Non-parametric induction motor rotor flux estimator based on feed-forward neural network

Siti Nursyuhada Mahsahirun, Nik Rumzi Nik Idris, Zulkifli Md. Yusof, Tole Sutikno Faculty of Manufacturing and Mechatronic Engineering Technology, Universiti Malaysia Pahang, Pahang, Malaysia Power Electronics and Drives Resarch Group, School of Electrical Engineering, Universiti Teknologi Malaysia, Johor Bahru, Malaysia Department of Electrical Engineering, Faculty of Industrial Technology, Universitas Ahmad Dahlan, Yogyakarta, Indonesia Embedded System and Power Electronics Research Group, Yogyakarta, Indonesia


INTRODUCTION
One of the critical challenges in the implementation of induction motor (IM) field-oriented control (FOC) is the parameter uncertainties [1]- [11]. Generally, IM rotor flux can be calculated based on voltage model (VM) and current model (CM) [12]- [16]. In FOC, rotor flux observer (RFO) based on VM performs poorly at low-voltage low-frequency operation [14]- [16]. This issue can be solved by CM RFO. However, due to the integral operation in the CM, the RFO became vulnerable to IM parameters, stator current and rotor speed measurement uncertainties. This has brought to the development of higher order RFO with optimization algorithm integration to manage drifts effect. All of these involve more complicated equations and process which then brought up to issues particularly in the systems stability and computational latency [17], [18].
With neural network (NN) system, rotor flux estimator (RFE) can be modeled without requiring detail knowledge of the IM mathematical model and all its drive systems [19]- [21]. The modeling process can be done using optimization algorithm performed by machine [22]- [24]. As for an RFO that generally developed based on state space model will requiring definitive mathematical model of the overall system [25]. Figure 1 shows previous IM NN RFE models based on literature review. Simoes and Bose [26] uses VM for the NN RFE training. The number of neurons in the 3-layers feed-forward NN (FFNN) is manipulated to fit the stator current and stator flux dq-stationary component to the rotor flux magnitude and the sine and cosine rotor flux angle as shown in Figure 1(a). The model can track both sine and cosine rotor flux angles particularly at the steady-state region and follows the rotor flux with apparent high frequency chattering along the trajectory. On the other hand, Venkadesan et al. [27] uses CM for the NN RFE training. Here, all the input and output signals are discretized. The number of neurons and number of layers are manipulated to fit dq-stationary components of the stator current and stator voltage for both past (k-1) and present (k) data to the dq-stationary components of the present (k) rotor flux a shown in Figure 1(b). This model is a 14-hidden-layers (h=14) cascade NN, implemented with Elliot activation function (E AF) in its cell body. It is capable of fitting rotor flux data based on current model up to 1.8e-6 mse. The network, which trained using Levenberg-Marquart algorithm (LMA) with 5,000-epochs; is then implemented in field programmable gate array (FPGA). It consumed 2,440 clock cycle when operated at 20 MHz clock.  [23] and (b) Venkadesen et al. [24] In this paper, a non-parametric IM FFNN RFE is proposed. The inputs are time continuous stator current and stator flux αβ-component while the outputs are the rotor flux αβ-component as shown in Figure 2. In order to simplify the reference frame component notation, we used αβ and dq to represent dqstationary and dq-rotating components respectively. All the process starting from data collection, training, experimentation, and evaluation process are performed using MATLAB/Simulink R2016b environment. The RFE is tested in IM FOC systems for step response and parameters uncertainties. The FFNN RFE architecture are constructed with a basic structure of a perceptron as illustrated in Figure 3. The first block of the perceptron in the input synapse region performs pre-processing process where the input signals are normalized into the neuron operational range. The normalized input signals are referred to as the perceptron inputs, [p]. Each 'p's are then multiplied with its respective weights [w] in the dendrite region before being fed into the cell body. The output from the dendrite region is referred to as dendrite output, [d]. In the cell body, three processes are performed. Those includes summation () of [dR] elements, addition of bias (b) and substitution to the activation function (f). The subscript 'R' refers to the R-th element of the input array of the respective block. The output of the cell body is referred to as the associative output (a). In the axon, each 'a's are feed forwarded to the next region. For a multilayer FFNN, the normalization and denormalization will only occur at the first hidden layer (HL) and output layer, respectively. The output layer is not considered as a HL. The number of neurons in the output layer is similar to the number of output variables of the NN. Denormalization occurs at the output layer. The signals process in FFNN ends in the

Data preparation
The rotor flux ( , ) data was obtained using CM (1) in a direct-FOC systems as shown in Figure 4. There are overall 603,968 datasets that are acquired based on reference speed continuous step manipulation (1.5 Hz square wave) for two seconds at no-load operation. It was aimed to capture both transient and steady-state responses of the overall systems. The data are then divided in a contiguous way into 40% for training, 30% for validation during training and 30% for global testing. For this purpose, a 2-HP cage IM are used as the motor under test (see Table 1).  1232 'trainlm'. The network is initialized using the Nguyen-Windrow method, which possesses some degree of randomness. It enables faster convergence as compared to when the weight and bias are set to zero at initial.
During the training process, the mse is calculated and the weight and biases are updated based on gradient decent method. This process is then repeated to a maximum of 1,000 times. In order to prevent overfitting, the validation checks are limited to 1000, the minimization gradient is limited to 1e-9, and the momentum update is limited to 1e10. To maintain the reproducibility, training, validation and testing data are fixed. Data division is performed using MATLAB function 'divideblock' which perform contiguous division.

The proposed FFNN-RFE architecture and performance
This RFE input set selection is justified by considering that stator flux is the most linearly related to the rotor flux while stator current is the most linearly related to the rotor speed. However, this RFE depends on the stator flux, which means it will require a separate module to estimate stator flux to be used in the FOC systems. Regardless the number of hidden layers is, the mse of the trained NN is exponentially decaying with the increase of n as shown in Figure 5. On the other hand, the mse is exponentially grow with the increase of h. The NN becomes more dependent to the information resolution as h increases. More neurons would be required to carry input signal information to be effectively processed by the succeeding h-th neurons.
The ttc presents pulled up at h=2 before decreasing with further increase of h as shown in Figure 6. Nevertheless, the further increase of h will also increase the mse. For example, a single-HL with 63-neurons consumes 3 hours 4 minutes as compared to 2-HL with 62-neurons that consume 24 hours 27 minutes and 3-HL with 60-neurons consume 16 hours 29 minutes ttc (See Table 2). Although the training process is done offline, ttc is still an important indicator for evaluating the performance of the implemented algorithm, particularly for online learning process where the NN are actively learned and improved in real-time. For these reasons, a single-HL is proposed to this application. Is has also noticed that the systems cannot converge effectively when only one neuron is placed at any HL. This is due to the saturation characteristics of the sigmoidal AF in the cell body that limits its capacity to carry information. For this application, the minimum neuron to be placed in any h must not be less than three as shown in Figure 7. Due to the bi-polar asymptotes of tan-sigmoid function, neurons with T AF are basically more sensitive to the input resolution than L. This means that neurons with T AF, passes higher resolution information as compared to L AF.

The NN-RFE performance in IM direct-FOC
The following results are captured at the speed transition from -100 rpm to 100 rpm of the IM FOC systems with its respective RFE models. The model n_20_1 is implemented to represent RFE performance in this proceeding section. The images in Figures 8 to 13 are arranged from left side, referring to the VM, CM, and NN model respectively. The dashed line refers to the model expected trajectory. The proposed RFE with DC-offset and parameter uncertainties. Input current offsets of 0.5 A and -0.5 A are introduced in isa and isc, respectively, while isb is left unchanged. The parameters uncertainties are imposed on Rs, Rr, Ls, Lm and Lr by considering reported literature Sawma et al. [29]. The initial values of the MUT's parameters are listed in Table 1.
The model is tested with the increased of Rs and Rr by 0.5  to imitate the heat conduction resistance during motor operation. For the Ls and Lr, an increase of 6%, respectively while for Lm, an increase of 2% has been applied. However, the FFNN RFE's inputs ie. the are are calculated based on backemf integral which is similar to the method used in VM. This makes its dependency to isa and isc accuracy becoming more prominent during the transitional and low speed operation as shown in Figure 8. Therefore, the proposed RFE model is unable to estimate the rotor flux for isa, isc and Rs uncertainties as compared to the CM as shown in Figure 9. Even so, these vulnerabilities are not due to the proposed FFNN RFE model itself but rather due to the stator flux input signals integrity, which is estimated by a separate stator flux estimator module.
Through this simulation implementation, the proposed RFE performance is proven to be not affected by Rr, Ls, Lm and Lr due to its non-parametric features as compared to VM and CM as shown in Figures 8  to 13. Table 3 comparatively summarize the characteristics of the proposed FFNN RFE. The sysmbol '/' and '' refers to 'sensitive' and 'not sensitive', respectively. The proposed model is mark as 'sensitive' with DCoffset and stator resistance uncertainties since the stator flux is estimated based on the generic method i.e., the back-emf integral. This does not apply if the stator flux is acquired using non-parametric approach. Although the FFNN RFE is a non-parametric model, it would still require motor parameters for the training process. The parameter uncertainties may occur during the parameter extraction process and motor operations. It is critically important to ensure that the extracted parameters integrity is sufficiently high as the RFE is developed based on the simulated CM model data of the extracted motor parameters.

CONCLUSION
The proposed IM RFE is a single-HL 20-neurons FFNN, trained using LMA and CM simulation data in FOC systems offline. The model is a non-parametric model, which makes it robust from parameters uncertainties during motor operation. However, it still requires a separated module to estimate stator flux as one of its input signals. In order to optimize the performance and training time consumption, the FFNN architecture is suggested to be developed with these three main suggestions; i) any of its HLs must be constructed with not less than 3-neurons, ii) cell body implementation with tan-sigmoid is more recommended than log-sigmoid activation function, and iii) single-HL is more recommended than multi-HL.