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Saliency-Tracking-Based Sensorless Control of AC Machines Using Structured Neural Networks Pablo García, Student Member, IEEE, Fernando Briz, Senior Member, IEEE, Dejan Raca, Student Member, IEEE, and Robert D. Lorenz, Fellow, IEEE
Abstract—The focus of this paper is the use of structured neural networks for sensorless control of ac machines using carrier-signal injection. Structured neural networks allow effective compensation of saturation-induced saliencies as well as other secondary saliencies. In comparison with classical compensation methods, such as lookup tables, this technique has advantages such as a physics-based structure, general scalability, reduced size and complexity, and correspondingly reduced commissioning time. When compared with traditional neural networks, structured neural networks are simpler, physically insightful, less computationally intensive, and easier to train. All make the proposed method an improved implementation for sensorless drives. Index Terms—Rotor position estimation, sensorless control, structured neural networks.
N OMENCLATURE νan , νbn , νcn ν q , νd , ν0 Ia , ib , ic I q , id , i0 Lσs , ∆Lσs h θe ωrm , θrm
Phase to neutral voltages. Voltages in a dq0 reference frame. Phase currents. Currents in a dq0 reference frame. Average and differential stator transient inductances. Harmonic order of the saliency relative to electrical angular units. Angular position of the saliency in electrical radians. Mechanical speed and position.
Paper IPCSD-06-079, presented at the 2006 Industry Applications Society Annual Meeting, Tampa, FL, October 8–12, and approved for publication in the IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS by the Industrial Drives Committee of the IEEE Industry Applications Society. Manuscript submitted for review October 15, 2005 and released for publication August 14, 2006. This work was supported in part by the Research Technological Development and Innovation Programs of the Principado of Asturias–ERDF, under Grant PB02-055 and in part by the Spanish Ministry of Science and Education-ERDF under Grant MEC-04-DP12004-00527 respectively, and the Wisconsin Electric Machines and Power Electronics Consortium (WEMPEC) of the University of Wisconsin, Madison, WI. P. García and F. Briz are with the Department of Electronics, Computer and Systems Engineering, University of Oviedo, 33204 Gijón, Spain (e-mail:
[email protected];
[email protected]). D. Raca is with the Department of Electrical and Computer Engineering, University of Wisconsin, Madison, WI 53706 USA, and also with Power Control Systems, Magnetek Inc., Menomonee Falls, WI 53051 USA (e-mail:
[email protected]). R. D. Lorenz is with the Departments of Mechanical Engineering and Electrical and Computer Engineering, University of Wisconsin, Madison, WI 53706 USA (e-mail:
[email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIA.2006.887309
∧ ∗ S, R s νqds _c νc , ω c , θ c ν0 s ν0sc ν0ch , V0c2h c ν0qd c ν0qd _c LQD0 wcc1 , . . . , wcc4
wph1 , wph2 ∆L
Estimated variables. Commanded variables. Number of stator and rotor slots. Injected carrier-signal voltage. Magnitude, frequency, and phase angle of the injected carrier-signal voltage. Zero-sequence voltage. Zero-sequence carrier-signal voltage. Magnitude of the hθe and −2hθe components of the zero-sequence carrier-signal voltage. Zero-sequence-voltage vector. Zero-sequence carrier-signal-voltage vector. Inductance matrix in a dq0 reference frame. Structured neural networks (SNN) coupling weights. Intermodulation-components phase-adjustment weights. Saturation-induced differential stator transient inductance estimated by the SNN. I. I NTRODUCTION
S
ALIENCY-TRACKING-BASED sensorless control methods have acquired significant importance during the last years in applications where sustained sensorless operation in the low- and zero-speed range, and/or position control are needed, as they overcome the limitations of methods based on the fundamental excitation [back electromotive force (EMF)]. Different implementations of saliency-tracking-based methods have been proposed [1]–[12]. While all of them share the same physical principles, significant differences between methods exist. The differences are related to the high-frequency excitation used, to the electric signals that are measured to obtain information on the saliency position, and to the methods used to track the saliency image. Carrier-signal-based methods use the inverter to inject a high-frequency carrier signal into the machine, which in the most common implementation, consists of a rotating voltage vector [1]. Interaction between the carrier signal and the saliencies present in the machine gives rise to specific frequency components in the resulting electric variables (currents and voltages). Rotor position estimation is feasible when a spatial saliency in the rotor couples with the stator windings producing measurable components in the stator terminals [1]. Unfortunately, other saliencies can also be present in the machine
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during its regular operation, most importantly, those caused by the saturation of the magnetic paths [4], [6], [8], [11], [18], [20]. These saliencies cause additional components in the measured signals, which add to those caused by the rotor-positiondependent saliency being tracked. If these additional components are not properly decoupled, they can result in serious degradation, including reduced estimation accuracy, reduced estimation bandwidth, and potential stability problems. Compensation of saturation-induced saliencies has usually been approached by means of lookup tables, which can be implemented in different ways [4], [6], [8]. In all of them, the table is built during an offline-commissioning process for different operating points of the machine. The lookup table is then accessed during the regular sensorless operation of the drive, and its information used for online decoupling of the saturation-induced components of the measured signals. Using a lookup table for decoupling of saturation-induced components has some limitations. First, it is not obvious the amount of information that needs to be stored. In addition, building the lookup tables is a tedious process, and usually, needs to be repeated for each new machine design and inverter configuration [8]. Another approach is to use a classical random neural network to learn, and then, decouple unwanted saliencies [11]. Major drawbacks of this option are the size and complexity of a suitable random network, the lack of a clear criterion for the number of layers and neurons, and the computational requirements for its implementation. These drawbacks result from the fact that prior knowledge of the physical structure of the system is ignored [13]. The use of structured neural networks [13] to decouple saturation-induced saliencies is proposed in this paper. When compared with traditional neural networks, structured neural networks will be shown to be a feasible alternative for the decoupling of saturation-induced saliencies. In addition, they have appealing properties for practical implementation in standard drives, like a relatively simple and insightful structure and reduced commissioning time and computational requirements. Furthermore, structured neural networks overcome limitations of classical neural networks, such as relatively slow convergence, inefficient neuron use, and unpredictable and uninsightful structure, as they fully incorporate all prior knowledge of the system being modeled into the network structure [13]–[16]. This technique can also be used to decouple other secondary saliencies in addition to saturation-induced saliencies. In this paper, intermodulation saliencies are chosen as secondary saliencies to be decoupled. The analysis and experimental results presented in this paper will focus on the case of a high-frequency carrier rotating voltage vector injection, whereby the resulting zero-sequence carrier-signal voltage is measured [4]. However, the method and the most relevant conclusions reached are valid and can be applied with minor modifications to other saliency-tracking-based sensorless control techniques, including negative-sequence carrier-signal current-based methods [1], methods that use different forms of carrier-signal excitation [10], and those which use the pulse-width-modulation excitation [7].
Fig. 1. Injection of the carrier-signal voltage and measurement of the zerosequence voltage.
II. S ALIENCY -T RACKING -B ASED S ENSORLESS T ECHNIQUES U SING THE Z ERO -S EQUENCE C ARRIER -S IGNAL V OLTAGE The carrier frequency model of a salient three-phase machine can be written as (1)–(3). In this model, high-frequency (transient) inductances are modeled as consisting of a spatial “h” harmonic component [3] dia νan = (ΣLσs + 2∆Lσs cos(hθe )) dt dib 2π νbn = ΣLσs + 2∆Lσs cos h θe − 3 dt dic 4π νcn = ΣLσs + 2∆Lσs cos h θe − . 3 dt
(1) (2) (3)
When the machine is fed by a carrier voltage vector (4) (Fig. 1), the resulting zero-sequence carrier-signal voltage (5) can be analytically obtained from (1)–(5), being of the form (6) [3] s jθc νqds _c = V c e ,
ωc =
dθc dt
1 s ν0s = (νan + νbn + νcn ) 3 s ν0sc = V0ch cos(ωc t ± hθe ) − V0c2h cos(ωc t ± 2hθe )
(4) (5) (6)
with V0ch = Vc ΣLσs ∆Lσs /(ΣLσs2 − ∆Lσs2 ) and V0c2h = Vc ∆Lσs2 /(ΣLσs2 − ∆Lσs2 ). From (6), saliencies in the machine are shown to modulate the phase of the zero-sequence carrier-signal voltage, which can be used for saliency-position estimation. It is also observed that the zero-sequence carrier-signal voltage consists of two components. However, if ∆Lσs Lσs , which is typically the case, the term V0c2h can be safely neglected [4]. A. Rotor Position Estimation Rotor position estimation using carrier-signal excitation is possible when rotor-position-dependent saliencies exist. Such saliencies will always be present in interior PM machines as a result of imbedded permanent magnets acting as barriers to flux linkage in d-axis. Consequently, machine reluctance varies as a second spatial electrical harmonic and can be used for carriersignal-based position tracking [17]–[22]. Rotor-positiondependent saliencies can exist in standard induction-machine
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TABLE I INDUCTION MOTOR PARAMETERS
Fig. 2. Frequency spectrum of the zero-sequence carrier-signal voltage. The machine was operated at rated flux, no load, and with ωe = ωr = 4 Hz. A carrier voltage of magnitude Vc = 20 V and frequency ωc = 2500 Hz was used.
designs with open or semiopen rotor slots, due to the combined effect of stator and rotor slotting [1], [5], [8], [12]. Key design parameters determining whether a machine shows a rotor slotting saliency are the number of stator and rotor slots and the number of poles [12]. The resulting zero-sequence carriersignal voltage caused by rotor–stator-slotting saliencies will be of the form (7), where ωrm and θrm are the mechanical speed and position, respectively, and R is the number of rotor slots [12] s = V0ch cos(ωc t+Rθrm ) = V0ch cos ((ωc +Rωrm )t) . ν0sc(θ rm ) (7)
Fig. 3. Schematic representation of a classical random (unstructured) feedforward neural network whereby all interconnections are automatically included.
B. Saturation-Induced and Intermodulation Components Saturation of the magnetic-flux paths in the machine causes saliencies, which result in additional components of the zerosequence carrier-signal voltage. Saturation-induced saliencies can be modeled using (1)–(6), with θe being the angular position of the flux-causing saturation. The most relevant saturation-induced harmonic component is obtained with h = 2, which means that saturation has the same effect on the north and south pole of each phase. Consequently, the resulting zero-sequence carrier-signal voltage caused by saturation is of the following form: s = V0ch cos(ωc t + 2θe ). ν0s(θ e)
(8)
In addition to the saturation-induced components, interaction between the saturation and the rotor–stator slotting harmonic will give rise to intermodulation components in the zerosequence carrier-signal voltage, having the following form: s = V0c2h cos(ωc t − 2θe ))(cos(R θrm + φr )). (9) ν0sc(θ rm θe )
A general expression of the zero-sequence carrier-signal voltage when fundamental excitation exists will be then of the following form: s s s s ν0sc = ν0sc(θ + ν0s(θ + ν0sc(θ . rm ) e) rm θe )
(10)
Saturation-induced components and intermodulation components present in the zero-sequence carrier voltage can result in large rotor position estimation errors and even stability problems, if they are not properly decoupled. Fig. 2 shows the frequency spectrum of the zero-sequence carrier-signal voltage when the induction machine was operated at rated flux and
rated load, and a rotating carrier voltage (4) of magnitude Vc = 20 V and frequency ωc = 2500 Hz was superimposed on the fundamental. The parameters of the machine are shown in Table I. The inverter-switching frequency was 10 kHz. The zero-sequence carrier-signal voltage was measured using an auxiliary resistor network, as shown in Fig. 1 [4]. The most relevant components of the zero-sequence carrier-signal voltage observed in Fig. 2 include: a rotor–stator slotting component at a frequency ωc + 14ωr ; saturation-induced components at frequencies ωc + 2ωe and ωc − 4ωe ; and an intermodulation component at a frequency ωc − 2ωe − 14ωr . III. S TRUCTURED V ERSUS U NSTRUCTURED N EURAL N ETWORKS Structured neural networks were first proposed in [13]. The structure of these neural networks is based on existing knowledge of the physics of the modeled system. Thus, they provide a powerful tool for modeling nonlinear systems and maintaining all the benefits of neural networks while significantly reducing computational complexity. Figs. 3 and 4 show an unstructured and a structured neural network, respectively. Compared to traditional unstructured neural networks, the structured neural network has several appealing properties, such as the following. 1) It provides insight about the physical representation of the process being learned. 2) It has a simpler structure than traditional neural networks. The number of layers and neurons are determined based on the physical model, no trial-and-error process is necessary to adjust the network topology.
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Fig. 4. Schematic representation of a structured neural network whereby interconnections between neurons are determined by the physical model and neuron basis functions are selected based on physical models.
3) It significantly reduces training time. Weights can be initialized with previously estimated values letting them vary within a specific range and avoiding local minimums in the training process. 4) Activation functions and adaptive weights have physical meaning. The basic elements for building a structured or traditional neural network are neurons. The major difference is that, in the case of structured neural networks, the neurons are designed to perform a specific operation. Basic types include summation and multiplication. Summation is realized with a Sigma neuron, while PI neuron is used for multiplication. Both types of neurons, as they appear in traditional neural networks, are depicted in Fig. 5. Neurons of a structured neural network would be much simpler as they would have only synapses that are actually used. In addition, structured neural networks use custom-basis (activation) functions instead of generic sigmoidal functions in order to be consistent with the physics of the particular application. Thus, sinusoidal and cosinusoidal basis functions are used in this application. IV. S ALIENCY D ECOUPLING AND R OTOR P OSITION E STIMATION U SING S TRUCTURED N EURAL N ETWORKS A structured neural network was built to decouple both saturation-induced and intermodulation components of the zero-sequence carrier-signal voltage. The structure of the network is divided into layers and subnetworks, each designed to model-specific saliencies. The first subnetwork estimates zero-sequence carrier-signal-voltage components due to
d LQD0 [iq id i0 ]T dt ΣL + 23 ∆L1 (2 + α1 ) √2 ∆L2 α2 = 3 2 3 L1 (1 − α1 )
Fig. 5.
Sigma and PI neurons. (a) Sigma neuron. (b) PI neuron.
saturation-induced saliencies. To devise this structure, effects of saturation-induced saliencies on the zero-sequence carriersignal voltage were modeled by transforming the abc model given by (1)–(3) to a dq0 equivalent model (11), shown at the bottom of the page, with LQD0 being of the form (12), also shown at the bottom of the page, where ∆L1 = ∆Lσs cos(hθe ) ∆L2 = ∆Lσs sin(hθe ) 2π h α1 = cos 3 2π α2 = sin h . 3 By solving (11) and (12) in discrete time, the following is obtained for the zero-sequence voltage: ν0 [k] = (2Lqd0 [k] − Lqd0 [k − 1])(3,1) iq [k] + (2Lqd0 [k] − Lqd0 [k − 1])(3,2) id [k] − Lqd0 [k](3,1) iq [k − 1]Lqd0 [k](3,2) id [k − 1]
where the numeric subindexes (i, j) of the inductances in (13) stand for the corresponding position in the inductance matrix (12). These terms suggest that components of the zerosequence carrier-signal voltage caused by saturation-induced
[νq νd ν0 ]T =
LQD0
(13)
(11) √2 ∆L2 α2 3
ΣL + 2∆L1 α1 −2 √ ∆L2 α2 3
ΣL
4 3 ∆L1 (1 − α1 ) −4 √ ∆L2 α2 3 + 23 ∆L1 (1 + 2α1 )
(12)
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Fig. 7. Proposed structured neural network to decouple saturation-induced and intermodulation-induced components.
Fig. 6. Proposed structure of saturation saliency subnetwork. The ∆L weights correspond to ∆Lσs in (12).
saliencies can be modeled as function of iq , id , and θe , evaluated at two consecutive sampling periods k and k1 of the discrete time control. By changing values of h, different saturation-induced components can be analyzed. A three-layer subnetwork structure is suggested by (11) and (13). 1) The first layer calculates the inductance terms as function of θe . To perform this calculation, PI neurons are used. The basis functions for the neurons are cosinusoidal and sinusoidal functions. All the weights in this layer are fixed by the physical model. 2) The second layer performs multiplications between the current components and the outputs of the impedances layer; using PI neurons as well. 3) The third layer consists of a Sigma neuron and has adjustable weights, which are trained to estimate the value of the differential inductance (∆Lσs ). This structure is shown in Fig. 6, where the weights are determined by (14) and (15). It is developed for decoupling of a single component. If more harmonics need to be decoupled, the structure can be repeated as many times as needed. In this layer, the only adaptive weight is the one that models the differential transient inductance (∆Lσs ), as indicated by the model. This parameter appears four times in the structured neural network. It can be treated as four independent weights in the training process. However, the four independently learned weights should converge to a single value, if the training has converged correctly 2π 2 h w(3,1) = cos(hθe )[k] 1 − cos 3 3 = w31 cos(hθe )[k] w(3,2) =
2√ 3 sin(hθe )[k] sin 3
= w32 sin(hθe )[k].
2π h 3
(14)
(15)
Fig. 8. Decoupling of saturation-induced and intermodulation-induced components of the zero-sequence carrier-signal voltage, and rotor position estimation using a tracking observer.
Better results are obtained if cross coupling between iq and id is also considered. For this purpose, additional adaptive terms are added in the coupling layer, as depicted using dashed blocks in Fig. 6. Once saturation-induced saliencies are computed, another set of layers estimate intermodulation saliencies, as shown in Fig. 7. These can be modeled as a multiplication in the time domain (convolution in the frequency domain) of the saturation-induced components and the rotor–stator slotting component. Although the phase of these harmonics is related to the phase of the rotor–stator slotting-induced and saturation-induced components, there is an unknown offset angle, which needs to be estimated by the network. The structure proposed is comprised of two orthogonal neurons, cos(Rθr ) and sin(Rθr ), which allows calculation of the phase of the harmonics by learning the proper weights. This structure is quite similar to the Discrete Fourier Transform with the adaptive weights being the Fourier coefficients computed by the training process. If a single saturation-induced component is modeled (h = 2), estimated intermodulation saliencies are at frequencies: ωc − 2θe + R ωrm , ωc + 4θe − R ωrm , ωc − 4θe + R ωrm , and ωc + 2θe − R ωrm . The intermodulation-layer structure would remain the same, if additional saturation saliencies were taken into account. Finally, all the harmonics to be decoupled (both saturationinduced and intermodulation components) are added in the output layer, which is implemented by a Sigma neuron and linear-basis function, as shown in Fig. 7. Once the network is trained, this output is subtracted from the measured zerosequence carrier-signal voltage to get the signal used for tracking the rotor position, as shown in Fig. 8. For the implementation of the method, the sampled zero-sequence voltage
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Fig. 9. Modified (simplified) structure of the subnetwork for the decoupling of saturation-induced saliencies for real-time implementation. The ∆L weights correspond to ∆Lσs in (12).
was converted into a carrier frame complex voltage vector (16) [3], [4] and low-pass filtered (see Fig. 8). The resulting zerosequence carrier-frame-voltage vector (17) has its phase angle modulated by the saliency position c = ν0 e−jωc ν0qd c jhθr ν0qd . _c = − jV0ch e
(16) (17)
While not strictly necessary, this transformation was found to be helpful as it enables the use of tracking methods specific to complex vectors to obtain the saliency position. V. R EAL -T IME I MPLEMENTATION I SSUES The proposed system of Fig. 8 was constructed for decoupling of saturation-induced and intermodulation components in order to improve the position and velocity estimation on the induction-machine drive of Fig. 1. Relevant issues for its implementation are analyzed in this section. A. Layer Structure The complete structured neural network has only 47 connections of which ten are adaptive, with four equal to each other (∆L weights). The initial topology of the network was built using the MATLAB neural-network toolbox. Some modifications were made to allow custom basis (activation) functions (sin and cos functions) and implementation of PI neurons needed for this application. It is easy to add more layers or features to the neural network, if additional secondary components need to be decoupled. To simplify the structure of the saturation-induced-saliencies subnetwork (Fig. 6), the modified structure shown in Fig. 9 is used in the real-time implementation. This topology has two advantages over the original structure: First, the number of layers is decreased by one, resulting in reduced real-time computa-
Fig. 10. (a) Magnitude and (b) phase of the 2ωe harmonics of the zerosequence carrier-signal voltage vector, as a function of slip and fundamental current level, used to build a lookup table for saturation-induced saliency decoupling.
tional requirements. Second, the subnetwork is more flexible due to the adaptive weights wcc1 − wcc4 that are introduced in the interconnection between the inductances layer and the coupling layer, which compensates for discrepancies between the physical model and the implemented structure. They are added in addition to fixed gains, labeled w31 − w32 , which have values of ±2 and ±1. Even though the additional adaptive gains are added, training time remains virtually the same. B. Training Process The structured neural network of Fig. 7 was trained using the Levenberg–Marquardt back-propagation algorithm. This structure allows for training in less than 10 s in the worst case, but in general, less than 2 s. This time is added to the time needed to capture data, which can be in the range of a few tens of seconds. Research is ongoing to reduce commissioning time using generalization properties of neural networks. To train the network, the machine was operated under various working conditions. The d- and q-axis currents in the stationary reference frame were used as inputs to the network and saturation and intermodulation components of the measured zero-sequence carrier-signal voltage as the target output. Saturation and intermodulation components of the measured zero-sequence carrier-signal voltage were obtained in a similar fashion to that used to build multidimensional lookup tables, an example of which is depicted in Fig. 10. However, instead
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Fig. 11. Test results for the network performance evaluation. Target (x-axis) versus network output (y-axis) for two different training processes. (a) Network has been correctly trained to the tested operating point. (b) Network has not been correctly trained to the tested opeerating point.
of being stored, this information is used to build complex time vectors containing the information that will be first learned and later decoupled by the SNN. It is noted that this measurement process could be significantly simplified, if additional layers to estimate the rotor position were added to the network. This issue is briefly discussed in Section V-C. The performance of the trained network was then assessed by operating the machine in working conditions different from those used for its training. Accurate estimation during this evaluation process will validate the training. Fig. 11 shows results for two cases of training. Target values are plotted on the x-axis and actual network outputs on the y-axis. Linear-regression analysis was performed between the network response and corresponding targets. The case shown in Fig. 11(a) is very close to a perfect match (T = A and R = 1, where R is the regression coefficient of correlation), meaning that the network is properly trained. By comparison, results shown in Fig. 11(b) reflect incorrect training. The training was also validated by plotting the evolution of adaptive parameter ∆L, as shown in Fig. 12. Different initial values of ∆L are used in different experiments, but the final estimates uniformly converged to virtually identical values. The only exception is experiment 6, in which the network converged to a local minimum. However, this has no influence on overall performance of the network as all adaptive gains varied in the same way.
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Fig. 12. Variation of ∆L weights as a function of the number of iterations of training process and the number of trainings performed. (a) Evolution of ∆L of inputs iq [k] and iq [k − 1]. (b) Evolution of ∆L of inputs id [k] and id [k − 1].
Fig. 13. Analysis of convergence of |∆L| weights.
Fig. 13 shows that all four values of ∆L converge to the same value by the end of training process. In this figure, the ∆L values are paired depending on the current component (q- or d-axis) associated with them. C. Further Improvements of the Training Process Training could be simplified by implementing a structuredneural-network tracking-state filter, as shown in Fig. 14. With this new subnetwork, it would be unnecessary to measure saturation and intermodulation components during the training
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Fig. 14. Implementation of a tracking observer using structured neural networks whereby the rotor angle θr for training process was measured using an encoder.
Fig. 16. Same as for with the machine being operated at rated-flux, 66% of rated load, and with ωe = 4 Hz and ωr = 2 Hz.
Fig. 15. (a) Estimated and actual components of the zero-sequence carriersignal-voltage vector due to saturation and intermodulation saliencies. (b) Component of the q-axis estimation error before intermodulation components are decoupled. (c) Component of the q-axis estimation error after intermodulation components are decoupled. The machine was operated at ratedflux, no-load, and with ωe = 4 Hz and ωr = 4 Hz.
process; instead, the actual rotor position could be used. The proposed tracking-state filter would have fixed weights, so the training time would remain the same. The rotor position could be measured using an encoder, as shown in Fig. 14. This training method would be appealing in applications where spectral separation between different components of the zero-sequence carrier-signal voltage is nonexistent. This is the case for PM synchronous machines, in which rotor-position-dependent and flux-position-dependent saliencies rotate in synchronism. Ongoing research is exploring this topic. D. Real-Time Implementation Once the network has been trained, the values of the adaptive weights are fixed and a set of difference expressions are automatically generated by the MATLAB code, which makes it easy to test different structures and training strategies. These expressions capture the behavior of each layer, reducing the number of operations that need to be processed in real time. All the algorithms were implemented in a fixed point DSP TMS320F2812 from Texas Instruments. Time required for the computation of the structured neural network was less than 5% of overall computational load.
Fig. 17. Estimated frequency spectrum of the zero-sequence carrier-signal voltage vector due to saturation and intermodulation saliencies, for the case of (a) machine operated at rated-flux, no load, and with ωe = ωr = 4 Hz and (b) machine operated at rated-flux, 66% rated load, and with ωe = 4 Hz and ωr = 2 Hz.
VI. E XPERIMENTAL R ESULTS The actual and estimated zero-sequence carrier-signalvoltage vector due to saturation and intermodulation saliencies, i.e., disturbing components that need to be decoupled, are shown in Figs. 15 and 16 for two different working conditions. The spectrum of the estimated zero-sequence carrier-signalvoltage vector is shown in Fig. 17. It is observed from Figs. 15 and 16 that the error in the estimated voltages has a similar magnitude for the case of no-load operation (Fig. 15) and loaded operation (Fig. 16). It is also observed that a certain error remains after intermodulation components are decoupled [Figs. 15(c) and 16(c)]. Because of the reduced magnitude of the intermodulation components for the test machine, these errors are of little importance. It is noted, however, that intermodulation components could have significant magnitudes for the case of machines with unskewed rotor slots. For that case, a better estimation of the intermodulation components could be obtained by adding flux-position estimation to the layer inputs and by modifying these inputs to be Rθr k − θe and Rθr k + θe at a price of a slight increase in the network complexity. Rotor position estimation results during steady-state operation for operating conditions different from those used to train the network are shown in Fig. 18. Position estimation errors are
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VII. C ONCLUSION Decoupling of saturation-induced saliencies and intermodulation saliencies using structured neural networks has been shown to be a viable method to improve saliency-trackingbased sensorless methods. Advantages with respect to using lookup tables include a simpler commissioning process and the ability to extend the decoupling network to as many harmonics as needed. Preliminary results shown in this paper demonstrate similar precision in decoupling saturation-induced saliencies to that obtained via previously published lookup-table-based methods. While the zero-sequence carrier-signal voltage has been used for the analysis and experiments presented in this paper, the method is easily extendable to practically all saliency-trackingbased sensorless methods. ACKNOWLEDGMENT The authors would like to thank the support and motivation provided by the University of Oviedo, Spain, and the Wisconsin Electric Machines and Power Electronics Consortium (WEMPEC) of the University of Wisconsin, Madison. R EFERENCES Fig. 18. Estimated rotor position and estimation error in mechanical degrees for two different working conditions. (a) Rated-flux, no load, and with ωe = ωr = 4 Hz. (b) Rated-flux, 66% rated load, and with ωe = 4 Hz and ωr = 2 Hz.
Fig. 19. Estimated rotor speed at rated-flux and 66% of rated-load.
Fig. 20. Sensorless position control when a position step from 0◦ to −360◦ is commanded. The machine was operated at rated flux and 66% of rated load.
in the same range than those reported in [4] and [11]. Rotor velocity estimation during steady-state operation is shown in Fig. 19. Sensorless position control when a step is commanded is shown in Fig. 20. A carrier-signal voltage of frequency fc = 2500 Hz and magnitude Vc = 20 V (peak) was used in all the experiments. Stable operation is observed in all the cases.
[1] P. L. Jansen and R. D. Lorenz, “Transducerless position and velocity estimation in induction and salient AC machines,” IEEE Trans. Ind. Appl., vol. 31, no. 2, pp. 240–247, Mar./Apr. 1995. [2] J. Cilia, G. M. Asher, and K. J. Bradley, “Sensorless position detection for vector controlled induction motor drives using an asymmetric outersection cage,” IEEE Trans. Ind. Appl., vol. 33, no. 5, pp. 1162–1169, Sep./Oct. 1997. [3] F. Briz, M. W. Degner, P. García, and R. D. Lorenz, “Comparison of saliency-based sensorless control techniques for AC machines,” IEEE Trans. Ind. Appl., vol. 40, no. 4, pp. 1107–1115, Jul./Aug. 2004. [4] F. Briz, M. W. Degner, P. García, and J. M. Guerrero, “Rotor position estimation of AC. Machines using the zero sequence carrier signal voltage,” IEEE Trans. Ind. Appl., vol. 41, no. 6, pp. 1637–1646, Nov./Dec. 2005. [5] A. Consoli, G. Scarcella, and A. Testa, “A new zero-frequency fluxposition detection approach for direct-field-oriented-control drives,” IEEE Trans. Ind. Appl., vol. 36, no. 3, pp. 797–804, May/Jun. 2000. [6] J. Holtz and H. Pan, “Elimination of saturation effects in sensorless position-controlled induction motors,” IEEE Trans. Ind. Appl., vol. 40, no. 2, pp. 623–631, Mar./Apr. 2004. [7] J. Juliet and J. Holtz, “Sensorless acquisition of the rotor position angle for induction motors with arbitrary stator windings,” IEEE Trans. Ind. Appl., vol. 41, no. 6, pp. 1675–1682, Nov./Dec. 2005. [8] N. Teske, G. M. Asher, M. Sumner, and K. J. Bradley, “Suppression of saturation saliency effects for the sensorless position control of induction motor drives under loaded conditions,” IEEE Trans. Ind. Electron., vol. 47, no. 5, pp. 1142–1150, Oct. 2000. [9] Y. Kim, S. Sul, and M. Park, “Speed sensorless vector control of induction motor using extended Kalman filter,” IEEE Trans. Ind. Appl., vol. 30, no. 5, pp. 1225–1233, Sep./Oct. 1994. [10] J. Ha and S. Sul, “Sensorless field-orientation control of an induction machine by high-frequency signal injection,” IEEE Trans. Ind. Appl., vol. 35, no. 1, pp. 45–51, Jan./Feb. 1999. [11] T. M. Wolbank, J. L. Machl, and T. Jäger, “Combination of signal injection and neural networks for sensorless control of inverter fed machines,” in Proc. IEEE PESC, Aachen, Germany, 2004, vol. 3, pp. 2300–2305. [12] M. W. Degner and R. D. Lorenz, “Position estimation in induction machines utilizing rotor bar slot harmonics and carrier frequency signal injection,” IEEE Trans. Ind. Appl., vol. 36, no. 3, pp. 736–742, May/Jun. 2000. [13] D. R. Seidl, “Motion and motor control using structured neural networks,” Ph.D. dissertation, Univ. Wisconsin-Madison, Madison, WI, 1996. [14] M. Dölen, “Modelling and estimation by structured neural networks for CNC machine tools,” Ph.D. dissertation, Univ. Wisconsin, Madison, WI, 2000.
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[15] D. R. Seidl, S. Lam, J. A. Putman, and R. D. Lorenz, “Neural network compensation of gear backlash hysteresis in position-controlled mechanisms,” IEEE Trans. Ind. Appl., vol. 31, no. 6, pp. 1475–1483, Nov./Dec. 1995. [16] D. R. Seidl, T. L. Reineking, and R. D. Lorenz, “Use of neural networks to identify and compensate for friction in precision, position controlled mechanisms,” in Proc. IEEE IAS Annu. Meeting, Houston, TX, 1992, vol. 2, pp. 1937–1944. [17] M. Corley and R. D. Lorenz, “Rotor position and velocity estimation for a permanent magnet synchronous machine at standstill and high speeds,” IEEE Trans. Ind. Appl., vol. 34, no. 4, pp. 784–789, Jul. 1998. [18] H. Kim and R. D. Lorenz, “Carrier signal injection based sensorless control methods for IPM synchronous machine drives,” in Proc. IEEE IAS Annu. Meeting, Seattle, WA, Oct. 2004, pp. 977–984. [19] M. Schrödl, Sensorless Control of AC Machines. Düsseldorf, Germany: VDI-Verlag, 1992. [20] J.-I. Ha, K. Ide, T. Sawa, and S.-K. Sul, “Sensorless rotor position estimation of an interior permanent-magnet motor from initial states,” IEEE Trans. Ind. Appl., vol. 39, no. 3, pp. 761–767, May/Jun. 2003. [21] H. Kim, M. C. Harke, and R. D. Lorenz, “Sensorless control of interior permanent-magnet machine drives with zero-phase lag position estimation,” IEEE Trans. Ind. Appl., vol. 39, no. 6, pp. 1726–1733, Nov./Dec. 2003. [22] S. Øverbø, “Sensorless control of permanent magnet synchronous machines,” Ph.D. dissertation, Dept. Electr. Power Eng., Norwegian Univ. Sci. Technol. (NTNU), Trondheim, Norway, Dec. 2004.
Pablo García (S’02) was born in Spain in 1975. He received the M.S. and Ph.D. degrees in electrical engineering and control from the University of Oviedo, Gijón, Spain, in 2001 and 2006, respectively. For the period 2001–2006, he has been awarded a fellowship of the Personnel Research Training Program funded by the Spanish Ministry of Science and Technology. He was a Visitor Scholar at the University of Wisconsin–Madison Wisconsin Electric Machines and Power Electronics Consortium (WEMPEC), in 2004. He is currently with the Department of Elecronics, Computer, and Systems Engineering, University of Oviedo. His research interests include sensorless control and diagnosis of induction motors, neural networks, and digital signal processing.
Fernando Briz (A’96–M’99–SM’06) received the M.S. and Ph.D. degrees in electrical engineering and control from the University of Oviedo, Gijón, Spain, in 1990 and 1996, respectively. From June 1996 to March 1997, he was a Visiting Researcher at the University of Wisconsin, Madison. He is currently an Associate Professor with the Department of Electrical, Computer, and Systems Engineering, University of Oviedo. His topics of interest include control systems, ac drives control, sensorless control, diagnostics, and digital-signal processing. Dr. Briz is the recipient of the 2005 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS Third Place Prize Paper Award and of two IEEE Industry Applications Society Conference prize paper awards in 1997 and 2004.
Dejan Raca (S’97) received the Dipl.Eng. degree in electrical engineering from the University of Novi Sad, Novi Sad, Serbia, in 1999. He is currently working toward the Ph.D. degree in electrical engineering at the University of Wisconsin, Madison. In 2006, he joined Magnetek Inc., Menomonee Falls, WI, where he is currently a Principal Engineer for control of electric machines and power electronics. He had previously been a Research and Teaching Assistant at the University of Wisconsin, Madison, in 2001–2006 and at the University of Banja Luka, Bosnia and Herzegovina, in 2000–2001. His current research interests include control of electric machines with a focus on sensorless control of permanentmagnet synchronous machines.
Robert D. Lorenz (S’83–M’84–SM’91–F’98) received the B.S., M.S., and Ph.D. degrees from the University of Wisconsin, Madison, and the M.B.A. degree from the University of Rochester, Rochester, NY. In 1969–1970, he did his Master thesis research in adaptive control of machine tools at the Technical University of Aachen, Aachen, Germany. From 1972 to 1982, he was a member of the research staff at the Gleason Works, Rochester, NY, working principally on high-performance drives and ultrahigh-precision synchronized motion control. Since 1984, he has been a member of the faculty of the University of Wisconsin, Madison, where he is the Mead Witter Foundation Consolidated Papers Professor of controls engineering in both the Department of Mechanical Engineering and the Department of Electrical and Computer Engineering. He was a Visiting Research Professor in the Electrical Drives Group of the Catholic University of Leuven, Leuven, Belgium, in the summer of 1989, and in the Power Electronics and Electrical Drives Institute of the Technical University of Aachen, Germany, in the summers of 1987, 1991, 1995, 1997, and 1999, respectively. He was the SEW Eurodrive Guest Professor, from September 1, 2000 to July 7, 2001. He is the Codirector of the Wisconsin Electric Machines and Power Electronics Consortium, which celebrated its 20th anniversary in 2001. It is the largest industrial research consortium on motor drives and power electronics in the world. His current research interests include sensorless electromagnetic motor/actuator technologies, real-time signal processing and estimation techniques, precision multiaxis motion control, and ac/dc drive and high-precision machine control technologies. He has authored more than 180 published technical papers and is the holder of 23 patents with three more pending. Dr. Lorenz is the IEEE Division II Director for 2005/2006, was the IEEE Industry Applications Society (IAS) President for 2001, a Distinguished Lecturer of the IEEE IAS for 2000/2001, past Chair of the IAS Awards Department, past Chairman of the IAS Industrial Drives Committee, and a member of the IAS Industrial Drives Committee, Electrical Machines Committee, Industrial Power Converter Committee, and Industrial Automation and Control Committee. He is an immediate past Chair of the Periodical Committee and past Chair of the Periodicals Review Committee for the IEEE Technical Activities Board. He is a member of the IEEE Sensor Council AdCom. He is the recipient of the 2003 IEEE IAS Outstanding Achievement Award, which honors his outstanding contributions and technological developments in the application of electricity to industry. He has won 21 IEEE prize paper awards. He is also a member of the American Society of Mechanical Engineers, Instrument Society of America, and The International Society for Optical Engineers. He is a Registered Professional Engineer in the States of New York and Wisconsin.
