems, since the magnetic flux and torque are easily controlled by the stator and rotor current, respectively. The introduction of Field Oriented Control meant a huge turn in the field of electrical drives, since with this type of control the robust induction machine can be controlled with a high performance [1]-[4],[18]-[27]. Later in the eighties a new control method for induction machines was introduced: Direct Torque Control (DTC) of induction motor, due to its simple structure and ability to achieve fast torque and flux control [1]-[21], has attracted more and more interest recent years. However, in low speed region the problem of how to accurately estimate stator flux-linkage and rotor speed still exists, leading to the deterioration of its performance [1]- [4].

Common disadvantages of conventional DTC are the high torque and flux ripples and stator resistance variation [6]-[21]. Many researchers already paid some attention to the first issue, i.e. the high torque and flux ripple, speed sensorless control based on MRAS method also becomes popular in recent years. Many efforts were made, [16] [27] to apply this method in various control strategies, but most of them can only estimate one parameter (usually, the rotational speed) at a time [10]-[22]. The variation of other parameters [10] [16], such as the resistance of stator or rotor winding, however, may lead to the inaccuracy of estimated speed [11][17],. That is one of the reasons why the performance of the speed sensorless AC drive will deteriorate at low speed range [21]-[23]. In this paper, an MRAS method, based on a fill-order induction motor model, is introduced and is applied to a direct torque control system [21]. The authors also proposed a novel modified DTC scheme to minimize the ripples in flux and torque in (IM) can be applied to realize not only single rotor speed estimation, but such as, rotor speed and stator resistance respectively[10], [16]-[21], like the rotor speed and stator resistance Rs has been compensated in this paper. Simulation results shows validate the effectiveness of the new method.

Direct Torque Control

The basic functional blocks used to implement the DTC scheme are represented in Figure.1. The instantaneous values of the stator flux and torque are calculated from stator variable by using a closed loop estimator [1]-[4], [7]-[9]. Stator flux and torque can be controlled directly and independently by properly selecting the inverter switching configuration [1] [4].

[FIGURE 1 OMITTED]

Voltage Source Inverter

In a voltage fed three phases, the switching commands of each inverter leg are complementary [1], [7]-[9]. So for each leg a logic state [C.sub.i] (i=a,b,c) can be defined. [C.sub.i] is 1 if the upper switch is commanded to be closed and 0 if the lower one in commanded to be close (first).

[FIGURE 2 OMITTED]

Since three are 3 independent legs there will be eight different states, so 8 different voltages. Applying the vector transformation described as [7]-[9]:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

As it can be seen in second, there are six non-zero voltage vectors and two zero voltage vectors which correspond to ([C.sub.1], [C.sub.2], [C.sub.3]) = (111)/ (000) as shown by Figure.3 [1] [3].

[FIGURE 3 OMITTED]

Stator flux control

Stator voltage components ([V.sub.sd], [V.sub.sq]) on perpendicular (d,q) axis are determined from measured values ([U.sub.o] and [I.sub.sabc]). Boolean switching controls ([C.sub.1], [C.sub.2], [C.sub.3],) by, [1]-[4],

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

and stator current components ([I.sub.s[alpha]], [I.sub.s[beta]]) :

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

The stator resistance can be assumed constant during a large number of converter switching periods Te [1]. The voltage vector applied to the induction motor remains also constant during one period [T.sub.e] [8]. The stator flux is estimated by integrating the difference between the input voltage and the voltage drop across the stator resistance as given by equations (4) [8] [9]:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

During the switching interval, each voltage vector is constant and (4) is then rewritten as in (5):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

In equation; [[PSI].sub.s0] stands for the initial stator flux condition.

In fact, we have d[[bar.[PSI]].sub.s]/dt [approximately equal to] [[bar.V].sub.s]. The following Fig.4 is established for the case [V.sub.s]=[V.sub.3].

[FIGURE 4 OMITTED]

Neglecting the stator resistance, (5) implies that the end of the stator flux vector will move in the direction of the applied voltage vector, as shown in Figure.4 [[PSI].sub.so] is the initial stator flux linkage at the instant of switching [1][3][4][6][8]. To select the voltage vectors for controlling the amplitude of the stator flux linkage, the voltage vector plane is divided into six regions, as shown in Figure.3. In each region, two adjacent voltage vectors, which give the minimum switching frequency, are selected to increase or decrease the amplitude of stator flux, respectively [1][4][7]-[9]. For instance, the vectors [V.sub.4] and [V.sub.3] are selected for to increase or to decrease the amplitude of stator flux when it is in region number 1. In this way, can be controlled at the required value by selecting the proper voltage vectors. The voltage vectors are selected for keeping the magnitude stator flux and electromagnetic torque within a hysteresis band [1] [3] [6] [7].

Stator flux and torque estimation

The magnitude of stator flux, which can be estimated by (6).

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)

The stator flux linkage phasor is given by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)

By comparing the sign of the components stator flux ([[phi].sub.sd] [[phi].sub.s[??]]) and the amplitude of stator flux, we can localize the zone where we find the flux. Electromagnetic torque calculation uses flux components (6), current components (3) and P, pair-pole number of the induction machine [1] [8] [9]:

[[GAMMA].sub.em] = p([[PSI].sub.sa][I.sub.s[beta]][I.sub.s[alpha]])(8)

As shown in Fig.3, eight switching combinations can be selected in a voltage source inverter, two of which determine zero voltage vectors and the others generate six equally spaced voltage vectors having the same amplitude[1][3][4][8],. According to the principle of operation of DTC, the selection of a voltage vector is made to maintain the torque and stator flux within the limits of two hysteresis bands. The switching selection table for stator flux vector lying in the first sector of the d-q plane is given in Tab.1 [1] [2] [3] [4].

Model Reference Adaptive System

The Model Reference Adaptive Systems (MRAS) approach uses two models. The model that does not involve the quantity to be estimated (the rotor speed .re in our case) is considered as the reference model. The model that has the quantity to be estimated involved is considered as the adaptive model (or adjustable model) [21]-[29]. The output of the adaptive model is compared with that of the reference model, and the difference is used to drive a suitable adaptive mechanism whose output is the quantity to be estimated (rotor speed in our case). The adaptive mechanism should be designed to assure the stability of the control system. Figure 1 illustrates the basic structure of MRAS [23], [26]-[29]. Different approaches have been developed using MRAS, such as rotor-flux-linkage estimation-based MRAS, back-EMF-based MRAS [21] [27] [29].

[FIGURE 5 OMITTED]

The model of an induction motor in stationary reference frame is used as follows [21]:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9)

Where

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (10)

Is = [[[[I.sub.s[alpha]] [I.sub.s[beta]]].sup.T], [[phi].sub.r] = [[[[PSI].sub.r[alpha] [[PSI].sub.r[beta]]].sup.T] (11)

[A.sub.11] ([R.sub.s]/[sigma][L.sub.s] + 1 - [sigma]/[sigma][T.sub.r])I,[A.sub.12]---1/[rho](1/[T.sub.r]) I - [omega]J

[A.sub.21] = (Lm/[T.sub.r] I), [A.sub.22] = ([rho][A.sub.12]) (12)

and

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (13)

a full-order observer model can be derived from (9) as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (14)

where: G is the gain matrix of the observer. In this paper, G is set to zero.

[[??].sub.s] : Estimated value of stator current

[[??].sub.r] Estimated value of rotor flux linkage

MRAS based on rotor flux-linkage estimation

The proposed MRAS is using state observer model with current error feedback and rotor current model as two models for flux estimation.Fig.3 shows the block diagram of the proposed MRAS[23][26][28].

The reference model is given by:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (15)

The adjustable model is given by:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (16)

where

[[PSI].sub.r[alpha]], [[PSI].sub.r[beta]] : Estimated values of rotor fluxes in state observer model [23] [24] [24]

[[PSI].sub.r[alpha]], [[PSI].sub.r[beta]] : Estimated values of rotor fluxes in rotor current model.

Rotor speed is obtained from the adaptation mechanism as follows:

[[??].sub.re] = ([K.sub.p] + [K.sub.i]/p) ([[PSI].sub.r[beta]] [[??].sub.r[alpha]]--[[PSI].sub.r[alpha]] [[??].sub.r[beta]])(17)

The presence of the pure integrators brings the problems of initial conditions and drift. In [28] [29], a low pass filter was used to replace the pure integrator, but the performance in the low speed range is not satisfying [28].

Speed and parameter estimation method

A novel speed sensorless control method can be established based on the full-order reference and adjustable model described above [21].

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (18)

where

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (19)

According to Popov's criterion of hyperstability, the following adaptive laws for rotor speed, stator and rotor resistances are obtained [12]-[17], [21]:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (20)

where

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (21)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (22)

where

[F.sub.RS] = -([e.sub.[alpha]s] [I.sub.[alpha]s] + [e.sub.[beta]s] [I.sub.[beta]s]), [k.sub.SI], [k.sub.SP] [greater than or equal to] 0 (23)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (24)

where

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (25)

The above adaptive laws are based on the fact that [I.sub.s] and [[PSI].sub.r] are known. However, [[PSI].sub.r] is not measurable in most of practical systems [19] [21]. Therefore, it is impossible to get the real value of [F.sub.Rr] directly. But generally, [absolute value of [e.sub.[alpha]s]/[rho]] is much greater than [e.sub.[alpha]r].

Hence by ignoring [e.sub.[alpha]r] and [e.sub.[beta]r] the troublesome [[PSI].sub.r], can be avoided, and the above three adaptive laws can be simplified as follows [12]-[17] [21]:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (26)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (27)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (28)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (29)

Where [??](0), [[??].sub.s](0), [[??].sub.r](0) are the initial values of [omega], [R.sub.s], [R.sub.r]. [12]- [17] [21],

Interpretation Results

Two Matlab / Simulink models were developed to examine the different control algorithms. One is for the basic DTC system, and the other for the modified DTC _MRAS system. In the simulations a 1kW, 230V, 60Hz squirrel-cage induction motor is employed whose nominal parameters are: P =2, [R.sub.s] = 7.1 [OMEGA], [R.sub.r] = 3.4 [OMEGA], [L.sub.s] = 0.831H, Lr = 0.831H, M = 0.8H,

J = 0.05kg[m.sup.2]. Figures (6 to 19) show the results simulation of the basic DTC and the proposed DTC_MRAS a step change in speed reference from [0[right arrow]80[right arrow]30] rpm.

As the Figures (6 and 12) show, it is observed that the speed tracks the reference values adequately, for two methods, but the response speed in basic DTC presented the ripple, what is well to show in Figures (6 and 11) the state errors set to 3 rad/sec for speed. Figures (7,9, 13and 15) Shows that the flux of the basic DTC and DTC_MRAS offers the fast transient responses That means the trajectory of stator flux established more quickly than that of the Conventional C_DTC. The torque and flux ripple of the basic DTC are 5Nm and 0.1Wb, respectively. However, the torque and flux ripple of the proposed DTC_MRAS is almost zero. The transient and steady state phase current is compared for the two methods, to see the Figures (11 and 17). In basic DTC, a high distortion in the current can be observed. It is seen from this result that the torque, flux ripple and stator current are reduced drastically by the proposed algorithm, and that because the speed, stator resistance, and rotor resistance, are estimated at a time, and the variation of stator resistance, Rs, has been compensated show Figures (18 and 19).

Simulation Results

[FIGURE 6 OMITTED]

[FIGURE 7 OMITTED]

[FIGURE 8 OMITTED]

[FIGURE 9 OMITTED]

[FIGURE 10 OMITTED]

[FIGURE 11 OMITTED]

[FIGURE 12 OMITTED]

[FIGURE 13 OMITTED]

[FIGURE 14 OMITTED]

[FIGURE 15 OMITTED]

[FIGURE 16 OMITTED]

[FIGURE 17 OMITTED]

[FIGURE 18 OMITTED]

[FIGURE 19 OMITTED]

Conclusions

In this paper, The proposed DTC Based MRAS method are suitable for estimating [[omega].sub.r], [R.sub.r], [R.sub.s] the same time and the change of stator resistance can be traced and compensated, The proposed DTC Based MRAS Method has been examined and compared with basic DTC. Simulation results show the effectiveness of the new method. The main improvements shown are:

* Low complexity

* Good dynamic response for flux and torque

* High robustness.

* Reduction of torque, stator flux and current ripples in transient steady state.

* No flux droppings caused by sector changes circular trajectory.

* The parameter of induction motor are estimated and compensated at a time.

Refrence

[1] Takahashi I and Noguchi T, " A New Quick-Response And High-Efficiency Control Strategy Of Induction Motor", IEEE Trans. On IA, Vol.22, No.5, Sept/Oct (1986), PP.820-827.

[2] Depenbrock, M,"Direct self--control (DSC) of inverter--fed induction machine", IEEE Trans. Power Electronics, Vol.3, No.4, Oct (1988), PP.420-829.

[3] Casadei, D, Profumo, F, Serra, G and Tani, A;" FOC DTC: Tox Viable Schemes for induction Motors Ttorque Control", IEEE Trans. Power Electronics. On PE, Vol.17, No.5, Sept(2002),

[4] Casadei, D. and Serra, G, "Implementation of direct Torque control Algorithme for Induction Motors Based on Discrete Space Vector Modulation", IEEE Trans. Power Electronics. Vol.15, No.4, JULY(2002),

[5] Thomas G. Habetler and Deepakraj M. Divan, "Control Strategies for Direct Torque Control Using Discrete Pulse Modulation", IEEE Transactions On Industry Applications, Vol. 21, No. 5, September 1991.

[6] Romeo Ortega, Nikita Barabanov and Gerardo Escobar Valderrama," Direct torque control of induction motors: stability analysis and performance improvement", IEEE Transactions on Automatic Control, Vol. 46, No. 8, (2001).

[7] R. Toufouti, H. Benalla, and Meziane S, "Three-Level Inverter With Direct Torque Control For Induction Motor", world conference on energy for sustainable development: technology advances and environmental issues, Egypt, 6-9 December 2004

[8] R.Toufouti, S.Meziane and H.Benalla, "Direct Torque Control for Induction Motor Using Fuzzy Logic", ICGST International Journal on Automatic Control and System Engineering (ACSE), October, 2006, volume (6), Issue (3), pages (47-53).

[9] S.Meziane, R.Toufouti and H.Benalla, " Review of Direct Torque and Flux Control Methods for Voltage Source Inverter Fed Induction Motor ", ICGST International Journal on Automatic Control and System Engineering (ACSE), June, 2006, volume (6), Issue (2), pages (17--24).

[10] F. Peng and T. Fukuo.," Robust speed identification for speed- sensorless vector control of induction motors," IEEE Transactions of Industrial Applications, 30:1234{1240, Sept. /Oct. 1994.

[11] Jawad Faiz, and Mohammad B. B. Sharifian, " Different Techniques for Real Time Estimation of an Induction Motor Rotor Resistance in Sensorless Direct Torque Control for Electric Vehicle," IEEE Transactions on Energy Conversion, Vol. 16, No. 1, March 2001

[12] L Umanand and S. R. Bhat, "On-line estimation of stator resistance of on induction motor for speed control applications, "IEE Proc. Electr. Power App., vol. 142, no. 2, pp. 97-103, 1995.

[13] Z. Zhang, G. E. Dawson, and T. R. Eastham, "Microcontroller based on-line identification of variable parameters in induction motors," Electric Machines and Power Systems, vol. 23, pp. 353-360, 1995

[14] T. Matsuo and T. A. Lipo, "A rotor parameter identification scheme for vector-controlled induction motor drives," IEEE Trans. on Ind. App.,vol. 21, no. 4, pp. 624-632, 1985.

[15] H. Chai and P. P. Acarnley, "Induction motor parameter estimation algorithm using spectral analysis," IEE Proc. B, vol. 139, no. 3, pp. 165-174, 1992.

[16] Yongdong Li, Jianwen Shao, "The Research of Fully Digitalized Direct Torque Control of Induction Motor", EACS'94.

[17] T. Abe and T. G. Habetter, al, "Evaluation of a High Performance Induction Motor Drive Using Direct Torque Control", PCC-Y OKOHAMAP3.

[18] Li Yongdong, Shao Jianwen and Si Baojun, "Direct Torque Control Induction Motor for Low Speed Drives Considering Discrete Effects of Control and Dead-time of Inverter", 1AS'97.

[19] M. P. Kazmierkowski, M. A. Dzienikowski, A. Kasprowicz, and S. Kanoza, "Speed sensorless control of DC link resonant inverter-fed induction motor drives," in PEMC, vol. 1, 1996, pp. 110-114.

[20] Jie Chen, Yongdong Li, "Virtual Vectors Based Predictive Control of Torque & Flux of Induction Motors and Speed Sensorlesq Drives", IASP9.

[21] Zhuohui Tan, Yongdong and Li Zhiyan Ji, "Speed Sensorless DTC and Parameter Estimation of Induction Motor Based on a Full-order MRAS Method ",

[22] Y. Hori C. Ta and T. Uchida., "MRAS-Based Speed Sensorless Control for Induction Motor Drives Using Instantaneous Reactive Power ", IECON, 1417{1422, Nov. /Dec. 1991.

[23] Joachim Holtz," Sensorless Control of Induction Motor Drives," Proceedings of the IEEE, Vol. 90, No. 8, Aug. 2002, pp. 1359-1394

[24] H. Sugimoto S. Tamai and M. Yano," Speed sensor-less vector control of induction motor with model reference adaptive system," Conference Record of IAS Annual Meeting, pages 189{195, 1987.

[25] D.W. Jin Y.A. Kwon.," A Novel MRAS Based Speed Sensorless Control of Induction Motor," IECON, 2:933{938, Nov. /Dec. 1999.

[26] Li Zhen, and Longya Xu, "Sensorless Field Orientation Control of Induction Machines Based on a Mutual MRAS Scheme," IEEE Transactions on Industrial Electronics, Vol. 45, No. 5, October 1998.

[27] M. N. Marwali and Ali Keyhani," A Comparative Study of Rotor Flux Based MRAS and Back EMF Based MRAS Speed Estimators for Speed Sensorless Vector Control of Induction Machines," IEEE Industry Applications Society Annual Meeting New Orleans, Louisiana, October 5-9, 1997.

[28] M. Cirrincione, and M. Pucci, "An MRAS-Based Sensorless High-Performance Induction Motor Drive with a Predictive Adaptive Model," IEEE Transactions on Industrial Electronics, Vol. 52, No. 2, April 2005.

S. Meziane, R. Toufouti and H. Benalla

Laboratory of Electrical Engineering,

Constantine University, Algeria

E-mail: [meziane_elc, toufoutidz, Benalladz]@yahoo.fr

Table 1: Switching table for Conventional DTC Sector Flux Torque 1 2 3 [DELTA][psi]=1 [DELTA][GAMMA]=1 [V.sub.2] [V.sub.3] [V.sub.2] [DELTA][GAMMA]=0 [V.sub.7] [V.sub.0] [V.sub.7] [DELTA][GAMMA]=1 [V.sub.6] [V.sub.1] [V.sub.2] [DELTA][psi]=0 [DELTA][GAMMA]=1 [V.sub.3] [V.sub.4] [V.sub.5] [DELTA][GAMMA]=0 [V.sub.0] [V.sub.7] [V.sub.0] [DELTA][GAMMA]=1 [V.sub.5] [V.sub.6] [V.sub.1] Sector Flux Torque 4 5 6 [DELTA][psi]=1 [DELTA][GAMMA]=1 [V.sub.5] [V.sub.6] [V.sub.1] [DELTA][GAMMA]=0 [V.sub.0] [V.sub.7] [V.sub.0] [DELTA][GAMMA]=1 [V.sub.3] [V.sub.4] [V.sub.5] [DELTA][psi]=0 [DELTA][GAMMA]=1 [V.sub.6] [V.sub.1] [V.sub.2] [DELTA][GAMMA]=0 [V.sub.7] [V.sub.0] [V.sub.7] [DELTA][GAMMA]=1 [V.sub.2] [V.sub.3] [V.sub.4]

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Title Annotation: | model reference adaptive system |
---|---|

Author: | Meziane, S.; Toufouti, R.; Benalla, H. |

Publication: | International Journal of Applied Engineering Research |

Article Type: | Report |

Geographic Code: | 1USA |

Date: | Jun 1, 2008 |

Words: | 3405 |

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