MULTI-BASIS WAVENET-BASED SPEED ESTIMATION IN DIRECT TORQUE CONTROLLED ASYNCHRONOUS MOTOR

: This paper presents a proposed method for speed estimation of asynchronous motor in Direct Torque Control (DTC) system, based on a new architecture of multi-basis wavenet model. Such multi-basis model utilizes multi-set daughter wavelets. Firstly, the structure and training algorithm of the proposed method is discussed. The descent gradient method is used to fulfill both system structure and parameters initialization. Secondly, the proposed speed estimator and the DTC asynchronous motor are combined based on stator current signal and the motor speed is then estimated online with the operation of the system. Finally, the effectiveness of this method is proved by simulation carried out using Matlab/Simulink library and compared with the actual results obtained from the dynamic equations of the motor. The simulation results are obtained over the entire speed of starting, load conditions and motor braking. These results show that the proposed method is effective for speed estimation in DTC drives


INTRODUCTION
The speed estimation in DTC asynchronous motor systems have developed during the last few years and become the main development direction of the AC speed adjustment [C.J. Chen, et al., 2007].Generally to establish the speed loop feedback in DTC system, information of rotor speed is essential.Installation sensor for detecting rotor speed will increase hardware cost and add some volume of system as well as the installation and maintenance bring many difficulties beside the mechanical error which affect the detection precision and performance of DTC control.
Several methods that eliminate the speed sensor have been developed.The observer-based [J.Maes, et al., 2000, H. Kubota, et al., 1993, G. Yang, et al., 1993, C. Lascu, et al., 2004, and Y. R. Kim, et al.,, 1992] and the Model Reference Adaptive System (MRAS) [C. Schauder, 1992, C. Lascu, et al., 2000. and T. BANA, et al., 2002] seem the most used methods for sensorless speed DTC system.However, the estimated speed is affected by machine parameters.Moreover, these methods need to detect all the terminal voltages and currents of the motor.A good technique for speed sensorless operation based on Neural Network (NN) has been presented over the last years [M.P. Kazmiorkowski, et al., 1997, andL. Brahim, et al., 1993].This method is based only on signals detected from motor terminals which eliminate the effect of motor parameters sensitivity on the estimated speed.However, the estimated speed could not be perfectible due to some problems such as trapping in to local minima and slow convergence.
The combination of NN with wavelet transform (wavenet), behaves good localization property in both time and frequency space and multi-scale property.It is used for the analysis of non-stationary signals and learning of the nonlinear functions [S.Mallat, 1999].This technique is also proposed to estimate the speed in DTC system [C. Zhi, et al., 2003 andM. A Alwan, et al., 2008].
In this paper, the theory of wavenet is presented and a method of speed estimation based on multi-basis wavenet is proposed.The proposed method includes multi-set daughter wavelets from different mother functions in the hidden layer which is believed useful to represent functions containing different signal cutting, ripples and rapid signal changes.The simulink model of DTC asynchronous motor system is implemented and a speed estimator based on the above proposed method is combined with the system based on one line of stator current signal.Simulation results include developed torque, stator current beside the rotor speed which is compared with the actual motor speed.Note that the theory of DTC control has not been discussed here, however it can be found in details in [G. S. Buja, et al., 2004].

WAVENET
Wavenet can be considered a particular case of the feed forward basis function neural network model.In ordinary network, several types of basis functions, such as radial basis functions, splines and polynomial functions of synapse neurons are used instead of sigmodial function.The connection weights are taken to represent the corresponding coefficients.The output layer performs the sum of the output of all synapse neurons.Since wavelets have been shown their excellent performance in non stationary signal analysis and nonlinear function modeling, the neural network using wavelet basis function, wavenet, provides higher availability of rate of convergence for the approximation than an ordinary feed forward neural network [S.Mallat, 1999].
The wavenet can be constructed by means of replacing the nonlinear sigmodial function with nonlinear wavelet basis function.Figure 1 illustrates the wavenet structure and Fig. 2 shows some typical wavelet functions.

Fig. 2 Some typical wavelet functions
The network exhibits a multi-input to multi-output nonlinear system, realizing mapping from n m R R  .The approximated output signal of the network can be expressed as follows M is the node numbers of the input layer, K is the node numbers of hidden layer, ki w is the weight between the k-th node of the hidden layer and the i-th node of the output layer, ) (t h is the mother wavelet, b a, are the dilation and translation and f is the linear function.

PROPOSED WAVENET SPEED ESTIMATOR
The structure of the proposed P -based wavenet speed estimator is shown in Fig. 3 and the set up of its training and estimation for online speed changes in DTC asynchronous motor system is shown in Fig. 4. (2) A single signal from one line current is used here which uses a single current sensor.This is useful for simplicity and economy [M. A. Alwan, et al., 2008].The hidden layer is of P different sets of daughter wavelets.The output of the wavenet is the motor speed which can be given as follows [C. Zhi, et al., 2003] In order to determine the adjustable weights where , q and l F are the number of training samples and the desired value of l y .To minimize the energy error E , a method of steepest descent which requires the gradients .The gradients of E are:

SIMULATION RESULTS
Two sets of daughter wavelet functions ) 2 (  P with seven neurons ) 7 (  K in each set are used to represent the hidden layer of a 2-basis wavenet speed estimator.The two mother wavelets used in these sets are Mexican hat and Shannon functions.These functions with their derivative with respect to the translation b are given as follows Mexican hat function and for Shannon function where . The wavenet speed estimator was trained off line before combining it with the DTC system based on data obtained from the conventional operation of the DTC system.The training is based on eq. 2 to 10 which can programmed in M-file in Matlab library as given in the Appendix.The simulation was carried out to verify the function of the speed estimator where the motor used in this system is a 3-ph, 1250 hp, 4160V, 150A, 6 poles, and 60 Hz induction motor (asynchronous motor).The simulation parameters of the motor are described as follows: . The rotor speed of the motor which is used to complete the torque loop in the DTC system (Fig. 4) is taken either from the actual value calculated from the dynamic motor equations or from the proposed wavenet speed estimator.
Figure 5 shows the actual rotor speed for starting the DTC system with no load from standstill to a speed of 100 rad./sec.through 2 seconds, then the speed is increased suddenly to 200 rad./sec.through the next 2 seconds.Figure 6 shows the estimated rotor speed identified by the proposed wavenet speed estimator for the case above.It shows higher dynamical following performance.The starting current and the starting torque for the same previous case are show in Fig. 7 and 8 respectively.

ROBUSTNESS
In order to test the robustness of the proposed method, the effect of system braking and sudden change for full load torque have studied on the performance of the torque control and speed changes.
To illustrate the performance of braking control, the operating mode have simulated without load and the motor runs at rated speed of 377.8 rad./sec., the braking starts at the instant of 3 sec.and the system is kept at standstill after the braking.Figure 9 and 10 show the actual and estimated speed during braking while Fig. 11 and 12 show the stator current and developed torque for the same mentioned case.The estimated speed follows the actual with an error less than 1% which reflect the ability of the proposed speed estimator.Figures 13-15 show the tests of robustness realized with sudden change in load torque from no load to full load of the motor used, 7490 N.m, at the instant t=4sec.and its elimination at t=6 sec.This process is repeated two times.In this case, the estimated speed is used as a feed back signal to complete the torque loop of the DTC system.The developed torque curve in Fig. 15 reflects the direct control of torque.The developed torque follows its demand quickly with a time less than 0.05 sec.
For the robustness of control, a braking case, the estimated speed follows its actual and for system loading when the speed is used as feed back signal, the DTC system gives an adequate accuracy of system performance.

CONCLUSIONS
The paper presents a new multi-basis wavenet speed estimator based on multi-set daughter wavelet functions in DTC asynchronous motor system.The multi-basis wavenet is useful because of high nonlinearity in the stator current waveform.The wavenet speed estimator is trained offline based on stator current information obtained from the conventional operation of the DTC system.The advantage of using multi-basis wavenet is the adequate speed estimated for different operating conditions.The simulation results reveals a good system performance.

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forgetting factors which are variable factors and can greatly reduce the number of iterations for convergence.

Fig
Fig. 5 Actual speed (electrical) during starting Fig. 9 Actual speed (electrical) during braking Fig. 13 Estimated speed (electrical) Fig. 14 Stator current during load change during load change.