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An Approach for Sensorless Position Estimation for Switched Reluctance Motors Using Artifical Neural Networks Erkan Mese David A. Torrey Department of Electric Power Engineering Rensselaer Polytechnic Institute Troy, NY 12180-3590

Abstract This paper presents a new approach to the sensorless control of the switched-reluctance motor (SRM). The basic premise of the method is that an Artificial Neural Network (ANN) forms a very efficient mapping structure for the nonlinear SRM. Through measurement of the phase flux linkages and phase currents the neural network is able to estimate the rotor position, thereby facilitating elimination of the rotor position sensor. The ANN training data set is comprised of magnetization data for the SRM with flux linkage (λ) and current (i) as inputs and the corresponding position (θ) as output in this set. Given a sufficiently large training data set, the ANN can build up a correlation among λ, i and θ for an appropriate network architecture. This paper presents the development, implementation, and operation of an ANN-based position estimator for a three-phase SRM.

1

Introduction

The switched reluctance motor (SRM) has been receiving attention for industry applications due to its low cost in mass production, reduced maintenance requirements, rugged behavior and large torque output over very wide speed range. On the other hand, torque ripple, acoustic noise and rotor position sensor requirements are often-cited disadvantages of the motor [1, 2]. A large number of methods have been introduced to accomplish position sensorless operation of the SRM during the last fifteen years. The fundamental principle used in position estimation is the extraction of rotor position information from stator circuit measurements or their derived parameters. Flux linkage is a function of the rotor position and the current through the phase winding. Compared to other types of electric machines, it is an advantage for an SRM not to have a rotor field disturbing the stator field. On the other hand, the nonlinear relationship between the electrical and mechanical terminals of the machine makes analytic calculation of rotor position impossible for a given flux linkage and current value. Moreover, accurate measurement would be much more difficult if more than one phase winding carries current simultaneously and the mutual coupling is not negligible. All of the proposed techniques try in one way or another to use the SRM as its own sensor [3]. Many of these techniques require manipulating the unexcited phase [4, 5, 6, 7]. Another approach is to use an observer [8], but the observer has a difficult time with the magnetic nonlinearities of the SRM. In another method [9], magnetization data are used for position estimation. The data are stored in a look-up table and interpolation is used to estimate rotor position. The major difficulty in this approach is the accurate modeling of SRM since simulated data are used instead of real-time experimental data. Recently, many publications have appeared in the literature based on using artificial intelligence techniques for motion control. These are summarized very well in [10]. Application of artificial intelligence

for position estimation in SRM drives is also studied by many researchers. In [11], magnetization data of only the aligned and unaligned positions are used from the measurements, then fuzzy reasoning is used to construct magnetization curves for the intermediate positions. This is one of the major contributions for the method since acquiring the magnetization data for several rotor positions is the main drawback of magnetization-data based approaches. It is also suggested in [11] that fuzzy-logic be used along with a coarse position estimator based on the dynamic equations of the system. This alleviates large memory requirements when the fuzzy-logic controller is the only estimator in the system. In another fuzzy reasoning based method proposed by [12], measured magnetization data for several rotor positions are stored in fuzzy rule-base tables, the position information is then retrieved from the tables during online operation. Furthermore, the performance of the estimator is improved by some additional features like fuzzy phase selection, fuzzy flux linkage and angle predictors in order to maintain robust sensorless operation of SRM. In [13], an ANN is used for identification and control purposes. A feedforward type of ANN is used to identify the dynamical states of an SRM. Naturally, the rotor position along with the speed is the output of the ANN. They successfully proved by simulation that the ANN can be used in a closed-loop system as a position and speed estimator. In another ANN based approach suggested by [14], it is assumed that the inductance is substantially varying as a sinusoidal function of rotor position and rotor pole numbers. This eliminates the requirement for a priori knowledge about the SRM inductance profile. This simplification allows derivation of an analytical relation to estimate rotor position. The idea of using an ANN is introduced when the main position estimation algorithm degrades at low speeds. The ANN is trained with the good estimates of position and is used to improve the performance at low speeds. This paper presents another approach to the sensorless control of the SRM. The approach can be classified within the magnetization-data based methods. The basic premise of the method is that an artificial neural network forms a very efficient mapping structure for the nonlinear SRM [15, 16, 17]. Through measurement of the phase flux linkages and phase currents the neural network is able to estimate the rotor position, thereby facilitating elimination of the rotor position sensor. The ANN training data set is comprised of magnetization data of the SRM for which flux linkage (λ) and current (i) are inputs and the corresponding position (θ) is the output in this set. Given a sufficiently large training data set, the ANN can build up a correlation among λ, i and θ for an appropriate network architecture [18]. Section 2 discusses the practical issues associated with the design and implementation of an ANN-based position estimator. A case study with off-line verification of an ANN is given in Section 3. Issues related to phase selection timing are discussed in Section 4. Sections 5 and 6 present an evaluation of the ANN-based estimator for a 11.5 kW 6/4 SRM. A comparative discussion between ANN based and fuzzy-logic based position estimators is given in Section 7.

2

ANN-Based Rotor Position Estimator for the SRM

The basic premise of the proposed method is that an ANN forms a very efficient mapping structure for the nonlinear SRM. Through measurement of the phase flux linkages and phase currents the neural network is able to estimate the rotor position, thereby facilitating elimination of the rotor position sensor. The ANN training data set is comprised of magnetization data for the SRM of which flux linkage (λ) and current (i) serve as inputs and the corresponding position (θ) as output in this set. Given a sufficiently large training data set, the ANN can build up a correlation among λ, i and θ for an appropriate network architecture. Then this off-line trained ANN can be evaluated against a test data set which may have different λ − i values. Figures 1 and 2 show how the ANN is trained off-line and then used as an on-line position estimator, respectively.

2.1

Construction of the Training Data Set

There are two possible ways to generate training data: model-based data generation and experiment-based data generation.

2

SRM INVERTER

RECTIFIER SRM

Shaft Encoder

C From AC Source

CT

V

i

Flux Estimator Gate Drivers i Current Regulator θon θoff Iref

λ

i

ADC

SRM Commutator Algorithm

Data Acquisition

θ

Algorithm

DSP BOARD λ

i

ANN

θest

-

θ + θerror

Offline Training Algorithm in PC

Figure 1: Collecting data and training an ANN. SRM INVERTER

RECTIFIER SRM C

From AC Source

CT

V

i

Flux Estimator Gate Drivers Current Regulator

i

θon θoff Iref

λ

i

ADC SRM

λ

Commutator Algorithm

θ

i

ANN Based Position Estimator

DSP BOARD

Figure 2: Usage of the trained ANN as a position estimator.

3

Model Based Data Generation: A suitable magnetization model for the associated SRM is used to generate the data [19, 20]. Given a proper model, flux linkage values are computed for randomly generated phase current and rotor position values so that the resulting flux linkage, phase current and rotor position values will judiciously cover the intended operating region. This method is used during the simulation study. Experiment Based Data Generation: In this approach the motor is run for certain operating points with a shaft encoder so that the magnetization characteristic is swept over certain regions, or, in a better approach, the motor is run from zero speed to full speed and every electric cycle of the flux linkage, phase current and rotor position is captured with a certain sampling rate. This allows more judicious coverage of the magnetization characteristic. This method is used during the experimental study.

3

A Case Study With Off-Line Verification of the ANN

An available 11.5 kW SRM with 6 stator poles and 4 rotor poles is used in order to validate the concept. For the first step, 1000 data points are generated randomly by using the model [19] λ(i, θ) = a1 (θ) [1 − exp(a2 (θ)i)] + a3 (θ)i

.

(1)

After generating the training data set of λ, i and θ, normalization is performed in the input space so that current and flux information is scaled between zero and one. However, there is no need to normalize the rotor position information since the output layer of the ANN uses a linear activation function. Both the design of the ANN and selection of optimum training parameters were performed by trial and error. A single layer multilayer feedforward ANN with 10 hidden neurons is found to be a good balance between estimation error and ANN complexity. The comparison of the ANN structures is based on minimizing the least-squared estimation error over the training data set.

3.1

Testing the Trained ANN for Arbitrary Operating Points of SRM

The performance of the trained network is tested against different operating points. The first task in this process is to obtain flux linkage and current waveforms. After capturing the waveforms by means of an SRM simulation program, flux linkage and phase current are normalized. At the last step of the verification, normalized flux linkage and phase current values are fed into the trained network to estimate rotor position. Then the estimated rotor positions are compared with real values of the rotor position. Figure 3 illustrates the flux linkage and phase current waveforms along with the rotor position estimation and the estimation error for an operating point. As seen from Fig. 3, the trained ANN is capable of estimating the rotor position with less than 3 electrical degrees of error over a particular interval of one electrical cycle. Outside the interval, on the other hand, error grows dramatically. This means that the phase cannot be used anymore; a more appropriate phase should be selected to continue the estimation. The best estimation interval falls within [180◦ , 360◦]; this is expected because the ANN was trained for this interval. A detailed look at the estimation error plots show that the effective estimation region is less than 180◦ . The reason for this is the tightly bunched up nature of the magnetization curves over certain angular intervals. As shown in Fig. 4, the area close to alignment has heavily localized data. In addition, regions around small current and close to unalignment have localized data as well. According to the convergence theorem for perceptron training rules [21], the number of training iterations necessary for separating two adjacent training patterns into two different classes increases when the distance between the two patterns gets close to zero. A consequence of training the network using significantly localized data is that we inevitably suffer from poor convergence of the training process and get lower estimation accuracy over the localized region. Although theoretically two phases are enough for estimation over the full electrical cycle, utilization of information from at least three phases will give better performance. 4

Phase Current

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Figure 3: Off-line estimation performance for n=1500 rpm, θon = 165◦, θcond = 150◦ , Iref = 150 A. 0.45

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Figure 4: The magnetization curves for a typical SRM tend to bunch up near the aligned position.

4

Phase Selection and Estimator Commutation

In the previous section, it was shown that at least two phase quantities should be measured to complete one electrical cycle. In practice we need three phase quantities due to data bunching within the magnetization characteristic. An important problem arises in the selection of the correct phase at the correct time to complete one cycle of estimation. This is required in order to achieve smooth transitions in the position estimation. Two adjacent phases in a 3 phase SRM have 120◦ spatial phase shift. In reality each phase is available for estimation on [180◦ , 360◦]. This suggests each phase can hand over its estimation duty to the next phase

5

at k θsc k θsc

= 180◦ + 120◦ = 300◦ ,

(2)

k where θsc is the spatial commutation angle of the conducting phase where it hands over the estimation duty k , to the next phase. This result requires that the estimator commutation angle for the conducting phase, θec should be k θec k θec

k θsc 300◦

> ≥

.

(3)

Up to this point, the estimator commutation angle is computed by considering two fundamental SRM features: 1. Motor operation uses the second (increasing inductance) half of the magnetization characteristic. 2. There is a 120◦ spatial phase shift between SRM phases. However, there is another commutation event going on between SRM phases, which is referred to as phase commutation. Phase commutation is manipulated by two independent variables: phase turn-on angle, θon , and phase conduction angle, θcond . Another dependent variable can be derived by adding these two angles and called the phase turn-off angle θoff . Low speed (chopping mode) and high speed (single pulse mode) operation present two different characteristics for estimator commutation. The reason for this can be explained as follows. Phase current continues to flow through the flyback diodes after the phase is turned off. This uncontrolled current flows until the current becomes zero. The duration of the uncontrolled current is quite short in the chopping mode compared to single pulse operation because of the relatively lower back emf. This requires the estimator phase to be commutated to the next phase after turning off the conducting phase. In this paper, some results are given for low speed operation. A detailed study of estimator commutation can be found in [22]. The first constraint on the phase commutation is that there should not be any gap between the turn off instant of a conducting phase and the turn on instant of the upcoming phase. Furthermore, overlapping of two conducting phases can be allowed. This is represented mathematically as k+1 k ≤ θoff θon k k θoff ≥ θec

,

(4)

,

(5)

k k+1 is the turn off angle of the conducting phase, θon is the turn on angle of the upcoming phase where θoff k and θec is the estimator commutation angle for the conducting phase.

The second constraint on the phase commutation angle sets a limit for the minimum allowable value of the conduction angle: (6) θcond ≥ 120◦ . The third constraint on the phase commutation angles puts a minimum limit on the turn-on angle for a given estimator commutation angle and conduction angle: k k θon > θec − θcond

.

(7)

These constraints are based on the assumption a conducting phase cannot be used after it is turned off. In reality, tail current and flux are still available for use. This practical consideration puts certain margins on the commutation angles. For instance, we still have 5◦ − 10◦ to go beyond the minimum turn-on angle limit or minimum conduction angle limit [22].

6

5

A Case Study with Online Verification of the ANN Based Position Estimator

This section examines the possibilities of using the ANN estimator in the real time operation of the SRM. Various operating conditions have been tested from zero to full speed with a successful start-up sequence. Simulation results show that the ANN can be used as a position estimator for the SRM with acceptably small estimation error. The simulation process includes three major steps: SRM simulation, ANN simulation and integration of these two by considering the issues like phase selection and estimator commutation. SRM simulation with Simulink is skipped since it is beyond the scope of this paper. Interested readers are referred to [23] for detailed information.

5.1

On-Line Simulation Results

On line simulation is performed by using the building blocks and estimator commutation strategies given in previous sections. Figure 5 shows the Simulink block diagram of the online simulation. The ANN weights are computed with off-line training as described above. The sampling period at the input terminals of the ANN estimator is selected as 75 µs. Figures 6 and 7 show estimation results during the start-up transient. 30/(pi)

ANN POSITION ESTIMATOR&COMMUTATOR

SRM THETA

current_A flux_A

current_A flux_A

THETA COM current_B

current_B theta_est

170

THETA ON

150

COND.

flux_B current_C flux_C

150

I_REF

flux_B current_C flux_C

MECHANICAL LOAD

TORQUE

INPUT

TORQUE SPEED

LOAD

0.2

(mrps)

COEFFICIENT

LOAD COEFFICIENT

t Clock1

To Workspace

1

Figure 5: The Simulink diagram for on-line simulation of ANN estimator driven SRM.

5.2

Performance Improvement By Using One Additional Flux Linkage Estimator

The studies showed that an ANN that is trained to estimate flux linkage for given current and rotor position performs better estimation than the one that is trained to estimate rotor position for given current and flux linkage. This is exploited to improve the estimator performance as follows. After estimating the rotor position by the original method described in the previous sections, the estimated rotor position along with phase current are fed into another ANN to estimate the flux linkage. The error between the real and estimated flux linkages reflects the difference between real rotor position and estimated rotor position. Then, the flux linkage error can be used to correct the estimated rotor position. The sampling period prevents us 7

Phase A Current(Amp.)

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0.5 0.4 0.3 0.2 0.1 0

Figure 6: Phase A current and flux linkage waveforms during startup.

Estimated Position

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Figure 7: Estimated rotor position and estimation error along with real rotor position during startup. Rotor positions and estimation error are given in electrical degrees.

from making an iteration more than one time. But even this single iteration can be used for satisfactory improvement. Figure 9 shows the flowchart of the complete estimator with flux linkage estimator. This process is effectively canceling the systematic errors in the position estimate. The flux estimator has one hidden layer with five neurons. Similar to the position estimator, the hidden layer neurons have a sigmoidal activation function but the output layer neuron has linear activation function. The sampling rate of real flux linkage and phase current quantities at the estimator input terminal is increased to 100 µs. Figure 8 shows the estimation results after modification. It is seen that the estimator performance is improved after modification at the expense lower resolution.

8

Before Modification

Estimation Error

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Estimation Error

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0.15 Time (second)

Figure 8: Error comparison between the original estimator and the modified one with one flux linkage estimator for the startup period. Estimation error is given in electrical degrees.

5.3

Performance Improvement By Using Two Additional Flux Linkage Estimators

As stated in the previous sections, the ANN rotor position estimator can only perform estimation on [180◦ , 360◦] due to the ambiguous nature of the magnetization characteristic caused by hysteresis. The improvement proposed in this section is focused on widening this estimation interval to [0◦ , 360◦ ]. This is quite useful for high speed operation where the turn-on angle has to be advanced so much that the phase commutation angles constraints given in Section 4 are partially violated. Four quadrant operation is also possible after this modification. For this purpose, a flux estimator with two different ANNs is designed so that one ANN makes flux linkage estimation on [0◦ , 180◦] and the second one estimates on [180◦ , 360◦ ]. The flowchart is very similar to the one given in Fig. 9. The only difference is two flux estimators are used during the flux estimation. The same ANN architecture and sampling rate are preserved in this modification. Figure 10 shows the estimation results after modification.

6

Experimental Verification of the Proposed Method

The experimental verification stage aims to show the capability of the proposed method during the real time operation. Possible practical limitations are also addressed by analyzing the experimental results. First of all a conventional SRM drive system is comprised of the following subsystems: the SRM, a conventional inverter with two switches per phase, IGBT gate drive circuits, Hall effect current sensors, an analog current regulator for chopping mode operation and controller (commutator) algorithm in a Digital Signal Processor (DSP). Electrical and mechanical parameters for the SRM under evaluation are given in Table 1; dimensions of the SRM are given in [19]. The SRM was directly coupled with a NEMA four pole 30 hp induction machine. The induction machine was excited through a four quadrant adjustable speed drive. Additional system elements to support sensorless operation include the flux linkage estimator and the position estimator for the proposed method. The experimental setup is shown in Fig. 11. Detailed discussion about each element of a conventional drive can be found in related literature [2, 23].

9

Flux Linkage: λ

Current: i

Main ANN for Position Estimation θ est1

Auxilary ANN for Flux Estimation λ

+

-

Σ λ K

θ correction +‘ θ est1 -

Σ

θ est_final

Figure 9: Position estimation improvement scheme by using an auxiliary ANN.

Table 1: Electrical and mechanical parameters of the SRM drive used in the experimental evaluation. Parameter Value Dc Bus Voltage 150 Base Speed 3000 Rated Continuous Power 11.5 Number of Phases 3 Number of Stator Poles 6 Number of Rotor Poles 4 Stator Pole Arc 32 Rotor Pole Arc 45 Turns per Pole 13 Aligned Phase Inductance 18 Unaligned Phase Inductance 0.67

Units V rpm kW

degrees degrees mH mH

• Flux Linkage Estimator: Flux linkage is not a quantity that can be explicitly measured at the SRM electrical terminals. It must be estimated by measuring phase winding voltage in addition to the phase

10

Before Any Modification

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Figure 10: Error comparison between the original estimator and the modified one with two flux linkage estimators for the startup period. Estimation error is given in electrical degrees.

32 Channel Analog FluxEstimator

TMS320C30 Board

ANN Based Position Estimator

11111111 00000000 111 00000000000 11111111

I_ref Look-up Table

0110 01

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θ

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11 00 11 00

Current

Gate Drivers

Regulator

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11 00 00 01 01 11

3 Phase

Phase Voltages

ADC

ASD

480 VAC

Shaft Encoder

SRM

IM

ASD:Adjustable Speed Drive

Transfer

SRM:Switched Reluctance Motor.

Turn_on Cond. Rectifier

I_ref

User Interface Algorithm

IM:Induction Machine 3 Phase 230 VAC Variac

Figure 11: Experimental setup for sensorless on-line operation.

current and using Faraday’s Law,


λ=

(v − Ri)dt ,

(8)

where λ is phase winding flux linkage, v is voltage across the phase winding, R is phase winding resistance, and i is phase current. This estimation algorithm can be implemented either through a software algorithm or through an analog circuit. Both methods have been investigated and our studies have shown that both methods have certain drawbacks and benefits. • Position Estimator: Real-Time implementation of the proposed method is performed in a TMS320C30 floating point Digital Signal Processor (DSP) from Texas Instruments. The board hosts not only po11

3µ

18µ

n io sit

ui

Es ar

aA at

ili 5µ

D

ux A 56µ

cq

y

N N A

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&

D A

as Ph

Co

m

m

eS

ut

el

at

ec

io

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tio

n

tim

at

or

sition estimation algorithm but also algorithms such as SRM commutation and flux estimation. Its 33 MHz clock speed is able to provide a 100 µs sampling rate for the original proposed estimator and 150 µs for the modified estimator. All algorithms are implemented in an single interrupt service routine (ISR) that is driven by an internal timer. The time budget of the ISR is given in Fig. 12. The C programming language is used during the development. Certainly, execution time of the ISR could be reduced by using assembly language of TMS320C30. The development system also includes an analog to digital converter (ADC) board to acquire flux linkage and current information. The ADC conversion time is 3 µs. However, the effective conversion time increases due to the overhead resulting from using C. The ANN weights obtained by offline training are stored in lookup tables. The sigmoidal activation function is also stored in a lookup table. This method reduced the execution time significantly. The total memory requirement for the whole algorithm is approximately 2 kilobytes.

7µ

Figure 12: The time budget of all algorithms executed in the ISR.

6.1

Problems with Real Time Flux Estimation

An important factor that directly effects the position estimation accuracy is the accuracy of the estimator input information. Flux estimator accuracy is a function of many factors depending upon the implementation strategy. In a software implementation of the flux estimator, the discretized version of the Faraday’s law is implemented in the DSP. By using the trapezoidal rule for integration, the flux equation can be rewritten as, λ(k) = λ(k − 1) + 0.5T (v(k) − Ri(k) + v(k − 1) − Ri(k − 1)) , (9) where λ(k) is the most updated flux estimation, λ(k − 1) is the flux linkage estimation from the previous sampling interval, v(k) is the most updated phase voltage sensing, v(k − 1) is the phase voltage sensing from the previous sampling interval, i(k) is the most updated phase current sensing, i(k − 1) is the phase current sensing from the previous sampling interval, R is the phase winding resistance, and T is the sampling period. The software algorithm enjoys simplicity in implementation and tuning flexibility. On the other hand, the accuracy of the estimated flux linkage is limited by the sampling rate. In particular, the estimation error increases during the current regulation mode where relatively high frequency voltage pulses are needed to be sensed and integrated. Although the sampling theorem is employed and the voltage is sampled at a frequency 3-4 times higher than the PWM frequency, the resulting flux estimation error is large enough to get a high estimation error in the position. As a result, the available DSP platform is not capable of operating at a frequency that is sufficiently high to reduce the error resulting from the low sampling frequency. In order to achieve more precise flux estimation, an analog flux estimator is built. An analog integrator forms the core of the analog flux estimator. This integrator basically implements the integral form of Faraday’s law. By using the analog approach better flux estimation performance has been achieved. Increased system cost and precise measurement in a harsh environment are the major drawbacks of the analog scheme. The details of the analog flux estimator can be found in [23]. Figure 13 shows position estimation error distributions with analog and digital flux estimators. Significant error reduction can be seen with the analog flux estimator. A similar error reduction could also be achieved by implementing the digital flux estimator in a new generation advanced DSP system that allows higher sampling frequencies. 12

Error Distribution with Analog Flux Estimator 120 100 # of Error

80 60 40 20 0 −8

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o

Errror θ ( ) Error Distribution with Digital Flux Estimator 100

# of Error

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Figure 13: Position estimation error distributions for two different flux estimators at 800rpm.

6.2

Experimental Results

Before presenting the experimental results, important steps taken during the preparation of sensorless operation are briefly discussed. A data acquisition algorithm is implemented in the DSP so that a significant region of the magnetization characteristic is covered by acquiring flux linkage, phase current and rotor position information. Figure 14 shows the experimental data used for ANN training. A suitable multilayer feedforward ANN was trained by using the MATLABTM Neural Network Toolbox. The same ANN configuration that was used during simulation was preserved. ANN implementation in the DSP is similar to the SimulinkTM implementation. In the final step, the ANN based estimator is integrated into the system by considering phase selection and estimator commutation issues. 0.5 0.45 0.4

Flux Linkage(Wb)

0.35 0.3 0.25 0.2 0.15 0.1 0.05 0

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60 Phase Current (A)

80

100

Figure 14: ANN training data after preprocessing.

13

120

After integrating the ANN based estimator into the SRM drive system, certain tests are conducted to learn more about the operation of the sensorless SRM drive. Figure 15 shows the SRM phase quantities at 400 rpm. These are phase current and flux linkage waveforms that represent only the portion utilized during the estimation, since we cannot use phase quantities during the entire conduction and freewheeling period. 100

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Figure 15: Phase current and flux linkage waveforms θon = 220◦ , θcond = 140◦ , Iref = 50 A.

for n=400 rpm,

Figure 16 shows the real and estimated rotor position at 400 rpm. The difference between real and estimated rotor position gives the error as given in Fig. 17 two different ways. Figures 18 and 19 show the same performance indices at 1000 rpm. 400

real θ

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Figure 16: Real and estimated rotor positions for n=400 rpm, θon = 220◦ , θcond = 140◦, Iref = 50 A. It is apparent from the experimental waveforms that the ANN-based position estimator is performing reasonably well during on-line operation. The estimation is consistent and the error is usually bounded on [−5◦ , +5◦ ]. Moreover, Figs. 17 and 19 show that the significant part of the error is bounded on [−2◦ , +2◦ ]. 14

10

error θ

o

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Figure 17: Estimation error profile and its distribution for n=400 rpm, θon = 220◦ , θcond = 140◦ , Iref = 50 A. 400

real θ

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Figure 18: Real and estimated rotor positions for n=1000 rpm, θon = 208◦ , θcond = 152◦, Iref = 50 A.

As stated before, the SRM has been running with the on-line ANN-based rotor position estimator, so the performance figures related with flux linkage and phase current belong to an SRM driven by a sensorless algorithm. Both flux linkage and phase current waveforms show very good consistency from one electrical cycle to another. There is no substantial peak in the phase current and this shows that the commutator is fed with consistent position information from the estimator. Another important result from the experimental waveforms is the ANN-based position estimator continues the consistent estimation even if the magnetic circuit of the SRM is saturated with high phase current. Another useful approach to assess performance is the application of the fast Fourier transform (FFT) to the error profile in order to analyze the estimation error. Figure 20 shows FFT results for two different speeds of the SRM. The frequency spectra show that the dominating component in the estimation error

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Figure 19: Estimation error profile and its distribution for n=1000 rpm, θon = 208◦ , θcond = 152◦ , Iref = 50 A.

is the electrical speed of the SRM. As shown in FFT spectra, the component at the electrical speed of the SRM increases as the speed gets lower. The main reason for this phenomena is the integration reset which is used to reset the flux linkage integrator at the end of each electrical cycle. The elapsing time at low speed before resetting the integrator is longer than the time at high speed, so the flux linkage estimation error grows until the integrator is reset. This leads to higher flux measurement error at lower speeds. Apparently this increases the rotor position estimation error at lower speed. Power Spectral Density for Estimation Error at 400rpm 600 500

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Figure 20: FFT of the position estimation error for n = 400 rpm and n = 1000 rpm.

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7

Comparison of ANN and Fuzzy-Logic Based Methods

The ANN-based method proposed in this paper and fuzzy-logic based approaches proposed by [11, 12] have many similarities in the aspect of relying on magnetization data. Both ANN and fuzzy-logic based methods do not require any SRM model to represent the relationship between the electrical and mechanical variables. The measurement of these variables is the only requirement. From this point of view, the methods can be classified as model-free rotor position estimation schemes. Since the entire operation of the SRM is bounded within the magnetization characteristic, other system variables such as load torque, inertia and viscous damping do not have any impact on the operation of estimators. Since both ANN and fuzzy models are universal approximators [24, 25], they can successfully handle the difficulties resulting from the inherent nonlinearity of SRM. Given the results of the related publications, both type of estimators are performing very well if minimum estimation error is the main performance criteria. If we compare the two methods in terms of memory requirements, the ANN-based method needs less memory than the fuzzy-logic based method. The ANN can perform estimation with only 40 different weights whereas the reported fuzzy rule base table has many more entries. In addition, the memory requirement for the fuzzy-logic based estimator even increases after the proposed enhancements. However, the enhancement suggested along with fuzzy-logic based method in [12] is a big advantage in comparison of the two methods since the outliers occurring at the input of the estimator can be cleaned substantially after this modification. If we compare the two methods in terms of the estimation update ratio, the ANN-based approach appears to be slower than fuzzy-logic based approach proposed in [12]. Although the reported update period in the fuzzy-logic estimator is limited by the ADC speed at 166.7 µs, the effective computation time is given as 33 µs. A faster ADC may decrease the update period to this limit. However, the ANN based estimator spends almost 90 µs in executing the estimation and control algorithms, well over one half of which is supporting the ANN. If we compare estimation update ratios of the ANN-based method in this paper and fuzzy-logic based method proposed in [11] where the memory requirement is significantly alleviated by a coarse position estimator, we can see that both estimators have the same update ratios at 100 µs. The conclusion we should reach with these update ratio comparisons is that there is a challenging tradeoff between the memory requirement and update ratio. Less computation time, which means a faster position estimator, can only be achieved by having more memory in fuzzy-logic based methods. Of course, the most realistic comparison requires all methods to be implemented in the same Digital Signal Processor. Finally, the effort spent during the preparation of ANN and fuzzy-logic based estimators is an important consideration. The training time for an ANN depends on the training method. The Levenberg-Marquardt technique has superiority over the classical backpropagation technique in terms of training time and it is comparable with the training time for a fuzzy-logic based estimator. In addition, training data for the ANNbased approach requires no preprocessing other than data normalization. However, the preprocessing step may take longer time in the fuzzy-logic based approach since the method requires examining the internal structure of the model [12].

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Summary and Conclusions

This paper proposes an approach for sensorless rotor position estimation in switched reluctance motors. The suggested method relies on the magnetization characteristic of the SRM which is a relation between electrical variables and mechanical variables. The electrical variables in this relation are flux linkage λ and phase current i and the mechanical variable is given as rotor position θ. The main goal is to estimate rotor position for given flux linkage and phase current values. An artificial neural network is conceived to be the appropriate solution to construct a map between the electrical and mechanical variables of SRM. The ambiguous nature of the magnetization characteristic allows estimation over half of one electrical cycle which corresponds to 180◦ . In practice, this interval is smaller than 180◦ because of the localized nature 17

of the magnetization characteristic around the aligned and unaligned positions. Overcoming the localization problem requires utilization of at least three phase quantities. Utilization of more than one phase requires an estimator commutation algorithm which makes the decision about the best phase for estimation. There are certain interactions between phase commutation angles and estimator commutation angles. For a properly selected and fixed estimator commutation angle, there are certain constraints on the phase commutation angles. As long as these constraints are obeyed, it is possible to complete an entire electrical cycle with different phase quantities. The investigations conducted throughout this research showed that a properly trained and utilized ANN is capable of estimating rotor position of SRM within acceptable accuracy limits. The method deserves consideration as a candidate for integration into practical SRM drive systems.

Acknowledgments The authors gratefully acknowledge the constructive criticisms of the reviewers. This work has been supported in part by the Niagara Mohawk Power Electronics Research Chair.

References [1] P. J. Lawrenson, J. M. Stephenson, P. T. Blekinsop, J. Corda, N. N. Fulton, “Variable-speed switched reluctance motors,” IEE Proc., Vol. 127, pt. B, pp. 253-265, 1980. [2] T. J. E. Miller, Switched Reluctance Motors and Their Control, Clarendon Press, 1993. [3] P. W. Lee, C. Pollock, “Rotor position detection techniques for brushless permanent-magnet and reluctance motor drives,” IEEE IAS Annual Meeting, pp. 448-455, 1992. [4] J. T. Bass, M. Ehsani, T. J. E. Miller, “Robust torque control of switched reluctance motor without shaft-position sensor,” IEEE Trans. on Industrial Electronics, Vol. IE-33, pp. 212-216, 1986. [5] P. P. Acarnley, R. J. Hill, C. W. Hooper, “Detection of rotor position in stepping and switched reluctance motors by monitoring of current waveforms,” IEEE Trans. on Industrial Electronics, Vol. IE-32, No. 3, pp. 215-222, 1985. [6] S. K. Panda, G. Amaratunga, “Switched reluctance motor drive without direct rotor position sensing,” IEEE IAS Annual Meeting, pp. 525-530, 1990. [7] M. Ehsani, I. Husain, A. B. Kulkarni, “Elimination of discrete position sensor and current sensor in switched reluctance motor drives,” IEEE Trans. on Industry Applications, Vol. IA-28, No. 1, pp. 128135, 1992. [8] A. Lumsdaine, J. H. Lang, M. J. Balas, “A state observer for reluctance motors,” Incremental Motion Control Systems Symposium, Champaign, Illinois, 1986. [9] J. P. Lyons, S. R. Macminn, M. A. Preston, “Flux/current methods for SRM rotor position estimation,” IEEE IAS Annual Meeting, pp. 482-487, 1991. [10] P. Vas, Artificial Intelligence-Based Electrical Machines and Drives: Applications of Fuzzy, Neural, Fuzzy-Neural, and Genetic Algorithm-Based Techniques, Oxford, New York, 1999. [11] L. Xu, J. Bu, “Position transducerless control of a switched reluctance motor using minimum magnetizing input,” IEEE IAS Annual Meeting, pp. 533-539, 1997. [12] A. Cheok, N. Ertugrul, “Model free fuzzy logic based rotor position sensorless switched reluctance motor drive,” IEEE IAS Annual Meeting, pp. 76-83, 1996.

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[13] A. Bellini, F. Flipetti, G. Franceschini, C. Tassoni and P. Vas, “Position sensorless control of a SRM drive using ANN-Techniques,” IEEE IAS Annual Meeting, pp. 533-539, 1998. [14] D. S. Reay, B. W. Williams, “Sensorless position detection using neural networks for the control of switched reluctance motors,” Proc. of IEEE International Conference on Control Applications, Vol. 2, pp. 1073-1077, 1999. [15] S. Haykin, Neural Networks: A Comprehensive Foundation, IEEE Press, 1994. [16] M. M. Hassoun, Fundamentals of Artificial Neural Networks, MIT Press, Cambridge, MA, 1995. [17] J. M. Zurada, Introduction to Artificial Neural Systems, PWS Publishing Co., 1995. [18] E. Mese, D. A. Torrey, “Sensorless position estimation for variable reluctance machines using artificial neural networks,” Proc. IEEE IAS Annual Meeting, pp. 540-547, 1997. [19] D. A. Torrey and J. H. Lang, “Modeling a nonlinear variable reluctance motor drive,” IEE Proc., Vol. 137, pt. B, pp. 314-326, 1990. [20] T. J. E. Miller, “Nonlinear theory of the switched reluctance motor for rapid computer-aided design,” IEE Proc., Vol. 137, pt. B, pp. 337-347, 1990. [21] M. L. Minsky and S. A. Papert, Perceptrons, MIT Press, 1988. [22] E. Mese, D. A. Torrey, “Optimal Phase Selection for a Rotor Position Estimator in a Sensorless Switched Reluctance Motor Drive,” International Conference On Electric Machines, Helsinki, Finland, 2000. [23] E. Mese, “Sensorless position estimation for Switched Reluctance Motors Using Artificial Neural Networks,” Ph.D. Thesis, Rensselaer Polytechnic Institute, 1999. [24] J. L. Castro, “Fuzzy logic controllers are universal approximators,” IEEE Trans. on Systems, Man, and Cybernetics, Vol. 25, pp. 629-636, 1995. [25] K. Hornik, M. Stinchcombe, H. White, “Multilayer feedforward networks are universal approximators,” Neural Networks, Vol. 2, pp. 359-366, 1989. Erkan Mese received the B.S. an M.S. degrees in electrical engineering from Istanbul Technical University, Istanbul, Turkey, and Ph.D. degree in Electric Power Engineering from Rennselaer Polytechnic Institute, in 1990, 1993, and 1999, respectively. From 1997 to 2000 he was employed by Advanced Energy Conversion LLC, Cohoes, NY as a development engineer. He was involved in the design of switched-reluctance drive systems for automotive applications. He is currently an Assistant Professor at Kocaeli University, Turkey. His research interests are in power electronics and electric machine drives. David A. Torrey received his B.S. in electrical engineering from Worcester Polytechnic Institute, and his S.M., E.E. and Ph.D. degrees in electrical engineering from M.I.T. He is on the faculty at Rensselaer Polytechnic Institute, where he is the holder of the Niagara Mohawk Power Electronics Research Chair and an associate professor in the Department of Electrical, Computer and Systems Engineering. His research activities are focused on all aspects of electric machine systems, with emphasis on switched-reluctance and brushless dc technology. David has been involved in IEEE activities which support power electronics through the Applied Power Electronics Conference. Dr. Torrey is a registered professional engineer in New York State, and a member of Sigma Xi, Tau Beta Pi, and Eta Kappa Nu.

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