Comparative study of various artificial intelligence approaches applied to direct torque control of induction motor drives

Abstract

In this paper, three intelligent approaches were proposed, applied to direct torque control (DTC) of induction motor drive to replace conventional hysteresis comparators and selection table, namely fuzzy logic, artificial neural network and adaptive neuro-fuzzy inference system (ANFIS). The simulated results obtained demonstrate the feasibility of the adaptive network-based fuzzy inference system based direct torque control (ANFIS-DTC). Compared with the classical direct torque control, fuzzy logic based direct torque control (FL-DTC), and neural networks based direct torque control (NN-DTC), the proposed ANFIS-based scheme optimizes the electromagnetic torque and stator flux ripples, and incurs much shorter execution times and hence the errors caused by control time delays are minimized. The validity of the proposed methods is confirmed by simulation results.

Keywords

adaptive neuro-fuzzy inference system (ANFIS) / artificial neural network / direct torque control (DTC) / fuzzy logic / induction motor

Introduction

Direct torque control (DTC) was proposed by Takahashi and Noguchi [1] in 1984 and Depenbrock [2], in 1985. Later, the DTC was developed to a commercial inverter by ABB Ltd. The DTC has major functions to separate the flux linkage and electromagnetic torque. It directly controls the flux and torque within the hysteresis band without requirements in modulations of currents, fluxes or complicated decupling operations. Based on the switching voltage table, the DTC has merits like simple structure and fast torque responses [3,4]. However, this control strategy causes the following major problems: torque ripple, uncontrolled switching frequency, and sensitivity to stator resistance variation [3-5]. Artificial intelligence can solve these problems to improve the DTC of induction machines. Soft computational methods, such as artificial neural networks, fuzzy logic and neuro-fuzzy, are familiar intelligent control methods, and have been applied by many researchers working in the drives area [6-8]. However, a lot of work remains to be done, not only in the drives area, but also in maturing the base technologies themselves.

The theory of fuzzy sets was introduced by Zadeh [9] in 1965, which led to the advent of fuzzy logic systems (FLSs). In general, FLSs are well known in the literature for their ability to model linguistics and uncertainties in systems. In general, instead of representing a system as a set of complex mathematical equations, fuzzy systems use simple empirical rules to represent input and output relationships [10]. The suitability of fuzzy control does not depend much on the number of inputs and outputs, but rather on the availability of human expert knowledge [10,11].

A neural network can be defined as a massively parallel distributed processor made up of simple processing units, which has a natural propensity for storing experiential knowledge and making it available for use [12]. This kind of unit is called neuron and the connection between two different neurons is called synaptic weight. The procedure to store experiential knowledge or learning process is called a learning algorithm, which modifies the synaptic weights in an orderly fashion to attain a desired design objective [13,14]. A most important criterion for a trained network is its generalization performance, which means the network can generate a reasonable output when it encounters a new input [12-15].

Combining neural networks and fuzzy logic, one such an approach is called the adaptive neuro-fuzzy inference system (ANFIS) [16]. The ANFIS is a class of adaptive multi-layer feed-forward network that is functionally equivalent to a fuzzy inference system. Each neuron in the ANFIS applies a particular function on incoming signals as well as a set of parameters relating to the neuron [17]. To identify the adaptive network parameters, this fuzzy inference method employs a hybrid learning algorithm which combines the gradient method and least squares estimate (LSE) [18]. Not only can this hybrid learning algorithm guarantees to find global minima, but it also decreases the convergence time of the network due to decreasing dimensions of research space in the gradient method [17,18].

In this paper, the principle of DTC was presented, and the fuzzy logic based direct torque control (FL-DTC) was developed. Besides, a neural network based direct torque control and a neuro-fuzzy based direct torque control were proposed. Finally, the simulation performance of this control strategy was illustrated.

Classical direct torque control (C-DTC)

Figure 1 shows the operating principle of the DTC, in which an adaptive model of motor plays an important role. The model receives as input the measured current and voltage of the motor. It produces precise instantaneous values of torque and flux. The set point values for the torque and flux are compared with the actual values, and the control signals are produced by two-point control of the hysteresis. The optimum pulse selector determines the position of the ideal switching inverter based on the output signals from regulators at two levels. These positions of the inverter switching voltage act on the motor current which, in turn, influences the torque and the motor flux, thus closing the loop of regulation [2,3,19].

In this paper, the vector expressions of the machine in the frame of reference linked to the stator were used:

(1)\{\begin{array}{l}{\overline{v}}_s=R_s{\overline{i}}_s+{\displaystyle \frac{d{\overline{\psi }}_s}{dt}},\hfill \\ {\displaystyle \frac{L_m}{L_s}}{\overline{\psi }}_s=\sigma {\tau }_r{\displaystyle \frac{d{\overline{\psi }}_r}{dt}}+(1-j{\omega }_r\sigma {\tau }_r){\overline{\psi }}_r,\hfill \end{array}.

where

\sigma =\mathrm{1}-{\displaystyle \frac{L_m^{\mathrm{2}}}{L_s{L}_r}}.

The electromagnetic torque is proportional to the vectorial product between the stator and rotor flux vector:

(2)T_e=p_p{\displaystyle \frac{L_m}{\sigma L_s{L}_r}}{\psi }_s{\psi }_r\sin \left(\widehat{{\overline{\psi }}_s{\overline{\psi }}_r}\right).

During the switching interval, each voltage vector is constant and is then rewritten as

(3){\overline{\psi }}_s(t)={\overline{\psi }}_s(\mathrm{0})+{\overline{v}}_s{t}_e-{\displaystyle \underset{\mathrm{0}}{\overset{t}{\int }}\left(R_s{\overline{i}}_s\right)}dt\begin{array}{lll}& or& \mathrm{\Delta }{\overline{\psi }}_s={\overline{v}}_s{t}_e\end{array}.

The magnitude of stator flux can be estimated by

(4){\psi }_{ds}={\displaystyle \underset{\mathrm{0}}{\overset{t}{\int }}(v_{ds}-R_s{i}_{ds})dt}\begin{array}{lll}& and& {\psi }_{qs}={\displaystyle \underset{\mathrm{0}}{\overset{t}{\int }}(v_{qs}-R_s{i}_{qs})dt}\end{array}.

The torque can be calculated using the components of the estimated flux and measured currents

(5)T_e=p_p({\psi }_{ds}{i}_{qs}-{\psi }_{qs}{i}_{ds}).

A table can be constructed that specifies the effect on the torque and flux magnitudes for each of the voltage vectors for each of the six sectors. This is called the optimal vector selection table, as presented in Table 1 for the case of a two level inverter.

Fuzzy logic based direct torque control

Fuzzy logic systems estimate a function without a mathematical model of how outputs depend on input data [10-20]. This property gives opportunity to the system to learn from experience with numerical or linguistic data. This classifies them as model-free estimator systems. Fuzzy systems are based on fuzzy sets which were first proposed in 1965 by Zadeh [9]. Fuzzy sets are extended forms of conventional “Boolean” sets that can handle the concept of partially true values between “completely true” and “completely false,” to deal with vagueness and uncertainty related to human linguistic and thinking principles of every day life [9-20].

The structure of the switching table can be translated in the form of vague rules. Therefore, the switching table and hysteresis comparators can be replaced by a fuzzy system whose inputs are the errors on the stator flux and electromagnetic torque denoted E_ψs and E_Te and the argument λ_s of the flux, the output being the command signals of the voltage inverter n. The fuzziness character of this system allows flexibility in the choice of fuzzy sets of inputs and the capacity to introduce knowledge of the human expert.

The ith rule R_i can be expressed as

(6)R_i:if{E}_{Te}is{A}_i,E_{\psi s}is{B}_i,and{\lambda }_{s}is{E}_i,thennisN.

where A_i, B_i and C_i denote the fuzzy subsets and N_i is a fuzzy singleton set.

The synthesized voltage vector n denoted by its three components is the output of the controller.

The inference method used in this paper is Mamdani’s [21] procedure based on min-max decision [22]. The firing strength η_i, for the ith rule is given by

(7){\eta }_i=\min ({\mu }_{A_i}(E_{Te}),{\mu }_{B_i}(E_{\psi s}),{\mu }_{C_i}({\lambda }_s)).

By fuzzy reasoning, Mamdani’s minimum procedure gives

(8){\mu }_{N_i}^{\prime }(n)=\min ({\eta }_i,{\mu }_{N_i}(n)),

where μ_A, μ_B, μ_C, and μ_N are membership functions of sets A, B, C and N of the variables E_Te, E_ψs, λ_s and n, respectively.

Thus, the membership function μ_N of the output n is given by

(9){\mu }_N(n)={\max }_{i=\mathrm{1}}^{\mathrm{72}}({\mu }_{N_i}^{\prime }(n)).

The universe of discourse of the stator flux error was chosen to share into two fuzzy sets, that of torque error in five and finally for the flux argument into seven fuzzy sets. This choice was based on Table 1. However, the number of membership functions (fuzzy set) for each variable can be increased and therefore the accuracy is improved. The fuzzy sets are characterized by standard designations N (negative), Z (zero), P (positive), NL (negative large), NS (negative small), PS (positive small), and PL (positive large). All the membership functions of fuzzy controller are illustrated in Fig. 2. The rules sets are listed in Table 2.

Neural networks based direct torque control (NN-DTC)

Method of gradient descent

The error backpropagation method minimizes the error resulting from approximating network by finding the optimal weights. Much research has indicated that this method calculates the optimal weights better especially in the case of layered networks [23]. In multi-layer networks, there arises the problem of adjusting the weights of neurons of hidden layers. A neural network with m + 1 layers, input y_j^0 (j = 1, 2,..., n₀) and output y_j^m (j = 1, 2,..., n_m) can be represented as Eq. (10) [13,14].

(10)y_i^m=f_i^m\left({\displaystyle \sum _{j=\mathrm{1}}^{n_{m-\mathrm{1}}}{w}_{ij}^m}{y}_j^{m-\mathrm{1}}+{\mathit{b}}_i\right),

where BoldItalic^m is the weight matrix (n_m × n_m-1) associated with the mth layer. The vector BoldItalic_i (i = 1,2,..., m) represents the bias value for each neuron i. The functionf_i^m(\cdot ) is a no decreasing operator, which can be linear or nonlinear applied to each output neuron i. The end of learning is dictated by the convergence of the matrix of weights BoldItalic^m to constant values. This objective has been achieved by minimizing squared error between the outputs y_i^m given by the network and desired outputs y_d for a given input vector. It is, therefore, to minimize the cost function below [13-23]:

(11)J={\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}{\displaystyle \sum _{k=\mathrm{1}}^{n_e}{\displaystyle \sum _{s=\mathrm{1}}^{n_m}{e}_s^{\mathrm{2}}}}(k),

with e_s(k) = y_d(k) - y_i^m(k); n_e, the number of samples; and n_m, the length of output vector BoldItalic. To minimize the cost function J, several methods were used in the literature, the most popular being the gradient method applied to the backpropagation of error. The main idea of this learning method is to propagate the output error on the neurons of hidden layers from the error of the output layer. The gradient calculated at the qth layer of n_m neurons is given by [14-24]

(12)g_{ij}^q={\displaystyle \frac{\partial J}{\partial w_{ij}^q}}={\displaystyle \sum _{k=\mathrm{1}}^{n_e}{\displaystyle \sum _{s=\mathrm{1}}^{n_m}{\displaystyle \frac{\partial J}{\partial y_s(k)}}}}{\displaystyle \frac{\partial y_s(k)}{\partial w_{ij}^q}}.

This can be reduced to

(13)g_{ij}^q=-{\displaystyle \sum _{k=\mathrm{1}}^{n_e}{\displaystyle \sum _{s=\mathrm{1}}^{n_m}{e}_s(k)}}{\displaystyle \frac{\partial y_s(k)}{\partial w_{ij}^q}}.

Taking into account the expression of y^s, Eq. (13) becomes [19,20]

(14)g_{ij}^q=-{\displaystyle \sum _{k=\mathrm{1}}^{n_e}{\displaystyle \sum _{s=\mathrm{1}}^{n_m}{e}_s(k){\displaystyle \sum _{r=\mathrm{1}}^{n_q}{\displaystyle \frac{\partial y^s(k)}{\partial y_r^q(k)}}{\displaystyle \frac{\partial y_r^q(k)}{\partial w_{ij}^q}}}}}.

For q= m (output layer),

(15){\displaystyle \frac{\partial y_r^q(k)}{\partial w_{ij}^q(k)}}={\displaystyle \frac{(\partial y_r^q(k)/\partial t_r^q(k))(\partial t_r^q(k)/\partial w_{ij}^q)}{{\dot{f}}_q(t_r^q(k))y_j^{q-\mathrm{1}}\delta (r-i)}},

where {\dot{f}}_q(\cdot ) is the derivative of the function f_q(\cdot ), and \delta (r-i)represents the Kronecker operator.

(16)$$\begin{gathered} \delta (r-i)=\{\begin{array}{lll}\mathrm{1}, \\ \mathrm{0},& if \\ if& r=i, \\ r\ne i.\end{array}. \end{gathered}$$

Equations (14) and (15) allow attempts to write Eq. (13) as

(17)g_{ij}^q={\displaystyle \frac{\partial J}{\partial w_{ij}^q}}=-{\displaystyle \sum _{k=\mathrm{1}}^{n_e}{\rho }_i^q}(k)y_j^{q-\mathrm{1}}(k),

with

(18){\rho }_i^q=\begin{array}{lll}{\dot{f}}_q[t_i^q(k)]e_i(k),& if& q=m\end{array},

(19){\rho }_i^q=\begin{array}{lll}{\dot{f}}_q(t_i^q(k)){\displaystyle \sum _{s=\mathrm{1}}^{n_q}{\rho }_s^{q+\mathrm{1}}(k)w_{si}^{q+\mathrm{1}},}& if& q\ne m\end{array}.

The equation of weight adaptation is given by

(20)w_{ij}^q(k+\mathrm{1})=w_{ij}^q(k)-\eta g_{ij}^q,

where η is the learning coefficient adjusted at each iteration; g_{ij}^q has been determined by previous calculations.

Neural network to emulate the switching table

This section presents the neural networks outline to emulate the table of inverter switching states of DTC. The table input signals are the electromagnetic torque error, stator flux error and the stator flux position. The output signals are the inverter switching states n_a, n_b and n_c. As the switching table depends only on electromagnetic torque error, stator flux error and sector angle where the flux is located, and induction motor parameters, this neural network can be trained independently of the set. With the modifications made ​​previously in the switching table reducing the training patterns and increasing the execution speed of the training process, this has been achieved by reducing the input data table for converting the analog signals to a digital bit for stator flux error, two bits for the torque error and three bits for the flux position, which has a total of six inputs and three outputs, and only 60-four training patterns. With these modifications, the network used to simulate has the advantage of not depending on the induction motor parameter variations. This can apply to any induction motor regardless of its power.

From the flux space vectors ψ_ds and ψ_qs, the flux angle λ and flux magnitude {\mathrm{\Psi }}_s can be calculated. The coding of the flux angle is given by {\xi }_{\mathrm{1}},{\xi }_{\mathrm{2}},and{\xi }_{\mathrm{3}} according to

(21){\mathrm{\Psi }}_s=\sqrt{{\psi }_{ds}^{\mathrm{2}}+{\psi }_{qs}^{\mathrm{2}}},\begin{array}{ll}& \begin{array}{ll}{\lambda }_s={\tan }^{-\mathrm{1}}\left({\displaystyle \frac{{\psi }_{ds}}{{\psi }_{qs}}}\right),& {\xi }_{\mathrm{1}}{\xi }_{\mathrm{2}}{\xi }_{\mathrm{3}}=encoder({\lambda }_s)\end{array}\end{array},

(22){\xi }_{\mathrm{1}}=\mathrm{1}\begin{array}{ll}\begin{array}{ll}& for\end{array}& {\psi }_{qs}\ge \mathrm{0}\end{array},\begin{array}{ll}& if\begin{array}{ll}not& {\xi }_{\mathrm{1}}=\mathrm{0}\end{array}\end{array},

(23)

(24)

The network structure used, as depicted in Fig. 3, has an input layer with six neurons, a first hidden layer with ten neurons, a second hidden layer with 13 neurons and an output layer with three neurons. After successful training, the weights and thresholds calculated are put into the neural network prototype that replaces the switching table. This network is incorporated as a part of the DTC, as shown in Fig. 3.

The weights and biases of the trained network of the optimum switching table are as follows:

{\mathit{w}}_1=\left[\begin{array}{cccccccccc}0.2012& 0.9194& -0.5798& 0.7720& 0.1327& -0.2287& -0.4059& 0.8863& 0.4704& 0.7110\\ -0.8470& 0.1691& 0.2499& 0.6869& -0.7163& 0.2231& 0.5970& 0.2272& -0.9401& 0.1023\\ 0.5515& -0.7016& 0.7350& -0.6469& 0.1105& 0.2075& -0.6061& -0.8746& 0.9981& -0.9540\\ 0.6032& 0.9908& -0.1095& 0.8808& -0.6795& 0.2544& -0.4474& -0.5970& 0.4645& 0.8602\\ -0.7810& 0.2097& -0.2282& -0.9983& -0.2180& 0.7707& 0.2390& 0.3195& 0.4779& 0.5302\\ -0.9843& -0.1146& 0.7951& 0.7501& 0.9603& -0.7411& -0.1826& 0.2242& -0.7087& -0.3503\end{array}\right]

{\mathit{w}}_2=\left[\begin{array}{ccccccccccccc}13.078& -22.505& 4.036& -21.746& -7.068& -31.897& 5.167& 17.364& -68.945& 33.904& -13.647& -71.914& -36.013\\ -41.641& -37.322& 11.091& -55.056& 14.012& 33.640& -70.197& 62.305& -44.305& -64.066& 24.091& 18.344& -31.566\\ -71.390& -15.798& -19.207& -27.130& 22.053& -55.869& -39.416& 21.331& 18.161& 63.603& -45.007& 30.204& -28.611\\ 20.464& 11.295& -62.799& -75.558& 13.306& 60.978& 12.311& -33.223& -41.414& -19.279& -51.887& 58.112& 26.479\\ -9.557& 66.190& 77.416& -49.009& 36.933& 27.481& -69.668& -25.135& 50.310& 20.444& -59.188& 15.454& -14.475\\ 67.002& 34.101& 22.050& 16.553& 68.054& 46.638& 51.520& 9.791& 11.607& 21.410& 72.663& 29.282& 55.455\\ -19.471& -12.679& 10.594& 60.203& -10.051& -19.516& 12.706& 61.003& 33.46& -44.244& 50.515& -17.732& -78.060\\ -38.680& 79.970& -47.705& -16.790& -21.200& 31.180& 16.141& -31.826& -7.521& 25.829& 49.311& 64.650& -13.920\\ 45.303& 54.229& -33.409& 11.305& 51.972& -14.332& -13.447& 51.294& -13.610& -17.556& 31.141& -16.613& -20.992\\ -28.264& 10.067& -70.097& -68.314& 76.889& 36.798& -8.460& 11.573& -41.401& 70.290& -17.716& -55.701& 31.403\end{array}\right],

{\mathit{w}}_3=\left[\begin{array}{ccc}6.312& -4.464& -3.406\\ -11.206& 9.261& -10.391\\ -4.912& -2.279& 1.280\\ -7.594& -9.417& -9.109\\ 5.920& 1.372& 3.581\\ 13.551& 7.669& -5.902\\ -5.300& 6.097& 1.142\\ -2.498& 2.334& -10.580\\ 1.160& -5.132& -4.021\\ -11.909& -1.353& -2.972\\ -1.766& 5.311& 3.559\\ -8.371& -10.006& 1.705\\ 3.345& 1.761& -8.066\end{array}\right],

{\mathit{\beta }}_1=\left[\begin{array}{l}0.412\hfill \\ -0.257\hfill \\ -0.879\hfill \\ 0.363\hfill \\ 0.914\hfill \\ -0.559\hfill \\ 0.130\hfill \\ -0.892\hfill \\ 0.618\hfill \\ -0.894\hfill \\ -0.443\hfill \end{array}\right],

{\mathit{\beta }}_2=\left[\begin{array}{c}-2.415\\ -5.663\\ 7.089\\ 1.406\\ -3.551\\ 8.346\\ -2.979\\ 2.593\\ -3.408\\ -1.616\\ 2.490\\ 5.375\\ -4.132\end{array}\right],

{\mathit{\beta }}_{\mathrm{3}}=\left[\begin{array}{l}\mathrm{37.560}\\ \mathrm{42.902}\\ \mathrm{22.433}\end{array}\right].

The coefficients of the ANN are trained using the data in Table 3.

Adaptive network-based fuzzy inference system based direct torque control (ANFIS-DTC)

An adaptive network-based fuzzy inference system (ANFIS) is a fuzzy inference system implemented in the framework of adaptive networks [16,17]. An adaptive network is a superset of all kinds of feed-forward neural networks with supervised learning capability. The ANFIS serves as a basis for constructing a set of fuzzy if-then rules with appropriate membership functions to generate the stipulated input-output pairs. The modeling and control techniques of the ANFIS are explained in Ref. [18]. And a number of various applications are demonstrated in Refs. [25,26]. This paragraph explains the architecture of the ANFIS and its learning algorithm for the Sugeno fuzzy models.

The proposed adaptive neuro-fuzzy inference systems (ANFISs) controllers have three variable inputs, the stator flux error E_ψs, electromagnetic torque error E_Te, and angle of flux stator λs. The output is the voltage space vector. The internal structure of the ANFIS is exhibited in Fig. 4.

Layer 1 Each node in this layer performs a MF:

(25)y_i^{\mathrm{1}}={\mu }_{A_i}(x_i)=\exp \left\{-{\left[{\left({\displaystyle \frac{x_i-c_i}{a_i}}\right)}^{\mathrm{2}}\right]}^{b_i}\right\},

where x_i is the input of node i, A_i is the linguistic label associated with this node, and (a_i, b_i, c_i) is the parameter set of the bell-shaped MF. y_i^1 specifies the degree to which the given input belongs to the linguistic label A_i, with the maximum equaling to 1 and minimum equaling to 0. As the values of these parameters change, the bell-shaped function varies accordingly, thus exhibiting various forms of membership functions. In fact, any continuous and piecewise differentiable functions, such as trapezoidal or triangular membership functions, are also qualified candidates for node functions in this layer.

Layer 2 Each node in this layer represents the firing strength of the rule. Hence, the nodes perform the fuzzy AND operation

(26)y_i^{\mathrm{2}}=w_i=\min ({\mu }_{A\psi s}(E_{\psi s}),{\mu }_{BTe}(E_{Te}),{\mu }_{C\lambda }({\lambda }_s)).

Layer 3 The nodes of this layer calculate the normalized firing strength of each rule

(27)y_i^{\mathrm{3}}={\overline{w}}_i={\displaystyle \frac{w_i}{{\displaystyle \sum _{i=\mathrm{1}}^n{w}_i}}}.

Layer 4 The output of each node in this layer is the weighted consequent part of the rule table

(28)y_i^{\mathrm{4}}={\overline{w}}_i{f}_i={\overline{w}}_i(p_i{E}_{\psi s}+q_i{E}_{Te}+m_i{\lambda }_s+n_i),

where {\overline{w}}_i is the output of layer 3, and {p_i, q_i, m_i, n_i} is the parameter set, which determine the ith component of vector desired voltage by multiplying weight y_i by voltage continuous V side of the inverter according to Eq. (29).

(29)V^{*}=y_{i}V.

Layer 5 The single node in this layer computes the overall output as the summation of all incoming signals

(30)y_i^{\mathrm{5}}={\displaystyle \sum _{i=\mathrm{1}}^n{\overline{w}}_i{f}_i},

which determines the vector reference voltage v_s^{*} (see Fig. 4), from

(31)v_s^{*}={\displaystyle \sum _{i=\mathrm{1}}^{\mathrm{9}}{y}_{i}V{e}^{j{\xi }_i^{*}}}.

The angle ξ is obtained from the actual angle of stator flux λ_s and angle increment dλ_i given by

(32){\xi }_i={\lambda }_s+d{\lambda }_i.

y_i (i= 1, 2,…, 9) are the output signals order i of the third layer respectively.

The model setting is listed in Table 4.

Table 5 represents the angle increment λ_i of reference voltage vector, where the torque and flux errors are represented by three subsystems: value, positive (P), zero (Z), negative (N) (Fig. 5).

Simulations results

To compare and verify the proposed approaches in this paper, a digital simulation based on Matlab/Simulink program with a Neural Network Toolbox, Fuzzy Logic Toolbox and ANFIS Toolbox was conducted to simulate the FL-DTC, NN-DTC and ANFIS-DTC, as displayed in Figs. 6, 7 and 8.The parameters of the induction motor in the simulation are as follows:

\mathrm{R}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d}\mathrm{p}\mathrm{o}\mathrm{w}\mathrm{e}\mathrm{r}=7.5 \mathrm{k}\mathrm{W},\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d}\mathrm{v}\mathrm{o}\mathrm{l}\mathrm{t}\mathrm{a}\mathrm{g}\mathrm{e}=220 \mathrm{V},\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d}\mathrm{f}\mathrm{r}\mathrm{e}\mathrm{q}\mathrm{u}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y}=60 \mathrm{H}\mathrm{z},{\mathit{R}}_{\mathrm{r}}=0.17 \mathrm{\Omega },R_{\mathrm{s}}=0.15 \mathrm{\Omega },L_{\mathrm{r}}=0.035 \mathrm{H},L_{\mathrm{s}}=0.035 \mathrm{H},L_{\mathrm{m}}=0.0338 \mathrm{H},\mathrm{a}\mathrm{n}\mathrm{d}J=0.14 \mathrm{k}\mathrm{g}\cdot {\mathrm{m}}^2.

Figures 6(a), (a′), 6(b), (b′), 6(c), (c′) and 6(d), (d′) show the torque and zoom torque response of the classical DTC, FL-DTC, NN-DTC and ANFIS-DTC respectively with a torque reference of 10, 15 and 20. Figure 7 shows the starting transient performance response of electromagnetic torque for the four control strategies: C-DTC, FL-DTC, NN-DTC and ANFIS-DTC. The ANFIS-DTC has the best transient response, where the motor torque is approximately built up in less than 0.0074 s. While Figs. 8(a), (a′), 8(b), (b′), 8(c), (c′) and 8(d), (d′) show the stator flux trajectory and zoom response of the C-DTC, FL-DTC, NN-DTC and ANFIS-DTC respectively with a stator flux reference of 1 Wb.

The minimum ripple for both electromagnetic torque and stator flux is obtained using ANFIS-DTC, where the torque ripple percentage is approximately 2.4%, and 1.3% for the flux ripple percentage, while the NN-DTC, FL-DTC and C-DTC have a relatively large ripple, where the torque ripple percentage is approximately 2.9%, 3.9% and 10.6% respectively, and approximately 1.6%, 2.1% and 2.3% respectively for the flux ripple percentage. Further, the ANFIS-DTC has the best transient response for the torque, where the rise time is 0.004 s, and the setting time 0.0074 s, faster than NN-DTC, FL-DTC, and C-DTC, where the rise time is approximately 0.006 s, 0.007 s, and 0.009 s respectively, and approximately 0.0082 s, 0.0085 s, and 0.1 s respectively for the setting time. Table 6 represents the results of this comparative study. It can be concluded that ANFIS-DTC is more accurate than NN-DTC, FL-DTC, and C-DTC, and promises to be the future choice for application in industrial drives.

Conclusions

In this paper, a comparative study of C-DTC, FL-DTC, NN-DTC and ANFIS-DTC for an inverter-fed induction motor drive was proposed. A better precision in the torque and flux responses was achieved with the ANFIS-DTC method with a great reduction in the execution time of the controller; hence the steady-state control error is almost eliminated. The application of adaptive neuro fuzzy inference system techniques simplifies hardware implementation of DTC. It is envisaged that ANFIS-DTC induction motor drives will gain wider acceptance in the future.

Notations

References

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