Diaplacement sensorless control strategy of bearingless induction motor

Abstract

To achieve the radial displacement self-sensing detection of a bearingless induction motor, a prediction model or estimation method of radial displacement based on least squares support vector machine (LS-SVM) is presented. Firstly, the nonlinear relationship between the radial displacement of bearingless rotor and the currents of two sets of stator windings is analyzed. Then, the stator current components of torque windings and suspension windings, and the rotor flux-linkage of torque system are taken as input variables, the acceleration of $\alpha$ and $\beta$ radial displacement components are taken as output variables, and based on the regression principle of LS-SVM, the predication model or estimation method of radial displacement based on LS-SVM is designed. Based on this, the radial displacement sensorless control system of a bearingless induction motor is constructed. Simulation results have shown that when the presented displacement estimation method is adopted, quicker tracking speed and higher tracking accuracy of radial displacement can be obtained; meanwhile the control system of bearingless induction motor has stronger ability of anti load torque disturbance.

Keywords

Bearingless induction motor displacement prediction model least squares support vector machine control system simulation analysis

1. Introduction

It is difficult for the motor supported by mechanical bearing to meet the requirement of long time and high speed operation, then the motor supported by magnetic bearing is widely developed [1, 2, 3], but the motor supported by magnetic bearing still has some disadvantages, such as more magnetic suspension cost, over speed difficulty, and limited critical speed [4, 5, 6]. Bearingless motor is a new type of electric machinery, which is proposed based on the comparability in structure between the magnetic bearing and the stator of AC motor. Compared with the motor supported by magnetic bearing, the bearingless motor has a series of advantages, such as shorter rotor shaft, higher critical speed, and lower magnetic suspension cost [7, 8, 9]. To achieve the stable suspension operation of bearingless motor, the negative feedback control of radial displacement is necessary, and the key lies in the accurate detection of the radial displacement [9, 10]. At present, the eddy current sensor is widely used to detect the radial displacement of bearingless rotor. But the displacement sensor occupies certain shaft length, and then limits the improvement of critical speed in a certain degree. In addition, the displacement sensor greatly improves the cost of control system.

About the radial displacement observation technology of magnetic suspension rotor, the existing researches are mainly focus on the motor supported by magnetic bearing [11]; about the radial displacement observation of bearingless motor, the references available are relatively few. In bearingless, there are several inductance parameters which change linearly with the radial displacement of bearingless rotor [12, 13]. Such as the self-inductance of suspension winding, the mutual inductance between torque windings and suspension windings. Then in references [12, 13, 14], according to these approximate linear relationship, and by high frequency excitation signal injection method, the extraction method of radial displacement is researched in detail. The high frequency excitation signal injection method are not affected by the fundamental physical phenomenon, and not sensitive to the parameters of bearingless motor, and then have stronger detection robustness. But the sustained high frequency excitation and the complex signal processing technology are required. In reference [15], aiming at a bearingless PM motor, according to the mutual inductance coupling relationship between torque windings and suspension windings, and by calculating the coupling flux-linkage of torque windings to suspension windings, a displacement estimation method is proposed; this method doesn’t need high frequency excitation signal, and is easy to realize; however, the accuracy of mutual inductance parameter directly influences the observation precision of radial displacement. And then, how to overcome the influence of motor parameter on the observation performance by machine learning theory is still a problem to be further studied. In reference [16], the neural network is used to the control system of permanent magnet synchronous motor, but some problems of neural network itself, such as slower convergence rate, easily falling into local minima, and more dependence of network structure design on expert experience, limit the application range of the presented method.

Support vector machine (SVM) is a newly machine learning method based on statistical learning theory [17], it can minimize the dependence of neural network on experience knowledge, and have some outstanding characteristics, such as small sample learning, stronger generalization ability, global optimization ability and fixed topological structure. The stronger self-learning ability and generalization ability of SVM facilitate the model identification and parameter estimation of bearingless motor [18, 19]. In reference [20], based on the model analysis of magnetic suspension switched reluctance motor, the estimation method of radial displacement and angular position is investigated based on least squares support vector machine (LS-SVM), but the presented method still can not completely get ride of the radial displacement sensor. In reference [21], based on the regression theory of relevance vector machine (RVM), the forecasting model of magnetic suspension switched reluctance motor with single windings is constructed, the radial displacement is estimated. And then, the uncertain and nonlinear problems are effectively solved by machine learning. In reference [22], according to the nonlinear relationship between current and radial displacement, the current is taken as input sample data, the radial displacement is taken as output sample data; and then using particle swarm optimized-least squares support vector machines (PSOLS-SVM), a predictive modeling of radial displacement for 3-degree-of-freedom hybrid magnetic bearing (3-DOF-HMB) is proposed. The presented method can provide a useful reference for the radial displacement estimation of bearingless motor. Nowadays, aiming at bearingless motor, the study on the radial displacement sensorless control technology based on LS-SVM has just started, and the existing research mainly focus on the bearingless synchronous motor. Aiming at bearingless induction motor, the references about LS-SVM displacement observation method is very scarce.

In this paper, the LS-SVM is introduced to the radial displacement observer of a bearingless induction motor, a radial displacement prediction model or estimation method is proposed. The radial displacement sensorless control system is constructed, and the system simulation verification and analyses have been made. The outline of this paper is as follows: Section 2 gives the working principle and model of bearingless induction motor; based on LS-SVM regression principle, Section 3 presents the prediction model of radial displacement; Section 4 gives the radial displacement sensorless control system structure, and the simulation analysis are described in Section 5; in Section 6 the full text is summarized and the conclusion is presented.

2. Working principle and model of bearingless induction motor

2.1 Working principle of bearingless motor

From the electromagnetic field principle, the Maxwell electromagnetic force is generated on the interface between iron core and air gap, and it is approximately vertical to their interface. When the air gap flux density is distributed symmetrically, the resultant radial force that acts on rotor equals to zero. However, when the rotor deviates from the stator center, the symmetric distribution of air gap magnetic field is broken, and the resultant radial force doesn’t equal to zero again. The resultant radial force is entitled unilateral magnetic pull. To achieve the stable suspension of rotor, it is necessary to generate a controllable radial force to counteract the unilateral magnetic pull and external radial load [4, 5].

For most bearingless motor, there are two sets of windings in the stator slots, including torque windings and suspension windings. Torque windings is the conventional AC motor windings, its number of pole pairs is $P_{1}$ , and the electrical angle frequency of current is $\omega_{1}$ ; The suspension windings is used to produce a suspension control magnetic field, its number of pole pairs is $P_{2}$ , and the electrical angle frequency of current is $\omega_{2}$ . When the suspension control magnetic field is superimposed on the original rotating magnetic field of AC motor, the balance and symmetry of air gap magnetic field is broken, the air gap magnetic field in some air gap area is enhanced, and that in the space symmetric area is weaken; and then a radial force is generated in the enhancement direction of air gap magnetic field. When the two sets of windings meet the conditions of “ $P_{2}=P_{1}\pm 1$ , $\omega_{2}=\omega_{1}$ ”, the produced radial force is controllable both in amplitude and in direction [5, 7]. The controllable radial force is the so-called controllable magnetic suspension force, which can be used to control the suspension of bearingless rotor [5]. Taking the four-pole bearingless motor with two-pole suspension windings as example, Fig. 1 shows the generation principle of controllable magnetic suspension force.

Figure 1.

Generation principle of controllable magnetic suspension force.

2.2 Mathematical model of magnetic suspension system

If defining dq is the coordinate system oriented by the rotor flux-linkage of torque system, then according to the working principle of bearingless induction motor, the mathematical model of controllable magnetic suspension force can be derived as follows [23]:

$\left\{{\begin{array}[]{l}F_{\alpha}=k_{m}(i_{s2d}\psi_{1d}+i_{s2q}\psi_{1q})% \\ F_{\beta}=k_{m}(i_{s2d}\psi_{1q}-i_{s2q}\psi_{1d})\\ \end{array}}\right.$ (1)

In Eq. (1): $F_{\alpha}$ and $F_{\beta}$ are the components of controllable magnetic suspension force along stationary $\alpha$ and $\beta$ coordinate axes; $i_{s2d}$ and $i_{s2q}$ are the current components of suspension windings in dq coordinate system; $\psi_{1d}$ and $\psi_{1q}$ are the air gap flux-linkage components of torque system in dq coordinate system.

According to the mechanical dynamics principle, the suspension motion equation of bearingless rotor can be derived as shown in Eq. (2).

$\displaystyle m\ddot{\alpha}=F_{\alpha}+f_{\alpha},\quad m\ddot{\beta}=F_{% \beta}+f_{\beta}$ (2)

In Eq. (2): $m$ is the mass of bearingless rotor; $f_{\alpha}$ and $f_{\beta}$ are the components of unilateral magnetic pull in $\alpha$ and $\beta$ directions, they can be expressed as “ $f_{\alpha}=k_{s}\alpha$ , $f_{\beta}=k_{s}\beta$ ”. Here, $k_{s}$ is a displacement stiffness coefficient that is determined by the structure of bearingless induction motor [23].

From Eq. (1), it is clear that the controllable magnetic suspension force has direct relationship with the air gap flux-linkage of torque system. The air gap flux-linkage components $\psi_{1d}$ and $\psi_{1q}$ of torque system can be calculated in real time as follows [23]:

$\displaystyle\left\{{\begin{array}[]{l}\psi_{1d}=L_{m1}(\psi_{r1}+L_{r1l}i_{s1% d})/L_{r1}\\ \psi_{1q}=L_{m1}L_{r1l}i_{s1q}/L_{r1}\\ \end{array}}\right.$ (3)

Where: $\psi_{r1}$ is the rotor flux-linkage; $L_{m1}$ is the exciting inductance; $L_{r1}$ is the self-inductance of rotor windings, $L_{r1l}$ is the leakage-inductance of rotor windings.

By arranging Eqs (1) $\sim$ (3), the model of magnetic suspension system can be derived as follows:

$\displaystyle\left\{{\begin{array}[]{l}\ddot{\alpha}=\displaystyle\frac{k_{m}}% {m}\cdot\frac{L_{m1}}{L_{r1}}[(\psi_{r1}+L_{r1l}i_{s1d})i_{s2d}+L_{r1l}i_{s1q}% i_{s2q}]+\frac{k_{s}\alpha}{m}\\ \ddot{\beta}=\displaystyle\frac{k_{m}}{m}\cdot\frac{L_{m1}}{L_{r1}}[L_{r1l}i_{% s1q}i_{s2d}-(\psi_{r1}+L_{r1l}i_{s1d})i_{s2q}]+\frac{k_{s}\beta}{m}\\ \end{array}}\right.$ (4)

From Eq. (4), it is clear that the radial displacement components are determined by the stator currents of two sets of windings and the motor flux-linkage of torque system; however, there exists a serious nonlinear coupling relationship between relevant variables. In addition, the accuracy of motor parameters also affects the accuracy of radial displacement estimation.

3. Displacement prediction modeling based on LS-SVM regression principle

To improve the anti interference ability and the robustness of displacement observation, the LS-SVM is used to approximate the nonlinear expression of displacement acceleration variable in Eq. (4). Then by the integral link, the estimated displacement is obtained.

3.1 Displacement prediction model based on LS-SVM

The adopted training data set can be expressed as $\{(x_{i},y_{i})\}_{i=1}^{N}$ . Where $N$ is the number of training samples, $x_{i}\in R^{n}$ is the input, $y_{i}\in R$ is the corresponding output. The function $\varphi(\cdot)$ reprents a nonlinear reflecting relationship. After the limited input variables are reflected to high dimensional feature space, optimal linear regression is needed. Then the adopted linear function of high dimensional feature space can be expressed as follows:

$\displaystyle y(x)=w^{T}\varphi(x)+b$ (5)

Where: $w$ reprents weight vector, $b$ is offset value.

If defining 2-nom of error is the loss function of LS-SVM, the optimization problem of LS-SVM regression algorithm can be expressed as follows:

$\displaystyle\left\{\begin{array}[]{l}\min J(w,\xi)=\displaystyle\frac{1}{2}w^% {T}w+\gamma\frac{1}{2}\sum\limits_{i=1}^{N}{\xi_{i}^{2}}\\ {s.t.}\ \ \ y_{i}=w^{T}\varphi(x_{i})+b+\xi_{i},i=1,2,\ldots,N\\ \end{array}\right.$ (6)

Where: $\gamma>0$ , $\gamma$ is a regularization parameter, i.e. penalty factor, it is a compromise parameter that is used to adjust the generalization ability and accuracy of model. $\xi$ is a relaxation factor of insensitive loss function.

According to Eq. (6), defining a Lagrange function as follows:

$\displaystyle L(w,b,\xi,a)=J(w,\xi)-\sum\limits_{i=1}^{N}{a_{i}}[w^{T}\varphi(% x_{i})+b+\xi_{i}-y_{i}]$ (7)

Where: $a_{i}\geqslant 0$ , $a_{i}$ is a Lagrange multiplier.

According to Karush-Kuhn-Tuch (KKT) conditions, setting the partial derivatives of Lagrange function to $w$ , $b$ , $\xi_{i}$ and $a_{i}$ are zero. Then:

$\displaystyle\left\{{{\begin{array}[]{l}{\frac{\partial L}{\partial w}=0\to w=% \sum\limits_{i=1}^{N}{a_{i}\phi(x_{i}),}}\\ {\frac{\partial L}{\partial b}=0\to\sum\limits_{i=1}^{N}{a_{i}=0,}}\\ {\frac{\partial L}{\partial\xi_{i}}=0\to a_{i}=\gamma\xi_{i},i=1,2,\cdots,N}\\ {\frac{\partial L}{\partial a_{i}}=0\to w^{T}\phi(x_{i})+b+\xi_{i}-y_{i}=0}\\ \end{array}}}\right.$ (8)

After $w$ and $\xi$ are eliminated, a matrix equation can be derived as follows:

$\displaystyle\left[{{\begin{array}[]{cc}0&{\bar{I}^{T}}\hfill\\ \bar{I}&{\Omega+\gamma^{-1}I}\\ \end{array}}}\right]\left[{{\begin{array}[]{*{20}c}b\\ a\\ \end{array}}}\right]=\left[{{\begin{array}[]{*{20}c}0\\ y\\ \end{array}}}\right]$ (9)

Where: $a=[a_{1};\cdots;a_{N}]$ ; $y=[y_{1};\cdots;y_{N}]$ ; $\Omega=\{\Omega_{ij}\}_{N\times N}$ , is a $N\times N$ dimensional function matrix, and $\Omega_{ij}=\varphi^{T}(x_{i})\cdot\varphi(x_{i})$ , $i=1,2,\ldots$ , $N$ ; $j=1,2,\ldots,N$ .

According to Mercer conditions, there exist two functions: one is reflecting function $\varphi(\cdot)$ , another is kernel function $K(\cdot,\cdot)$ . The two functions satisfy the following relationship equation:

$\displaystyle K(x_{i},x_{j})=\varphi(x_{i})^{T}\varphi(x_{j})$ (10)

Commonly used kernel functions include polynomial function, sigmoid function and radial basis function, etc. For higher accuracy can be obtained by radial basis function, and the radial basis function is relatively easy to achieve, it is selected as the kernel function, its function is as follow:

$\displaystyle K(x_{i},x_{j})=\exp[-|x_{i}-x_{j}|^{2}/(2\sigma^{2})]$ (11)

Where: $\sigma$ is the kernel width.

Figure 2.

Topological structure of LS-SVM.

By Least squares method, the parameters $a$ and $b$ in Eq. (9) can be obtained; substituting Eqs (8) and (10) into Eq. (5), then the regression function of LS-SVM can be derived as follow:

$\displaystyle y(x)=\sum\limits_{i=1}^{N}{a_{i}K(x_{i},x)+b}$ (12)

According to the model of magnetic suspension system in Eq. (4), the stator current components $i_{s1d},i_{s1q},i_{s2d},i_{s2q}$ and the rotor flux-linkage are taken as the input of LS-SVM.

Figure 2 shows the LS-SVM topology diagram, in which the acceleration of $\alpha$ radial displacement is taken as the fitting output variable. After a second order integral, the $\alpha$ radial displacement can be obtained from the fitting output variable. Because the fitting principle and LS-SVM topology diagram of $\beta$ radial displacement component are similar, and will not be presented here.

3.2 Realization of radial displacement prediction model based on LS-SVM

According to Eq. (4), $\{i_{s1d},i_{s1q},i_{s2d},i_{s2q},\psi_{r1}\}$ is selected as input sample, $\{\ddot{\alpha},\ddot{\beta}\}$ is selected as output sample. In order to facilitate the off-line training and fitting, two learning machines are designed for LS-SVM. Then based on the prediction model derived from off-line training, the estimation value of radial displacement can be obtained by integral operation. The specific implementation steps can be concluded as follows:

The first step is the collection of training sample. In this article, the training samples are obtained from the analytical inverse dynamical decoupling control system of a bearingless induction motor [20]. In the practical operation range, adopting normal distribution random signal as input, it continues 3s, the sampling period is 1ms. During sampling period, the $i_{s1d},i_{s1q},i_{s2d},i_{s2q},\psi_{r1},\alpha$ and $\beta$ signals are sampled. After the sampled datum are smooth filtered, based on the five-point numerical differentiation algorithm, the acceleration signals $\ddot{\alpha}$ and $\ddot{\beta}$ are derived, and then the training sample set $\{i_{s1d},i_{s1q},i_{s2d},i_{s2q},\psi_{r1},\ddot{\alpha},\ddot{\beta}\}$ are constituted. From the 3000 sets of sample datum, selecting 2000 sets as training sample set, which are used for the off-line training of predication model; the other 1000 sets are taken as test sample set, which are used to test the fitting precision and the generalization ability of the trained LS-SVM model. The second step is offline training for LS-SVM. Taking $u=(i_{s1d},i_{s1q},i_{s2d},i_{s2q},\psi_{r1})$ as the training input of LS-SVM, and taking $(\ddot{\alpha},\ddot{\beta})$ as the training output of LS-SVM. Two learning machines are established to train LS-SVM; a radial basis function is chosen as the kernel function; by grid search method, the optimal penalty factor $\gamma$ (a regularization parameter) and kernel width $\sigma$ of radial basis function are obtained, and then the LS-SVM model with better training accuracy is obtained. In the training process of LS-SVM, the penalty factor and the kernel width determine the training accuracy and complexity of LS-SVM. Figure 3 shows the schematic diagram of offline training and radial displacement observation based on LS-SVM.

Figure 3.

Schematic diagram of offline training and displacement observation.

4. Radial displacement sensorless control system

Figure 4 shows the radial displacement sensorless control system schematic diagram of a three-phase bearingless induction motor. The control system includes two parts, i.e. the inverse dynamic decoupling control system of a bearingless induction motor, and the prediction of the radial displacement.

In the part of inverse dynamic decoupling control system [23], by connecting in series the inverse system model in front of the original system of a bearingless induction motor. And then the bearingless induction motor system is decoupled into four pseudo linear second order integral subsystems; include a motor speed subsystem, a rotor flux-linkage subsystem, and two radial displacement component subsystems. Then the closed-loop controllers are designed for each pseudo linear integral subsystem, and the dynamic decoupling control of a bearingless induction motor is achieved.

In the part of prediction and estimation of radial displacement, the rotor flux-linkage $\psi_{r}$ , the stator current components of two sets of windings along $d$ and $q$ coordinate axes are send to the LS-SVM prediction model of radial displacement. And then, the estimated radial displacement signal is obtained, and the closed-loop negative feedback control of magnetic suspension system can be realized.

5. System simulation and analysis

To verify the validity of the LS-SVM displacement prediction model, according to Fig. 4, simulation study has been made. The parameters of a bearingless induction motor are shown in Table 1.

Table 1
Parameters of bearingless induction motor

Parameter	Description	Value
$r$	Stator inner diameter (mm)	62
$l$	Effective core length (mm)	82
$\delta$ ${}_{1}$	Air gap of auxiliary bearing (mm)	0.2
$P$	Power of motor (kW)	2.2
$R_{s}$	Stator winding resistance ( $\Omega$ )	1.6
$R_{r}$	Rotor winding resistance ( $\Omega$ )	1.423
$L_{s1l}$	Leakage inductance of torque windings (H)	0.0043
$L_{r1l}$	Leakage inductance of rotor windings of torque system (H)	0.0043
$L_{m1}$	Exciting inductance of torque system (H)	0.0859
$J$	Rotation inertia of motor (kg.m ${}^{2}$ )	0.024
$R_{s2}$	Suspension stator winding resistance	2.7
$L_{s2l}$	Leakage inductance of suspension stator windings (H)	0.00398
$L_{m2}$	Exciting inductance of suspension system (H)	0.230

Figure 4.

Structural block diagram of radial displacement sensorless control system.

When the bearingless induction motor starts with no-load, the response curves of $\alpha$ and $\beta$ radial displacement components are shown in Figs 5 and 6. Hereinto, the solid line is the response curve of the radial displacement sensorless control system; the dotted line is the response curve of the control system with radial displacement sensor.

Figure 5.

Response curve of $\alpha$ displacement.

Figure 6.

Response curve of $\beta$ displacement.

From the simulation results in Figs 5 and 6, there are following analyses:

After the sensorless control system is started, the bearingless rotor reaches a stable suspension state within 0.2 S. Compared with the control system with radial displacement sensor, during the starting suspension stage of displacement sensorless control system, the displacement overshoot is increased, but the overshoot is in the 0.03 mm range. The reason of the displacement overshoot increase is that there is a transient process of relevant variables in the starting stage of bearingless induction motor, such as the motor flux-linkage, the magnetic suspension control current, and so on. The transient processes of relevant variables lead to the error between the estimated displacement and the actual displacement. Thus, the control precision of the displacement is influenced for a short time.

Either the LS-SVM displacement observer or the actual displacement sensor are adopted, after a adjustment stage of about 0.2 S, the rotor can be stabilized at the center of the stator, and in steady state, the estimated displacement is always consistent with the actual value. The simulations results have indicated that the presented estimation method of radial displacement can provide a reliable displacement feedback signal for the control system, and the radial displacement sensorless operation control of a bearingless induction motor can be realized.

Figure 7.

Response curve of displacement sensorless control system of bearingless induction motor.

In order to verify the dynamic decoupling performance of the radial displacement sensorless control system, the given speed and radial displacement signals are suddenly changed at different times. In order to verify the anti load disturbance capability of the displacement sensorless control system, an 8.4 N.m rated load torque is suddenly added at the moment of 2.0 s; and the rated load torque is suddenly removed at the moment of 2.5 s. Figure 7 gives the response curve of the radial displacement sensorless control system of a bearingless induction motor.

Figure 8.

Response curve comparison of $\alpha$ displacement between before and after adding high frequency harmonic noise.

Figure 9.

Response curve comparison of $\beta$ displacement between before and after adding high frequency harmonic noise.

From the simulation results in Fig. 7, there are following analyses:

When one of the motor speed, $\alpha$ and $\beta$ radial displacement components is suddenly changed, the other variables are not affected basically, or affected by very small. The simulation results have shown that based on the presented displacement sensorless control system, a strong dynamic decoupling control performance can be achieved between the torque system and the magnetic suspension system, and that between the two radial displacement components can be achieved.

During the sudden change process of load torque, the motor speed only has a very slight fluctuation, and then it quickly returns to its given value. The radial displacement is almost unaffected by the load torque, or the effect is very small. The simulation results have shown that the radial displacement sensorless control system has a stronger anti load capacity.

In the output voltage of actual PWM inverter, there inevitably exists high frequency harmonic voltage. In order to close the real conditions, a high frequency harmonic interference signal is added on the output end of torque winding, whose frequency and amplitude are 10 KHz and $\pm$ 10 V respectively. Then between before and after adding the high frequency harmonic interference signal, the simulation comparisons have been carried out. Figures 8 and 9 give the contrast response curves of $\alpha$ and $\beta$ radial displacements. In order to facilitate the performance analysis of radial displacement observation, the radial displacement response curves of the control system with actual radial displacement sensor are presented also.

From Figs 8 and 9, it can be seen that when the displacement sensorless control system is subjected to a high frequency harmonic interference, fast radial displacement tracking can still be realized by LS-SVM observer in $\alpha$ and $\beta$ directions; however, the overshoots of the $\alpha$ and $\beta$ radial displacement components are increased relatively. The reason for the radial displacement overshoot increase is that the high frequency harmonic voltage causes the weak variations of the stator current and the motor flux linkage.

6. Conclusion

In order to reduce the control system cost of a bearingless induction motor, an estimation method of rotor radial displacement based on LS-SVM is presented. Firstly, the mathematical model of magnetic suspension system is established. Then, the stator current variables of torque windings and suspension windings, and the rotor flux-linkage of torque system are taken as the input samples of LS-SVM, the accelerations of radial displacement in $\alpha$ and $\beta$ directions are taken as the output samples. Based on the regression principle of LS-SVM, from two LS-SVM learning machines, the prediction models of the displacement accelerations are offline trained and fitted. By a second order integral operation on the obtained displacement acceleration variable, the estimated value of the rotor displacement is obtained. Adopting the LS-SVM observation method of radial displacement, the radial displacement sensorless control system of a bearingless induction motor is constructed. According to the simulation results, there are following conclusions:

When the presented displacement observation method is adopted, a fast response speed and high tracking precision of radial displacement can be obtained, and a reliable feedback signal of radial displacement can be provided for the control system of a bearingless induction motor.

When the presented displacement observation method is adopted, during the starting suspension stage of bearingless rotor, the displacement overshoot is slightly larger than that of the control system with radial displacement sensor. But after the system reaches stable operation state, the estimated value of radial displacement is always consistent with the actual value.

Based on the presented radial displacement estimation method, when the presented radial displacement sensorless control system is adopted, the good decoupling control between the torque system and the magnetic suspension system, and that between the two radial displacement components can be achieved. In addition, the displacement sensorless control system has a good ability to resist load torque.

However, there are still some deficiencies that need to be improved in the follow-up study. Compared with the control system with displacement sensor, during the starting suspension stage of displacement sensorless control system, the displacement overshoot is increased; the reason lies in that there is a transient process of relevant variables in the starting stage, which leads to the error between the estimated displacement and the actual displacement. When the displacement sensorless control system is interferenced by a high frequency harmonic, the overshoot of radial displacement is increased; the reason lines in that the high frequency harmonic voltage causes the weak variations of the stator current and the motor flux linkage. Although the displacement acceleration observation algorithm based on LS-SVM is studied in detail, the influence of integral initial value and accumulative error is not considered. These are the problems to be further studied and optimized.

Footnotes

Acknowledgments

The supports of Natural Science Foundation of China (51277053), International Cooperation Project on Sci. and Tech. of Henan Province (114300510029), and Nature Science Fund of Henan Province Education Bureau (2010B510011), are acknowledged.

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Diaplacement sensorless control strategy of bearingless induction motor

Abstract

Keywords

1. Introduction

2. Working principle and model of bearingless induction motor

2.1 Working principle of bearingless motor

3.1 Displacement prediction model based on LS-SVM

5. System simulation and analysis

Table 1 Parameters of bearingless induction motor

Footnotes

Acknowledgments

References

Table 1
Parameters of bearingless induction motor