An Improved Sensorless Control of Induction Motor Using ADALINE: Theory and Experiment

Sensorless speed control of three-phase Induction Motor (IM) allows systems to be installed easily in many applications avoiding the fragility and the high cost of mechanical speed sensors [1].

However, several numbers of important research have been published about sensor algorithms among them, the state observers.

They consist of modelling the induction motor by dynamic mathematical equations [2]. There are two classes of observers [3]. The first class: stochastic observers who are designed to eliminate measured signals’ noises. Kalman filter represents the optimal stochastic observer [4, 5], where its main problem is the cost of computationally is more intensive, as long as, the second of deterministic observers class neglect the noise [6] (Luenberger, MRAS …).

The MRAS (Model Reference Adaptive System) consists to estimate rotor flux and rotor speed separately. That's means, it uses Luenberger as a current and flux observer. These last are injected into the adaptive mechanism and compared with a measured current to calculate the rotor speed.

Intensive research effort has been focused on using PI controllers as an adaptation scheme. The simple structure of the PI regulator and the reduced cost of its realization lead to be used in 80% of industry applications [7, 8]. However, obviously and basically the determination of the proportional and integrator parameter (PI) is not optimal. Usually, most of the time these parameters are selected by the classic "try and error" method. that is to say, during the synthesis of the regulator, the values are being varied in each test so that the estimation errors are gradually being eliminated during the successive performances. In addition, these parameters remain fixed throughout the operation of the motor. which makes this observer not robust for internal and external changes (speed reversal, load charge….).

For this reason, artificial intelligence such as; genetic algorithms, fuzzy logic, artificial neural networks are introduced to enhance these kinds of observers [9-14], ... Previous studies have only been carried out in theory, because they are limited with algorithm complexity and the computing load. Furthermore, most of these studies have suffered from poorly developed in real-time.

In this paper, to overcome the previously cited drawbacks of the existing observers, an ADALINE (ADAptive LInear NEuron) algorithm [15, 16] is proposed. Its main advantages are that it is quick and simple to implement. Moreover, in parallel to other neural schemes that used multi-layer feed-forward [17-19], the ADALINE avoids delaying caused by calculation load.

That's why it has been had selected rather than the other techniques.

It is now well confirmed from a variety of studies in electrical engineering that, this algorithm proves its effectiveness in different fields such as the estimate and compensate for harmonics from an AC line [20], minimization the undesirable torque ripple for permanent magnet motor drive [21], and Identification of parameters of induction motor at standstill state [22, 23].

A new application of ADALINE is presented in this work, it is motivated by the desire to obtain improvement speed estimation, that uses an adaptive mechanism based on online learning, to replace the conventional PI controller.

However, adaptive linear neurons compute the proportional and integrator gains from the estimated model and measured currents.

The remainder of the paper is ordered as follows: in section 2, a description of direct field-oriented control of IM. Section 3 describes Neural MRAS for induction motor. Section 4 investigates the experimental results of Neural Luenberger in comparison with classical adaptive. Finally, section 5 gives some concluding remarks.

Generally, for nonlinear systems (induction motor), an adaptive observer is used to separate the estimation of the rotor speed from all the other variables (stator currents and rotor flux). This technique provides a good solution for the IM non-linearity problem. Figure 2 shows the principle of the neural adaptive observer. In this structure, there are two cascading loops. First, the state vector variables are estimated by a linear flux observer which considers the speed to be a known parameter. the latter is calculated in the second loop by an adaptive mechanism. The purpose of this paper is to explore a new adaptation scheme to improve the MRAS observer.

2.png

Figure 2. Principal of adaptive observer

3.1 System model

In order to reduce the size of the state vector, and consequently the complexity of the model, the hypothesis of decoupling of the mechanical mode (the rotor speed) with regard to the electric modes (stator currents) and magnetic (rotor flux) has been applied. Considering speed as a known parameter, the space-state of the induction motor will be a linear system.

The matrix representation that will allow the synthesize of the observer will therefore be the following:

$\begin{aligned} \frac{d}{d t} x &=A(x)+B(u) \\ &=\left(\begin{array}{cc}A_{11} & A_{12} \\ A_{21} & A_{22}\end{array}\right)\left(\begin{array}{l}i_{s} \\ \varphi_{r}\end{array}\right)+\left(\begin{array}{l}B_{1} \\ 0\end{array}\right) \end{aligned}$                 (3)

with:

$A_{11}=-\left\{\mathrm{Rs} /(\sigma \mathrm{Ls})+(1-\sigma) /\left(\sigma \tau_{r}\right)\right\} \mathrm{I}=a_{r 11} I$

$A_{12}=M s r /(\sigma L s L r)\left\{\left(1 / \tau_{\mathrm{r}}\right) \mathrm{I}-\mathrm{W}_{\mathrm{r}} \mathrm{J}\right\}=a_{r 12} I+a_{i 12} J$

$A_{21}=\left(\mathrm{Msr} / \tau_{\mathrm{r}}\right) \mathrm{I}=a_{r 21} I$

$A_{22}=-\left(1 / \tau_{r}\right) I+\omega_{r} J=a_{r 22} I+a_{i 22} J$

$B_{1}=(1 / \sigma L s) I=b_{1} I$

$I=\left(\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right)$ and $J=\left(\begin{array}{cc}0 & -1 \\ 1 & 0\end{array}\right)$

where, $x=\left[\begin{array}{llll}i_{s d} & i_{s q} & \varphi_{r d} & \varphi_{r q}\end{array}\right]^{T}$, and y=[i_sd i_sq]^T.

3.2 Flux observer

One of the major issues of the direct field-oriented vector control of the induction motor is that the rotor flux is not directly measurable, and therefore its estimation from known variables (stator currents and voltages) is indispensable. The flux observer is given in ref. [13] for the system (3) can be described by the following equations:

$\frac{d}{dt}\hat{X}=A\hat{X}+BU+G({{\hat{i}}_{s}}-{{i}_{s}})$                  (4)

where, the symbol ^ is used to describe the estimated variables, The gain matrix G is determined so that observer (4) can be stable.

$G=-\left[ \begin{align}  & {{g}_{1}}{{I}_{1}}+{{g}_{2}}{{J}_{2}} \\ & {{g}_{3}}{{I}_{1}}+{{g}_{4}}{{J}_{2}} \\  \end{align} \right]$

To ensure a good estimate of the rotor flux, it must choose the observation gain G such that (A-GC) is asymptotically stable, i.e.: the eigenvalues of (A-GC) matrix must have a negative real part.

$\left\{ \begin{align}  & {{g}_{1}}=(k-1)({{a}_{r11}}+{{a}_{r22}}) \\ & {{g}_{2}}=(k-1){{a}_{i22}} \\ & {{g}_{3}}=({{k}^{2}}-1)(c{{a}_{r11}}+{{a}_{r21}})-c(k-1)({{a}_{r11}}+{{a}_{r22}}) \\ & {{g}_{4}}=-c(k-1){{a}_{i22}} \\   \end{align} \right.$

Because the induction motor itself is stable in typical operation, then the adaptive observer will be also stable.

3.3 Speed estimation

The deterministic observer MRAS presented in ref. [13] uses a PI adaptation mechanism to estimate rotor speed. The adaptation stability has been proved by the means of the estimation error. It has been derived by the Lyapunov theory by choosing an adequate candidate function

$\begin{aligned} e &=X-\hat{X} \\ \Delta A=\hat{A}-A &=\left[\begin{array}{cc}0 & -\Delta \omega_{r} J / c \\ 0 & \Delta \omega_{r} J / c\end{array}\right] \end{aligned}$            (5)

where, $c=\left(\sigma L_{s} L_{r}\right) / M_{s r}$ and $\Delta \omega_{r}=\hat{\omega}_{r}-\omega_{r}$.

Lyapunov function candidate:

$V={{e}^{T}}e+{{({{\hat{\omega }}_{r}}-{{\omega }_{r}})}^{2}}/\lambda $         (6)

where, λ is a positive constant.

The derivate of V in time:

$\frac{d}{d t} V=e^{T}\left\{(A+G C)^{T}+(A+G C)\right\} e-\left(2 \Delta \omega_{r}\left(e_{i d s} \hat{\varphi}_{d r}-e_{i q s} \hat{\varphi}_{q r}\right)\right) / c+2 \Delta \omega_{r} \frac{d}{d t} \widehat{\omega}_{r} / \lambda$                (7)

The following speed estimation equation is obtained, by the equating the second and the third term of the Eq. (7).

$\frac{d}{dt}{{\hat{\omega }}_{r}}=\lambda ({{e}_{ids}}{{\hat{\varphi }}_{dr}}-{{e}_{iqs}}{{\hat{\varphi }}_{qr}})/c$               (8)

The speed generation is carried out using the following equation:

${{\hat{\omega }}_{r}}={{K}_{p}}({{e}_{ids}}{{\hat{\varphi }}_{qr}}-{{e}_{iqs}}{{\hat{\varphi }}_{dr}})+{{K}_{i}}\int{({{e}_{ids}}{{{\hat{\varphi }}}_{qr}}-{{e}_{iqs}}{{{\hat{\varphi }}}_{dr}})dt}$                      (9)

This PI controller is designed to calculate rotor speed with the following transfer function:

${{C}_{PI}}(S)={{K}_{p}}+{{K}_{i}}\frac{1}{s}$         (10)

The PI controller is a required module for the adaptive observers. The setting of PI controller parameters can be considered as an optimization problem or it is a question of finding the optimal solution of the controller gains. Several analytical techniques have been proposed to calculate the adapter components meanwhile they presented a challenge for the adaptive observer. The gains [Kp, Ki] are often selected by a classical method “try and error”. It is about performing as plenty of tests as necessary and adjusting various attempts until acceptable gains are established. It is iterative, it takes time and generally, the gains founded by that classical strategy are not precise to be included in the training of high performances. Besides, these adaptive mechanisms are unsatisfactory because they can be adversely affected by certain conditions (Since these gains are fixed).

For these reasons, considering that is generally challenging to set proper PI parameters, the ADALINE algorithm is integrated as a learning module to automatically calculate the pair of parameters [Kp, Ki].

3.4 The ADALINE neural network

Learning ADALINE ADAptive LInear NEurons is made online and is based on minimizing the error by performing a calculation so that the ADALINE weights converge to optimal coefficients (LMS algorithm) [20].

An artificial ADALINE is a network that has just an input and only one output, during the experiment the ADALINE adjusts its weights immediately after including the input vector [15].

3.png

Figure 3. ADALINE learning rule topology

It is a very simple structure with input vector x(k) is multiplied with suitable weight factors w(k), and the obtained results are summed up and introduced to the output vector y(k) (Figure 3).

${{y}_{k}}=\sum\limits_{i=1}^{n}{x{{(i)}_{k}}{{w}_{k}}=x_{i}^{T}{{w}_{k}}}$         (11)

${{w}_{k+1}}={{w}_{k}}+\Delta w$      (12)

3.5 ADALINE for adaptive scheme speed estimation

The synthesis of the conventional PI controller was done according to the proceeding of KUBOTA [13]. Its major problem is in the method used to calculate the pair of gains [Kp, Ki]. They are obtained by test and error. those gains are unadjustable. However, they clearly are not valid for overcoming long-term problems in different situations.

4.png

Figure 4. Block diagram of neural adaptive neural observer

The main contribution of this paper is to resolve the problem of tuning these two adaptation parameters using the neural network algorithm of ADALINE (Figure 4). they are learned online in each iteration with two weights. w₀ is for auto-tuning the Kp (proportional gain). And a second weight w₁ is used for learning the integral parameter [8].

The ADALINE algorithm calculates the intelligent gains [Kp, Ki] in each iteration for guaranteeing the convergence of the estimated speed to the real one regardless of the system conditions. This learning rule is making possible the simplification of the intelligent controller, reduces the cost of calculation, and at the same time improves the observer's stability.

A new adaptive mechanism for MRAS observer was developed in this paper, which estimates speed and flux for sensorless vector control of induction machine. PI parameters of the adaption mechanism are learned online with the ADALINE network. It means that the gains of the regulator are self-tuned in each iteration during all the operations of the system. So that the speed estimation converges to the real value.

According to the experimental results obtained the application of ADALINE type artificial intelligence makes it possible to achieve these objectives: the speed of response and the robustness with regard to the disturbances of the load, which makes it possible to obtain an accurate estimation. It is characterized by its ease of implementation and its short calculation time. It can be concluded that this applied strategy allows a visible improvement of the vector control and the estimation of the speed.