A speed sensor fault-tolerant control of the CPPM machine for electric vehicle.
Permanent magnet synchronous machine (PMSM) based propulsion system is wildly used in electric vehicles (EVs) due to its high torque capability and power density . However, flux-weakening in PMSM is achieved by armature reaction to demagnetize the magnets. This approach results in significant power losses and may lead to irreversible demagnetization of permanent magnets .
The hybrid excitation synchronous machine (HESM) is proposed to avoid the above-mentioned problems -. The consequent-pole permanent-magnet (cPPM) machine is a special type of HESM that combines the fixed excitation generated by the permanent magnet with the variable flux provided by an excitation winding located in the stator. Adjusting the direction and magnitude of the excitation current can change the combined flux easily.
In the automotive context, the reliability and the continuous operation capability are important issues. The current, voltage, and speed sensors are required to work properly during the operation of the propulsion control. In the EV case, the resolver is extensive chosen due to its superiority in wide temperature range and high humidity and other harsh environment conditions. Nevertheless, the speed sensor is less reliable than the electrical sensors due to the mechanical coupling. The fault conditions such as intermittent connection or complete outage may lead to danger of the drive system immediately, if no proper actions are taken. The resolver fault detection can be accomplished by the resolver-to-digital converter (RDC) with a proper configuration. Therefore, the speed sensor reconfiguration scheme must be investigated to obtain a fault-tolerant operation in EVs. Extensive research has been carried out -. AFTC of induction motor with maximum-likelihood voting is introduced in . The virtual speed sensors implemented by adaptive observer and extended Kalman filter work with the encoder simultaneously. Reference  proposed a position estimation method based on an unknown input observer without voltage knowledge. Reference  presents a FTC with automatic reconfiguration scheme. Indirect vector controller, sensorless vector controller, sensorless scalar controller and open-loop Volt/Hertz controller are chosen by a fault detector. Reference  studies the sensor fault detection and isolation method in interior-PMSM based on the extended Kalman filter, in which all the sensor faults are detected and isolated. However, the implementation of the extended Kalman filter is difficult and the performance will be deteriorated at very low speed due to parameters variations .
In this context, a FTC strategy for a CPPM machine in EV propulsion is proposed in case of speed sensor failure. The speed sensor FTC strategy is implemented combining the HF voltage injection method with the extended EMF method. The experimental results on a 25 kW CPPM machine verify the effectiveness of the proposed speed sensor FTC strategy.
II. MATHEMATICAL MODEL OF THE CPPM MACHINE
A. Description of the CPPM Machine
The basic construction of a CPPM machine is shown in Fig. 1. The armature core is divided into two parts with an excitation winding in the center. The rotor is divided into two also.
The permanent magnets provide a fixed air-gap flux. When the DC current is injected into the excitation winding, another flux is generated from one iron pole to the next one. These two parts establish the main flux of the CPPM machine.
B. Fundamental Model of the CPPM Machine
In the actual rotor reference, the flux linkage equations of the CPPM machine can be described as :
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (1)
where superscripts 'r' represents the variable in actual rotor reference frame. [[psi].sup.r.sub.d] and [[psi].sup.r.sub.q] are the d-axis and q-axis flux respectively. [[psi].sub.f] is the excitation flux. [L.sub.d] and [L.sub.q] are the d-axis and q-axis inductance respectively. [L.sub.f] is the excitation inductance. [i.sup.r.sub.d] and [i.sup.r.sub.q] are the d-axis and q-axis current respectively. [i.sub.f] is the excitation current. [M.sub.sf] is the inductance between d-axis and excitation windings. [[psi].sub.pm] is the permanent magnet flux.
Then, the voltage components are expressed as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (2)
where [u.sup.r.sub.d] and [u.sup.r.sub.q] are the d-axis and q-axis voltage respectively. [u.sub.f] is the excitation voltage. [R.sub.s] and [R.sub.f] are the stator and excitation resistance respectively. [[omega].sub.r] is the electric angular velocity. [rho] is the differential operator.
The torque is expressed as
[T.sub.e] = 1.5[N.sub.p][([[psi].sub.pm] + [M.sub.sf][i.sub.f])[i.sup.r.sub.q] + ([L.sub.d] - [L.sub.q])[i.sup.r.sub.d][i.sup.r.sub.q], (3)
where [T.sub.e] is the electromagnetic torque. [N.sub.p] is the number of pole pairs.
III. SPEED SENSOR FAULT-TOLERANT CONTROL
A momentary lack of rotor position information may lead to overcurrent due to decoupling failure . In this situation, the rotor position must be reconstructed by a proper rotor position estimation method. A HF voltage injection method is applied at low speed region to avoid the poor performance caused by the low magnitude of the back-EMF. Furthermore, an extended EMF method is performed at high speed region to achieve a speed sensor fault-tolerant operation in the entire speed region.
A. HF Voltage Injection Method
At low speed region, the frequency of the injected voltage is much higher than the rotor electric angular frequency. The HF resistance terms, the dq-axis cross coupling terms and back-EMF terms can be neglected . Thus, the simplified HF voltage equations are given as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (4)
where the subscript 'h' represents HF component of the variables.
Because the HF voltage is not injected into the excitation winding, the cross coupling component between the d-axis and excitation winding in (4) can be decoupled as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (5)
Due to the special structure of the CPPM machine, the self-inductance of the excitation winding [L.sub.f] is much larger than [M.sub.sf]. Thus, the cross coupling component can be neglected. Therefore, (5) can be simplified as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (6)
where j is the operator (1[angle][pi]/2). [z.sub.dh] and [z.sub.qh] are the d-axis and q-axis impedance respectively.
The rotor position error is defined as
[??] [equivalent to] [theta]-[??], (7)
where [theta] is the rotor position. Superscripts '^' represent the variable in estimated rotor reference frame. Superscripts '~' represent the error of variable between actual rotor reference and estimation rotor reference.
Transforming (6) into the estimation rotor reference frame with [??], the resultant HF current can be expressed as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (8)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (9)
Equation (8) shows that the HF currents contain the rotor position estimation error when the HF voltage is injected. Because the HF components of the dq-axis are completely decoupled, the injection of HF voltage into d-axis will not generate the torque ripples. Therefore, the HF current response can be obtained as (11) when the HF voltage as (10) are injected into
[u.sup.[??].sub.dh] = [u.sub.inj]cos[[omega].sub.c]t, (10)
where [[omega].sub.c] is the carrier signal frequency, [u.sub.inj] is the carrier signal magnitude:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (11)
A signal processing shown in Fig. 2 is applied to obtain [??] from (11). A second-order Butterworth band-pass filter (BPF) is applied to extract the HF current. Because the HF voltage injection method is only adopted at low speed region, the pass band of the BPF is set to [900 Hz, 1100 Hz] with a 1 kHz injection voltage. The BPF can be described by following differential equation
[H.sub.BPF](z) = 0.0592 1 - [z.sup.-2]/1-1.5252[z.sup.-1] + 0.8816[z.sup.-2]. (12)
Then, a multifunction with sin([[omega].sub.c]t) and a first-order low-pass filter (LPF) is used to extract the fundamental signal containing [??] from [i.sup.[??].sub.qh]. The cut-off frequency is set to 500 Hz considering the delay and stop band attenuation. The LPF can be described by following differential equation
[H.sub.LPF](z) = 0.1367 1 + [z.sup.-1]/1-0.7266[z.sup.-1]. (13)
If is sufficiently small, the resultant signal as (14) can be used to track the rotor position and speed by the phase locked loop (PLL) observer
f([??]) = [u.sub.inj]([L.sub.dh] - [L.sub.qh])/4[[omega].sub.c][L.sub.dh][L.sub.qh]sin2[??] [approximately equal to] K[??]. (14)
Equation (14) shows that the position error can be obtained if the significantly difference between [L.sub.dh] and [L.sub.qh] is existed. In order to verify this magnetic saliency of the CPPM machine, a FEA approach and measurement of HF impedances of the CPPM machine are carried out.
Fig. 3 presents the measurement results of HF impedance characteristics of the CPPM machine according to the method described in . The HF voltage is injected from 0 degree (d-axis) to 90 degree (q-axis) and to 180 degree (negative d-axis). The results indicate that the d-axis HF impedance is significantly smaller than the q-axis one under various excitation currents. When the excitation current increases, a larger decrement of q-axis HF impedance is obtained.
The flux distributions shown in Fig. 4 are obtained to clarify the magnetic saliency of the CPPM machine. The windings and the flux generated by them are orthogonal as shown in Fig. 4(a). The semi-closed slot is used in the stator of the CPPM so that the HF flux passes through the air gap and the rotor. The flux of the d-axis stator windings passes through the bridges, which are the highly saturated parts. The flux of the q-axis stator windings passes through the iron pole or the iron core area above V-shape permanent magnet pole. These paths are relatively less saturated than the bridge paths; thus, the q-axis HF impedance is larger than d-axis one. As shown in Fig. 4(b) and Fig. 4(c), the flux of the iron pole can be enhanced or weakened by the positive or negative excitation current, respectively. The FEA results indicate that the magnetic flux density of the iron poles increases with the increasing of the excitation current. Thus, the decrement of q-axis HF impedance is more than the d-axis one. Exorbitant positive excitation current leads saturation on both d- and q-axis, but the significant impedance difference is still obtained. The FEA analysis and measurement results confirm the magnetic saliency of the CPPM machine.
B. Extended EMF Method
When the machine operates in the flux-weakening region, the HF voltage injection method is ineffectiveness, because the voltage has been fully utilized. Therefore, the position estimation for the CPPM machine at high speed region based on the extended EMF is proposed.
The stator voltage in (2) can be rewritten as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (15)
[E.sub.ex] = [[omega].sub.r][[L.sub.d] - [L.sub.q])[i.sup.r.sub.d] + [M.sub.sf][i.sub.f] + [[psi].sub.pm]-([L.sub.d] -[L.sub.q])([rho][i.sup.r.sub.q]). (16)
Transforming (15) and (16) into estimated rotor reference frame, the following model is obtained:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (17)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (18)
Due to the special structure of the CPPM machine, the self-inductance of the excitation winding [L.sub.f] is very large. This means the derivative of excitation current is relatively small compared with the extended EMF and can be neglected. The second term of (18) can be ignored when the speed estimation error is sufficiently small. Thus, (18) can be expressed as
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (19)
As shown in Fig. 5, an extended EMF observer is designed to estimate [e.sup.[??].sub.d] and [e.sup.[??].sub.q]. A LPF is applied to suppress the disturbance caused by the derivative term. The [lambda] is the time constant of the filter.
The observer results are used to generate the rotor position error signal as follows
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (20)
Similarly, a PLL observer is used to track the rotor position and speed.
C. Combination of HF Voltage Injection and Extended EMF Methods
To perform a smooth transition between two methods, a hybrid observer should be designed. The linear combination of the two rotor position estimated results would lead to instability when the two independent PLL observers are operating simultaneously. Thus, a linear combination of the error signals generated by HF voltage injection method and extended EMF method can be given as
[[??].sub.com] = [alpha][[??].sub.hf] + (1-[alpha])[[??].sub.emf], (21)
where [[??].sub.hf] and [[??].sub.emf] are the position error generated by the HF voltage injection method and extended -EMF method respectively. [[??].sub.com] is the combined position error signal. a is given as
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (22)
where [[omega].sub.up] and [[omega].sub.low] are the up and low speed limitation.
When the position error signals are combined with this method, proper rotor position estimation can be performed. When the estimated rotor speed becomes a little higher than [[omega].sub.up], the HF voltage should be cancelled to avoid disturbances.
D. Switching Method for the Speed Sensor FTC
The actual rotor position and speed are obtained from the resolver for a proper operating. When the speed sensor fault signal generated by RDC is detected, the rotor position and speed should be obtained from the speed sensor FTC instead. The PLL observer is implemented by a PI controller and an integrator. An incorrect initial state of the PI controller may lead to position estimation failure. Therefore, the PI controller should be controlled by the speed sensor fault signal. When the system is working properly, the integral term is replaced by the actual rotor speed, and the proportional term is ignored. Thus, the output of the PI controller follows the actual rotor speed. When the speed sensor fault signal is detected, the combined position error [[??].sub.com] is inputted into the PI controller and an integrator to track the rotor speed and position. Thus, the initial state of the PI controller can be obtained properly when the failure of speed sensor occurs.
IV. EXPERIMENTAL RESULTS
To verify the effectiveness of the proposed speed sensor FTC strategy, the control functions were implemented according to Fig. 7 in a control board, which was constructed by the TMS320F2808 digital signal processor. Tamagawa TS2225 resolver and Analog Device AD2S1210 RDC were adopted to obtain the rotor position and speed. The experimental test was performed on a 25-kW CPPM machine, employing a dynamometer as the mechanical load. The parameters of the CPPM are listed in Table I.
The experimental setup for the drive system is shown in Fig. 6.
In the experiment, the input voltage of the driver was limited to 110 V; thus, the rated speed was converted to 1500r/min. The current loop and rotor position estimation were implemented with a 100-qs sampling time, and the speed loop was set to 300-[micro]s. The injection condition was selected as 35 V-1000 Hz. [[omega].sub.up] and [[omega].sub.low] were set to 600 r/min and 400 r/min, respectively.
A. Speed Sensor FTC at Low-speed Region
Fig. 8 presents the experimental results for the HF voltage injection method at 100 r/min with 50 % rated load. The results show that the proper rotor position is estimated, and a stable operation of the CPPM machine can be obtained without using the speed sensor.
A series of tests under different speed and load conditions is carried out to evaluate the dynamic performance in case of speed sensor failure and reconstruction. Fig. 9 presents the dynamic response when the speed sensor failure occurs at 100 r/min with 75 % rated load. At 0.43 s, the speed sensor failure is detected. The HF voltage is injected immediately. The rotor position is reconstructed quickly after a short transient process. The position error increases based on the amount of load . However, the stability of the system is guaranteed. The results confirm the effectiveness of the speed sensor FTC strategy at low-speed region.
Fig. 10 presents the dynamic response of the CPPM machine when speed sensor failure occurs at 2500 r/min with 30 % rated load. The extended EMF method is used to track the rotor position when the speed sensor failure occurs. The fixed parameters of the CPPM machine applied in the FTC strategy introduce some position error. When the position error is greater than zero, a negative d-axis current is obtained in actual rotor reference frame. The objective flux, which should be weakened in the flux-weakening region, is partially weakened by the negative d-axis current. Thus, a higher excitation current response is obtained when the speed sensor failure occurs.
C. Speed Sensor FTC at Medium-speed Region
Fig. 11 presents the dynamic response of the CPPM machine when speed sensor failure occurs at 500 r/min with 75 % rated load. The error signals from HF voltage injection method and extended EMF method are combined in this speed region. The position error is reduced due to the combination of two position estimation method.
Fig. 12 presents the performance of the CPPM machine operating in speed sensor fault condition. A slope speed reference of 100 r/min, 2000 r/min, and 100 r/min, is applied with 50 % rated load respectively. The speed response indicates a smooth transition between the two methods. The experimental results confirm that the reliability and continuous operation capability of the drive system is enhanced in the entire speed region when the speed sensor FTC is applied.
This paper proposes a speed sensor FTC strategy for EVs using a CPPM machine-based drive system. The HF voltage injection method and the extended-EMF method are combined to track the rotor position when the speed sensor failure is detected. The magnetic saliency of the CPPM machine is analysed by the FEA method and confirmed by measurement of a CPPM machine. The proposed speed sensor FTC strategy has been confirmed by the experimental results. High dynamics and a smooth transition could be guarantee when the speed sensor failure occurs.
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Zheran Li (1), Yesong Li (1), Xinhua Li (2)
(1) Department of Control Science and Engineering, Automation Institute, Huazhong University of Science and Technology, Hubei, China
(2) School of Electrical & Electronic Engineering, Hubei University of Technology, Hubei, China,
Manuscript received September 3, 2013; accepted December 13, 2013.
This research was funded by a grant (No. 2012ZX04001-012) from The National Major Science and Technology Projects of China.
TABLE I. THE CPPM MACHINE PARAMETERS. Parameters Value Unit Rated voltage 220 V Rated power 25 kW Rated speed 3000 r/min Rated excitation current 10 A Number of pole pairs 4 -- Stator resistance 0.0163 n Excitation winding resistance 1.3702 n d-axis inductance 0.24 mH q-axis inductance 0.35 mH Mutual inductance between d-axis and 1.5 mH excitation windings Self-inductance of excitation winding 39.5 mH Flux linkage established by magnets 0.058 Wb
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|Author:||Li, Zheran; Li, Yesong; Li, Xinhua|
|Publication:||Elektronika ir Elektrotechnika|
|Date:||Jul 1, 2014|
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