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Estimation of temperature in turbo-molecular pump based on motor resistance online identification
Vacuum 169 (2019) 108935
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Estimation of temperature in turbo-molecular pump based on motor resistance online identification
T
Bangcheng Hana,d, Kai Xionga,c, Kun Maoa,b,c,∗ a
Beijing Engineering Research Center of High-speed Magnetically Suspended Motor Technology and Application, Beihang University, Beijing, China Research Institute of Frontier Science, Beihang University, Beijing, China c Ningbo Innovation Research Institute, Beihang University, Ningbo, China d Hangzhou Innovation Institute, Beihang University, Hangzhou, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Vacuum Turbo-molecular pump (TMP) Temperature estimation Discount factor recursive least squares (DFRLS) Resistance online identification
The temperature of the turbo-molecular pump (TMP) system has to be monitored in real-time for long stable operation in a high vacuum environment. Since the high-speed motor is the major heat source of the TMP system, the thermal sensors such as Pt100 are widely used to measure the temperature via being embedded in the motor stators. However, these thermal sensors require extra wires and signal conditioning circuits, which increase the complexity of installation. In order to solve this problem, a real-time online estimation method for the temperature of the TMP driven motor is proposed in this paper. First of all, the resistance identification model of the high-speed motor used in TMP system is built. After that, an improved recursive least squares (RLS) algorithm, which introduces a discount factor to overcome the problem of data saturation and weak dynamic tracking, is used to identify the resistance of the motor stator windings. Then, the temperature of the TMP could be estimated indirectly based on the linear relationship between the motor stator resistance and the temperature. At last, the proposed method is tested in a self-developed magnetically levitated turbo-molecular pump (MLTMP) system, and the experimental results verify its validity and reliability.
1. Introduction Owing to the advantages of short time starting, high compression ratio and vacuum, turbo-molecular pump (TMP) has been widely used for high vacuum applications such as integrated circuits, solar coating, and physical vapor deposition [1,2]. It consists of high-speed motor, rotor blade, stator blade, etc. With the requirement of long-time operation in the high vacuum environment, the copper loss and iron core loss generated in the motor would lead to the temperature rise of the TMP system [3,4]. Therefore, it is crucial to monitor the temperature of the TMP system in real-time for long-time stable operation. Otherwise, the overheating problem would cause performance degradation of the motor permanent magnet (PM) and deformation of the rotor retaining sleeve, which may break rotor dynamic balance [5] and increase system loss. Temperature measurement methods could be classified into two categories. Thermal sensors such as thermal resistor (e.g., Pt100), thermocouple, infrared thermometer, and fiber Bragg grating [6–9] are commonly used for motor temperature measurement. In Ref. [10], the
stator temperature is measured by a Pt100 in the permanent magnet synchronous motor (PMSM). Similarly, the Pt100 is installed in the stator windings for temperature monitoring in Ref. [11]. In Ref. [12], the Pt100 is attached to the exterior housing of TMP to measure the approximate temperature of stator blades. The temperature could be measured easily by using single Pt100, but it can only be measured at a fixed position of stator windings. In order to measure the complete temperature field, five Pt100 thermal resistors have been embedded in the different positions of the TMP stator [13]. Nevertheless, the use of too many wires would increase the complexity and difficulty of installation. In conclusion, extra wires and signal conditioning circuits are required in traditional temperature measurement method, which may cause the system high cost, difficult installation and low reliability. Therefore, the sensorless temperature measurement methods have also been developed. Temperature measurement methods via sensorless technique reported in the literature can be divided into numerical method and resistance-identification-based temperature estimation method [14,15]. In Ref. [16], thermal analysis of the TMP is carried out by finite element
∗ Corresponding author. Research Institute of Frontier Science, BeiHang University, Beijing Engineering Research Center of High-speed Magnetically Suspended Motor Technology and Application, Beijing City, Haidian District, Xueyuan Road NO. 37, China. E-mail address: [email protected] (K. Mao).
https://doi.org/10.1016/j.vacuum.2019.108935 Received 31 May 2019; Received in revised form 5 September 2019; Accepted 7 September 2019 Available online 09 September 2019 0042-207X/ © 2019 Elsevier Ltd. All rights reserved.
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mounting spot. In order to measure the complete temperature field, a number of Pt100 thermal resistors are required, which in turn contributes to a great deal of wires and reduces the system reliability. In spite of this, single Pt100 is mostly used in TMP system for temperature monitoring because of its simplicity.
analysis (FEA) tools. Normally, the numerical method relies on thermal models and FEA tools. Besides, the TMP system cannot respond to temperature rise in real-time due to the thermal parameter variation. Thus, parameter-identification-based method is commonly designed to estimate the average temperature of the high-speed motor in real-time. N. Z. Popov and his partners calculate the temperature based on the input impedance of PMSM at elevated frequencies [17]. Additionally, for real-time thermal management, D. W. Simon describes two techniques applied to measure the windings' resistance through angle and magnitude current injection [18]. Furthermore, the recursive least squares (RLS) algorithm has been proposed in Ref. [19] to identify the stator windings' resistance, which could be used for stator temperature online estimation. Nonetheless, the problem of data saturation and low stability would exist with the RLS algorithm. Based on the above analysis, the parameter-identification-based temperature estimation method could be used to monitor the temperature of the high-speed motor, while it has not been applied in the TMP system yet. This paper is organized as followings. Firstly, Section Ⅱ introduces some limitations in traditional temperature measurement method of the TMP. After that, a novel temperature estimation method for the TMP is proposed in Section Ⅲ, which is based on resistance online identification using discount factor recursive least squares (DFRLS). Then, the proposed method is tested in a self-developed magnetically levitated turbo-molecular pump (MLTMP) system, and the experimental results are given in Section Ⅳ. Finally, Section Ⅴ concludes this paper.
3. Proposed temperature estimation method based on identification of resistance Considering the problems existing in the traditional temperature measurement method, it is necessary to study an online measurement method specifically for the TMP system. 3.1. Temperature equation of TMP system According to Refs. [20,21], the relationship between resistance of the motor stator copper coils and the temperature variation is approximately linear, which can be expressed as Eq. (2).
Rs = R 0 [1 + αCu (Ts − T0)]
where R0 and Rs are the windings' resistance at T0 and Ts, respectively, αCu is the coefficient of the copper. In the temperature range of −50°C150 °C, the copper resistance has stable chemical and physical properties, and αCu is assumed as 4.1 × 10−3 °C−1 [22]. Then, according to Eq. (2), the equation for temperature of motor stator windings can be written as Eq. (3).
2. Traditional temperature measurement method of TMP system
Ts = Pt100 thermal resistors are widely used in TMP temperature measurement system. Commonly, Pt100 thermal resistors are installed in the motor stator windings which are the highest temperature positions of TMP. The installation diagram of Pt100 is shown in Fig. 1. The resistance and the temperature of Pt100 can generally be expressed by the following approximate relationship as Eq. (1).
Rs = R 0 [1 + αPt (Ts − T0)]
(2)
1 ⎛ Rs − 1⎞ + T0 αCu ⎝ R 0 ⎠ ⎜
⎟
(3)
3.2. Resistance identification model of SPMSM The resistance identification model is established in surface permanent magnet synchronous motor (SPMSM). For simplicity, it is assumed that the stator core magnetic saturation and high-order harmonics can be ignored, the motor back electromotive force (BEMF) is sine wave, and the stator resistance is three-phase symmetrical, i.e. Then the dynamic voltage equation in synchronous rotating coordinates can be written as Eq. (4).
(1)
where T0 is the environment tempe rature, R0 and Rs represent the resistance of Pt100 at T0 and Ts, respectively, and αPt is the temperature coefficient of Pt100. The temperature measurement system of TMP system using Pt100 is shown in Fig. 2. Pt100 is connected to an external Wheatstone bridge circuit, which would generate a voltage difference signal when the TMP system temperature rises. A differential amplifier is used to amplify the voltage difference signal and its output would be transmitted to a data acquisition card (DAC). Meanwhile, the upper computer reads the data of DAC and the temperature of stator could be obtained. It can be observed that the traditional temperature measurement method using Pt100 provides only the local temperature at the sensor
⎧ dtd = − LSs id +
di
R
1 u LS d
+ ωr iq
⎨ diq
R − L s iq S
1 u LS q
− ωr id −
⎩ dt
=
+
1 ω ψ LS r f
(4)
where id、iq and ud、uq denote current and voltage of d, q-axis, respectively, Rs is motor stator windings' resistance, Ls is d, q-axis inductance, Ψf is the PM flux linkage, ωr is electricity angular velocity. When TMP runs for a long time at high-speed and steady-state, it could be assumed that ωr is a known parameter since the speed and load of TMP would not change. Hence, Eq. (4) can be modified to the steadystate voltage form as Eq. (5).
⎧ud = Rs i d − Ls ωr iq ⎨uq = Rs i q + LS ωr i d + ωr ψf ⎩
(5)
As can be seen from Eq. (5), the parameters of SPMSM can be obtained directly only based on q-axis steady-state voltage equation. For simple analysis, rewrite the q-axis steady-state voltage equation shown as Eq. (6).
uq = Rs i q + LS ωr i d + ωr ψf
(6)
According to Eq. (6), the q-axis steady-state voltage equation contains 3 unknown parameters, which require at least 3 linearly independent equations to solve. However, when the motor operates at maximum efficiency with id = 0, two linearly independent equations are sufficient to obtain the stator resistance. Fig. 3 is the single speed step response of SPMSM which could be
Fig. 1. Pt100 installation diagram. 2
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Fig. 2. Temperature measurement system of the Pt100.
divided into acceleration stage and steady stage. It can be found that when the motor reaches rated speed, the amplitude of q-axis current is much smaller than before because its load torque is small in high vacuum environment. When the rotor frequency is ramped up through ωr1 to ωr2, Ψf could be identified at the start-up of the TMP. After reaching a constant speed ωr2, Ψf could be regarded as a constant since the PM flux linkage of SPMSM would not change much in the steady stage.
⎧uq1 = Rs i qm + ωr1 ψf ⎨uq2 = Rs i q0 + ωr 2 ψf ⎩
(7)
According to the data in Fig. 3, two linearly independent equations shown as Eq. (7) could be built. Then, the equation-based algorithm identification model of the stator windings resistance can be expressed as Eq. (8).
Fig. 3. Single step of speed response.
Fig. 4. Block diagram of the control system. 3
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⎧ ψf = ⎨ Rs = ⎩
It can be observed that the identification result is determined by discount factor since the criterion function is obtained by summing a number of terms with discount factor. By minimizing the criterion function, the estimated parameter vector θˆ (k) would satisfy Eq. (17).
uq2 − Rs i q0 ωr 2 uq2 ωr1 − uq1 ωr 2 i q0 ωr1 − i qm ωr 2
(8)
Consequently, according to the identification model shown in Eq. (8) and the acquired data, the resistance of stator windings could be identified online. During the steady-state operation of TMP, the windings' temperature changes relatively slowly, which indicates that the change of stator resistance is also slow. Here, the time interval Δt between the resistance identification is 3 min. Fig. 4 is the block diagram of the control system. It can be observed that the data of the q-axis current and q-axis voltage are collected for calculating the stator windings resistance.
−1 θˆ (k ) = (HkT Γk Hk ) HkT Γk Yk
Define the covariance matrix P(k) as Eq. (18).
P (k ) = [λP −1 (k − 1) + Λ (k ) ϕ (k ) ϕT (k )]−1 1⎡ = λ ⎢I − ⎣
(10)
y (k ) = uq (k )
(11)
T θ (k ) = [ Rs ψf ]
(12)
⎧ θˆ (k ) = θˆ (k − 1) + K (k )[y (k ) − ϕT (k ) θˆ (k − 1)] ⎪ −1 λ (k ) K (k ) = P (k − 1) ϕ (k ) ⎡ Λ (k ) + ϕT (k ) P (k − 1) ϕ (k ) ⎤ ⎣ ⎦ ⎨ ⎪ P (k ) = 1 [I − K (k ) ϕT (k )] P (k − 1) λ (k ) ⎩
ε (k ) = y (k ) − ϕT (k ) θˆ (k − 1)
(14)
(15)
where k is the number of beats of the selected data, Γ(k,i), Λ(i), and λ denote discount factor, weighting factor, and forgetting factor, respectively. The discount factor contains forgetting factor and weighting factor. By introducing the discount factor, the criterion function is defined as Eq. (16).
⎧ 0 ε (k ) ≥ 10−2 y (k ) ⎪ 0.1 10−4 y (k ) ≤ ε (k ) < 10−2 y (k ) ⎨ 0.5 10−5 y (k ) ≤ ε (k ) < 10−4 y (k ) ⎪ −5 ⎩1 ε (k ) < 10 y (k )
k i=1
(20)
(21)
(22)
where ε(k) is the prediction deviation according to the current model, θˆ (k-1) is the parameter estimation at time of k-1. The prediction deviation is a scalar, representing a single step of information during the iteration. The selection of weighting factor is related to the prediction deviation. When the variation of deviation is small and stable, Λ(i) is set to a value with large confidence. However, when the variation of deviation is large due to measured data with large uncertainties, Λ(i) is set to a value with small confidence. Therefore, according to the variation of deviation, the value of Λ(i) is set into 4 segments, which includes untrusted data, low confidence data, high confidence data and fully trusted data. The value of Λ(i) can be expressed as Eq. (23).
(13)
Introducing the discount factor shown as Eq. (15).
∑ Γ (k, i)[y (k ) − ϕT (k ) θ]2
(19)
According to Eq. (19), in order to make the algorithm track timevarying parameters, the covariance matrix P(k) cannot be 0 when the time approaches infinite. Obviously, P(k) does not approach to 0 when the forgetting factor is introduced. Hence, in the process of data accumulation, the forgetting factor could reduce the influence of older data, which achieves the dynamic characteristics of identification model. For the identification model of PMSM, a small change in the forgetting factor may cause a significant change in the identification performance. Therefore, the selection of the forgetting factor is crucial. Usually, λ satisfies 0 < λ ≤ 1 and it should better be set close to 1 [23]. Here, λ is set to 0.9995. The weighting factor is multiplied directly to each term in the criterion function to reduce the weight of values with large uncertainties and achieve the stability characteristics of identification model. The prediction deviation is defined as Eq. (22).
Then, Eq. (9) could be written in the form of a matrix as shown in Eq. (14).
J (θ) =
− 1)
Then, according to Eq. (15), Eq. (17), Eq. (19) and Eq. (20), the DFRLS algorithm model [24–27] can be shown as Eq. (21).
The output matrix Yk, the information matrix Hk, and the noise matrix Vk are defined as shown in Eq. (13).
Γ (k , i) = Λ (i) λk − i
⎤
Define the gain matrix K(k) as Eq. (20).
(9)
ϕT (k ) = [iq (k ) ωr ]
P (k − 1) ϕ (k ) ϕT (k )
⎥ P (k λ + ϕT (k ) P (k − 1) ϕ (k ) Λ (k ) ⎦
K (k ) = Λ (k ) P (k ) ϕ (k )
where ϕT(k), θ(k), y(k) and e(k) denote the input vector, the parameter vector, the output data and the interference noise data, respectively. Moreover, ϕT(k) and θ(k) are 2-dimensional vector. On the basis of Eq. (6), ϕT (k ) , y(k) and θ(k) could be shown as Eq. (10), Eq. (11) and Eq. (12), respectively.
Yk = Hk θ + Vk
(18)
Based on Eq. (15) and matrix inversion lemma [23], Eq. (18) could be written as Eq. (19).
Comparing with the equation-based algorithm using the data of a certain state point, a better approach is to use an efficient iterative identification algorithm, which has more data to ensure the reliabity and accuracy of identification. Among the existing literature, the RLS algorithm is widly used for parameter identification in engeering because of its simplicity. However, serious data saturation problems will exist in RLS algorithm as the observed data grows, making the parameter identification value insensitive to new data and reducing the dynamic accuracy. Therefore, this paper proposes an improved RLS algorithm with discount factor for resistance identification. Considering that noise interference would exist in TMP systems inevitably in the process of operation, the DFRLS identification model based on Eq. (6) could be presented as follows.
T ⎡ ϕ (1) ⎤ ⎡ e (1) ⎤ ⎡ y (1) ⎤ ⎢ ϕT (2) ⎥ ⎢ ⎥ ⎢ y (2) ⎥ YK = ⎢ ,H = , V = e (2) ⋯ ⎥ K ⎢ ⋯ ⎥ K ⎢ ⋯ ⎥ ⎢ T ⎥ ⎢ e (k ) ⎥ ⎢ y (k ) ⎥ ⎣ ⎦ ⎦ ⎣ ⎣ ϕ (k ) ⎦
−1
k
⎤ ⎡ P (k ) = ⎢∑ Γ (k , i) ϕ (i) ϕT (i) ⎥ ⎣ i=1 ⎦
3.3. Resistance online identification method based on DFRLS algorithm
y (k ) = ϕT (k ) θ (k ) + e (k )
(17)
(16)
(23)
Besides, when Λ is taken as 1, the DFRLS algorithm equals to RLS 4
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Table 1 Experimental TMP parameters. TMP Parameters
Value
Inlet flange Number of pole pairs Volume flow rate N2 (L/s) Ultimete pressure (Pa) Rate speed (r/min) Flux Linkage (Wb) Phase resistance (Ω) Phase inductance (mH)
ISO400 1 4100 1 × 10−7 21000 0.0182 0.28 0.24
motor temperature, the TMP system operates continuously for 24 h and the identified resistance used to estimate temperature is recorded every 30 min. The TMP reaches the rated speed of 21000r/min after 8 min of acceleration. During this time, according to Eq. (7), the estimation of PM flux linkage of motor based on equation-based algorithm, RLS algorithm and DFRLS algorithm are 0.0177Wb, 0.0186Wb, 0.0180Wb, respectively. Here, the equation-based algorithm represents Eq. (8) using data only from a single measurement at time k. Fig. 9 shows the identification experiment results of stator resistance Rs based on different identification algorithms. When the motor stopped, the resistance of the winding at room temperature is defined as the static value. It can be observed that the estimated stator resistance is higher than the static value due to the temperature of the stator windings rise. Fig. 9 a) is the identification results of Rs within 24 h. From Fig. 9 a), during the 24 h, the curves of resistance identified by RLS algorithm and DFRLS algorithm converge to a stable value, while the curve based on equation-based algorithm shows no sign of convergence, because the input data are small compared to the inherent noise, resulting in the identified resistance values fluctuate a lot at different time. Besides, the curve of DFRLS algorithm has smaller fluctuation than the other two algorithms. Fig. 9 b) is the identification results of Rs starting at 11:00. When the identification process is close to the convergence state, the fluctuation level of resistance identification is defined as Eq. (24).
Fig. 5. Single step of speed response-data segments.
algorithm with the forgetting factor. Furthermore, when λ and Λ are taken as 1, the DFRLS algorithm equals to standard RLS algorithm. For the sake of iteration convenience, the data segments shown in Fig. 5 are used for DFRLS algorithm identification model. In Fig. 5, L denotes the length of the data segments. Fig. 6 is the diagram of temperature online estimation method based on DFRLS algorithm. The resistance of the stator windings is identified firstly. Then, the temperature could be estimated. 4. Experiments 4.1. Experiment platform setup To confirm the validity of the proposed method, tests are implemented on a self-developed MLTMP testing platform. Table 1 shows its main parameters. The system consists of a power source, a control circuit box, a backing pump, a Pt100 temperature meter and a TMP which is shown in Fig. 7. The Pt100 thermal sensors are also used to monitor the temperature in real-time. In order to minimize measurement error, three Pt100 thermal resistors are embedded in the TMP stator windings every 120 mechanical degrees as shown in Fig. 8. 4.2. Resistance identification result with different identification methods
δR = In order to estimate the temperature of TMP system, three resistance-identification-based temperature estimation methods are implemented on the testing TMP. As described in Section Ⅲ, the data segments at different time are taken out to identify the parameter of motor. The length of the data segment is 2000 and the time between two samples is 10 ms. Additionally, in order to accurately monitor the
R c max − R c × 100% Rc
(24)
where Rc denotes the convergence value of resistance, Rcmax denotes the maximum value of resistance when the identification process is close to the convergence state, and δR denotes the fluctuation level. The results in Fig. 9 show that the fluctuation level of resistance identification based on the RLS algorithm is 2%, while that of the
Fig. 6. Diagram of proposed temperature online estimation method. 5
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Fig. 7. Experimental platform.
range of −70 °C to +500 °C. The temperature coefficient of Pt100 is 0.003851 °C-1, and the tolerance class of Pt100 is F 0.15. Moreover, three Pt100 are exposed to the room temperature 27.2 °C to determine the T0 and R0. Then, in order to calculate the slopes α of Pt100, they are also exposed to 50 °C. Three Pt100 are labeled T1, T2 and T3, respectively, and the testing results of Pt100 are shown in Table 2. According to the testing results of three Pt100, the differences of offsets T0 and slopes α between three Pt100 are small, which is no more than 1%. In addition, when the current flows through the Wheatstone bridge circuit, the connecting wires and the Pt100 will cause additional temperature uncertainties. The uncertainty of the Wheatstone bridge circuit is designed to be no more than 0.2%. However, it can be found that the temperature values measured by three Pt100 are different. In order to minimize measurement error, three temperature values are averaged as shown in Fig. 10. The averaged temperature is used as a reference for testing to verify the feasibility of proposed identification method. Fig. 11 shows that the proposed algorithm could effectively estimate TMP's stator temperature, comparing with the traditional measurement method based on Pt100. Therefore, the resistance-identification-based temperature estimation method is feasible. It can be observed that the value of the TMP's stator temperature changes slowly within 24 h. The fluctuation level of temperature identification is defined as Eq. (25).
Fig. 8. The motor stator of tested TMP with three Pt100 thermal resistors.
DFRLS algorithm is 0.7%. Apparently, the DFRLS algorithm has less fluctuation and better stability. In addition, the convergence time of the RLS algorithm is 0.27s, while that of the DFRLS algorithm is 0.16s, which is nearly 33.3% shorter. It shows that with the forgetting factor, the influence of older data in the fitting algorithm is reduced, making the identification algorithm is sensitive to the new data. Therefore, the DFRLS algorithm has a faster convergence rate and better dynamic characteristics during the convergence process. Combine with the above analysis, discount factor plays a significant role in convergence speed and stability performance for identification system.
δT =
ΔT × 100% TA
(25)
where TA denotes the average temperature of Pt100, ΔT denotes the maximum variation between identification temperature and the average temperature, and δT denotes the fluctuation level. Compared with the average temperature, the estimated temperature fluctuations based on equation-based algorithm are relatively large. Its maximum error reaches 27.5%. Obviously, this method cannot be applied directly. However, the maximum error of the RLS algorithm reduces to 6.2%, which improves the accuracy of temperature estimation. After adopting the DFRLS algorithm with discount factor, the accuracy of the temperature estimation is further improved compared with the RLS, and its maximum error decreases to 2.3%. Therefore, it is evidently demonstrated that the proposed DFRLS algorithm can achieve a
4.3. Temperature estimation results with different estimation methods In order to compare the temperature of the stator windings with different estimation methods, the temperature is recorded every 30 min. The Pt100 used here is M222 A platinum resistance temperature detector produced by Heraeus. It has an operating temperature 6
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Fig. 9. Identification experiment results of stator resistance Rs.
faster convergence capability and less fluctuation, which is in accordance with the theoretical analysis.
Table 2 The testing results of Pt100. Sensors number
Offsets T0 (°C)
R0 (Ω)
Slopes α
T1 T2 T3
27.4 27.2 27.1
109.94 109.67 109.54
0.003848 0.003850 0.003849
5. Conclusion In this paper, the TMP system temperature is investigated with different measurement methods. The following conclusions are obtained through analysis and experiment. 7
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Fig. 10. Average temperature curves of TMP system. According to identified stator resistance previously, the temperature of TMP system can be estimated based on Eq. (3). Fig. 11 provides the comparison results of temperature estimation of TMP system in 24 h.
finite element software to calculate the temperature distribution in the motor and find out the position of the highest temperature point, which could provide more basis for the fault diagnosis of the TMP system.
1) Compared with traditional temperature measurement method used in TMP system, the proposed method based on identification algorithm has the advantages of cheapness, easy installation, high reliability and less signal conditioning circuits. 2) The proposed DFRLS algorithm could improve real-time tracking performance and the stability of the estimation of the temperature, which is suitable for long-term monitoring of the TMP motor temperature. 3) With the proposed method based on resistance identification algorithm, the average temperature of motor stator could be calculated which is suitable for the thermal protection of TMP system. Besides, the thermal model of the TMP system should also be analyzed with
Acknowledgements This work was supported in part by the Supported by Beijing Natural Science Foundation under Grant 4191002, by the National nature science foundation of China under Grant 61573032, by the National Nature Science Foundation of China under Grant 61374029.
Fig. 11. Estimation experiment results of TMP system temperature. 8
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References
55–62. [14] G.D. Demetriades, H.Z.D.L. Parra, E. Andersson, et al., A real-time thermal model of a permanent-magnet synchronous motor, IEEE Trans. Power Electron. 25 (2) (2010) 463–474. [15] K. Lee, D. Jung, I. Ha, An online identification method for both stator resistance and back-EMF coefficient of PMSMs without rotational transducers, IEEE Trans. Ind. Electron. 51 (2) (2004) 507–510. [16] B.C. Han, Z.Y. Huang, Y. Le, Design aspects of a large scale turbomolecular pump with active magnetic bearings, Vacuum 142 (2017) 96–105. [17] N.Z. Popov, S.N. Vukosavic, E. Levi, Motor temperature monitoring based on impedance estimation at PWM frequencies, IEEE Trans. Energy Convers. 29 (1) (2014) 215–223. [18] S.D. Wilson, P. Stewart, B.P. Taylor, Methods of resistance estimation in permanent magnet synchronous motors for real-time thermal management, IEEE Trans. Energy Convers. 25 (3) (2010) 698–707. [19] Y. Xu, U. Vollmer, A. Ebrahimi, et al., Online estimation of the stator resistances of a PMSM with consideration of magnetic saturation, 2012 International Conference and Exposition on Electrical and Power Engineering, EPE, 2012, pp. 360–365. [20] D.D. Reigosa, F. Briz, P. Garcia, et al., Magnet temperature estimation in surface PM machines using high-frequency signal injection, IEEE Trans. Ind. Appl. 46 (4) (2010) 1468–1475. [21] B.N. Jia, P. Yu, A.G. Song, Sensor Technology[M], Southeast University Press, 2007. [22] Electrician Safety technology[M], Shanghai Institute of Safety Production Science Press, 2005. [23] F. Ding, System Identification - Performance Analysis of Identification Methods [M], Science Press, 2014. [24] L. Ljung, System Identification:Theory for the User [M], Tsinghua University Press, 2002. [25] R. Ghazali, Y.M. Sam, M.F. Rahmat, et al., On-line identification of an electro-hydraulic system using recursive least square, Proceedings of 2009 IEEE Student Conference on Research and Development, SCOReD, 2009, pp. 471–474 2009. [26] Y. Li, K.K. Parhi, STAR recursive least square lattice adaptive filters, IEEE Trans. Circuits Syst. II : Analog Digital Signal Process. 44 (12) (2002) 1040–1054. [27] F. Ding, T. Chen, Performance bounds of forgetting factor least-squares algorithms for time-varying systems with finite measurement data, EEE Trans. Circuits Syst. I: Regular Papers 52 (3) (2005) 555–566.
[1] L. Piroddi, A. Leva, F. Casaro, Vibration control of a turbomolecular vacuum pump using piezoelectric actuators, Proceedings of the 45th IEEE Conference on Decision & Control, IEEE, 2006, pp. 6555–6560. [2] F.C. Hsieh, P.H. Lin, D.R. Liu, F.Z. Chen, Pumping performance analysis on turbomolecular pump, Vacuum 86 (7) (2012) 830–832. [3] M. Ganchev, C. Kral, T. Wolbank, Identification of sensorless rotor temperature estimation technique for permanent magnet synchronous motor, Power Electronics, Electrical Drives, Automation and Motion, IEEE, 2012, pp. 38–43. [4] T. Alberto, A survey of state-of-the-art methods to compute rotor eddy-current losses in synchronous permanent magnet machines, Electrical Machines Design, Control & Diagnosis, IEEE, 2017, pp. 12–19. [5] G. Liu, K. Mao, Investigation of the rotor temperature of a turbo-molecular pump with different motor drive methods, Vacuum 146 (2017) 252–258. [6] R. Größle, N. Kernert, S. Riegel, K. Wada, Model of the rotor temperature of turbomolecular pumps in magnetic fields, Vacuum 86 (7) (2012) 985–989. [7] M. Ganchev, B. Kubicek, H. Kappeler, Rotor temperature monitoring system, XIX International Conference on Electrical Machines, ICEM, 2010, pp. 1–5. [8] D. Díaz Reigosa, F. Briz, Degner, et al., Magnet temperature estimation in surface PM machines during six-step operation, IEEE Trans. Ind. Appl. 48 (6) (2012) 2353–2361. [9] A. Mohammed, J.I. Melecio, S. Djurovíc, Open-circuit fault detection in stranded PMSM windings using embedded FBG thermal sensors, IEEE Sens. J. 19 (9) (2019) 3358–3367. [10] D. Díaz Reigosa, D. Fernandez, H. Yoshida, et al., Permanent-magnet temperature estimation in PMSMs using pulsating high-frequency current injection, IEEE Trans. Ind. Appl. 51 (4) (2015) 3159–3168. [11] G.D. Feng, C.Y. Lai, N. Kar, Expectation maximization particle filter and Kalman filter based permanent magnet temperature estimation for PMSM condition monitoring using high-frequency signal injection, IEEE Trans. Ind. Informat. 13 (3) (2017) 1261–1270. [12] J. Wolf, B. Bornschein, G. Drexlin, et al., Investigation of turbo-molecular pumps in strong magnetic fields, Vacuum 86 (4) (2011) 361–369. [13] Z.Y. Huang, B.C. Han, K. Mao, C. Peng, J.C. Fang, Mechanical stress and thermal aspects of the rotor assembly for turbomolecular pumps, Vacuum 129 (2016)
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Vacuum journal homepage: www.elsevier.com/locate/vacuum
Estimation of temperature in turbo-molecular pump based on motor resistance online identification
T
Bangcheng Hana,d, Kai Xionga,c, Kun Maoa,b,c,∗ a
Beijing Engineering Research Center of High-speed Magnetically Suspended Motor Technology and Application, Beihang University, Beijing, China Research Institute of Frontier Science, Beihang University, Beijing, China c Ningbo Innovation Research Institute, Beihang University, Ningbo, China d Hangzhou Innovation Institute, Beihang University, Hangzhou, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Vacuum Turbo-molecular pump (TMP) Temperature estimation Discount factor recursive least squares (DFRLS) Resistance online identification
The temperature of the turbo-molecular pump (TMP) system has to be monitored in real-time for long stable operation in a high vacuum environment. Since the high-speed motor is the major heat source of the TMP system, the thermal sensors such as Pt100 are widely used to measure the temperature via being embedded in the motor stators. However, these thermal sensors require extra wires and signal conditioning circuits, which increase the complexity of installation. In order to solve this problem, a real-time online estimation method for the temperature of the TMP driven motor is proposed in this paper. First of all, the resistance identification model of the high-speed motor used in TMP system is built. After that, an improved recursive least squares (RLS) algorithm, which introduces a discount factor to overcome the problem of data saturation and weak dynamic tracking, is used to identify the resistance of the motor stator windings. Then, the temperature of the TMP could be estimated indirectly based on the linear relationship between the motor stator resistance and the temperature. At last, the proposed method is tested in a self-developed magnetically levitated turbo-molecular pump (MLTMP) system, and the experimental results verify its validity and reliability.
1. Introduction Owing to the advantages of short time starting, high compression ratio and vacuum, turbo-molecular pump (TMP) has been widely used for high vacuum applications such as integrated circuits, solar coating, and physical vapor deposition [1,2]. It consists of high-speed motor, rotor blade, stator blade, etc. With the requirement of long-time operation in the high vacuum environment, the copper loss and iron core loss generated in the motor would lead to the temperature rise of the TMP system [3,4]. Therefore, it is crucial to monitor the temperature of the TMP system in real-time for long-time stable operation. Otherwise, the overheating problem would cause performance degradation of the motor permanent magnet (PM) and deformation of the rotor retaining sleeve, which may break rotor dynamic balance [5] and increase system loss. Temperature measurement methods could be classified into two categories. Thermal sensors such as thermal resistor (e.g., Pt100), thermocouple, infrared thermometer, and fiber Bragg grating [6–9] are commonly used for motor temperature measurement. In Ref. [10], the
stator temperature is measured by a Pt100 in the permanent magnet synchronous motor (PMSM). Similarly, the Pt100 is installed in the stator windings for temperature monitoring in Ref. [11]. In Ref. [12], the Pt100 is attached to the exterior housing of TMP to measure the approximate temperature of stator blades. The temperature could be measured easily by using single Pt100, but it can only be measured at a fixed position of stator windings. In order to measure the complete temperature field, five Pt100 thermal resistors have been embedded in the different positions of the TMP stator [13]. Nevertheless, the use of too many wires would increase the complexity and difficulty of installation. In conclusion, extra wires and signal conditioning circuits are required in traditional temperature measurement method, which may cause the system high cost, difficult installation and low reliability. Therefore, the sensorless temperature measurement methods have also been developed. Temperature measurement methods via sensorless technique reported in the literature can be divided into numerical method and resistance-identification-based temperature estimation method [14,15]. In Ref. [16], thermal analysis of the TMP is carried out by finite element
∗ Corresponding author. Research Institute of Frontier Science, BeiHang University, Beijing Engineering Research Center of High-speed Magnetically Suspended Motor Technology and Application, Beijing City, Haidian District, Xueyuan Road NO. 37, China. E-mail address: [email protected] (K. Mao).
https://doi.org/10.1016/j.vacuum.2019.108935 Received 31 May 2019; Received in revised form 5 September 2019; Accepted 7 September 2019 Available online 09 September 2019 0042-207X/ © 2019 Elsevier Ltd. All rights reserved.
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mounting spot. In order to measure the complete temperature field, a number of Pt100 thermal resistors are required, which in turn contributes to a great deal of wires and reduces the system reliability. In spite of this, single Pt100 is mostly used in TMP system for temperature monitoring because of its simplicity.
analysis (FEA) tools. Normally, the numerical method relies on thermal models and FEA tools. Besides, the TMP system cannot respond to temperature rise in real-time due to the thermal parameter variation. Thus, parameter-identification-based method is commonly designed to estimate the average temperature of the high-speed motor in real-time. N. Z. Popov and his partners calculate the temperature based on the input impedance of PMSM at elevated frequencies [17]. Additionally, for real-time thermal management, D. W. Simon describes two techniques applied to measure the windings' resistance through angle and magnitude current injection [18]. Furthermore, the recursive least squares (RLS) algorithm has been proposed in Ref. [19] to identify the stator windings' resistance, which could be used for stator temperature online estimation. Nonetheless, the problem of data saturation and low stability would exist with the RLS algorithm. Based on the above analysis, the parameter-identification-based temperature estimation method could be used to monitor the temperature of the high-speed motor, while it has not been applied in the TMP system yet. This paper is organized as followings. Firstly, Section Ⅱ introduces some limitations in traditional temperature measurement method of the TMP. After that, a novel temperature estimation method for the TMP is proposed in Section Ⅲ, which is based on resistance online identification using discount factor recursive least squares (DFRLS). Then, the proposed method is tested in a self-developed magnetically levitated turbo-molecular pump (MLTMP) system, and the experimental results are given in Section Ⅳ. Finally, Section Ⅴ concludes this paper.
3. Proposed temperature estimation method based on identification of resistance Considering the problems existing in the traditional temperature measurement method, it is necessary to study an online measurement method specifically for the TMP system. 3.1. Temperature equation of TMP system According to Refs. [20,21], the relationship between resistance of the motor stator copper coils and the temperature variation is approximately linear, which can be expressed as Eq. (2).
Rs = R 0 [1 + αCu (Ts − T0)]
where R0 and Rs are the windings' resistance at T0 and Ts, respectively, αCu is the coefficient of the copper. In the temperature range of −50°C150 °C, the copper resistance has stable chemical and physical properties, and αCu is assumed as 4.1 × 10−3 °C−1 [22]. Then, according to Eq. (2), the equation for temperature of motor stator windings can be written as Eq. (3).
2. Traditional temperature measurement method of TMP system
Ts = Pt100 thermal resistors are widely used in TMP temperature measurement system. Commonly, Pt100 thermal resistors are installed in the motor stator windings which are the highest temperature positions of TMP. The installation diagram of Pt100 is shown in Fig. 1. The resistance and the temperature of Pt100 can generally be expressed by the following approximate relationship as Eq. (1).
Rs = R 0 [1 + αPt (Ts − T0)]
(2)
1 ⎛ Rs − 1⎞ + T0 αCu ⎝ R 0 ⎠ ⎜
⎟
(3)
3.2. Resistance identification model of SPMSM The resistance identification model is established in surface permanent magnet synchronous motor (SPMSM). For simplicity, it is assumed that the stator core magnetic saturation and high-order harmonics can be ignored, the motor back electromotive force (BEMF) is sine wave, and the stator resistance is three-phase symmetrical, i.e. Then the dynamic voltage equation in synchronous rotating coordinates can be written as Eq. (4).
(1)
where T0 is the environment tempe rature, R0 and Rs represent the resistance of Pt100 at T0 and Ts, respectively, and αPt is the temperature coefficient of Pt100. The temperature measurement system of TMP system using Pt100 is shown in Fig. 2. Pt100 is connected to an external Wheatstone bridge circuit, which would generate a voltage difference signal when the TMP system temperature rises. A differential amplifier is used to amplify the voltage difference signal and its output would be transmitted to a data acquisition card (DAC). Meanwhile, the upper computer reads the data of DAC and the temperature of stator could be obtained. It can be observed that the traditional temperature measurement method using Pt100 provides only the local temperature at the sensor
⎧ dtd = − LSs id +
di
R
1 u LS d
+ ωr iq
⎨ diq
R − L s iq S
1 u LS q
− ωr id −
⎩ dt
=
+
1 ω ψ LS r f
(4)
where id、iq and ud、uq denote current and voltage of d, q-axis, respectively, Rs is motor stator windings' resistance, Ls is d, q-axis inductance, Ψf is the PM flux linkage, ωr is electricity angular velocity. When TMP runs for a long time at high-speed and steady-state, it could be assumed that ωr is a known parameter since the speed and load of TMP would not change. Hence, Eq. (4) can be modified to the steadystate voltage form as Eq. (5).
⎧ud = Rs i d − Ls ωr iq ⎨uq = Rs i q + LS ωr i d + ωr ψf ⎩
(5)
As can be seen from Eq. (5), the parameters of SPMSM can be obtained directly only based on q-axis steady-state voltage equation. For simple analysis, rewrite the q-axis steady-state voltage equation shown as Eq. (6).
uq = Rs i q + LS ωr i d + ωr ψf
(6)
According to Eq. (6), the q-axis steady-state voltage equation contains 3 unknown parameters, which require at least 3 linearly independent equations to solve. However, when the motor operates at maximum efficiency with id = 0, two linearly independent equations are sufficient to obtain the stator resistance. Fig. 3 is the single speed step response of SPMSM which could be
Fig. 1. Pt100 installation diagram. 2
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Fig. 2. Temperature measurement system of the Pt100.
divided into acceleration stage and steady stage. It can be found that when the motor reaches rated speed, the amplitude of q-axis current is much smaller than before because its load torque is small in high vacuum environment. When the rotor frequency is ramped up through ωr1 to ωr2, Ψf could be identified at the start-up of the TMP. After reaching a constant speed ωr2, Ψf could be regarded as a constant since the PM flux linkage of SPMSM would not change much in the steady stage.
⎧uq1 = Rs i qm + ωr1 ψf ⎨uq2 = Rs i q0 + ωr 2 ψf ⎩
(7)
According to the data in Fig. 3, two linearly independent equations shown as Eq. (7) could be built. Then, the equation-based algorithm identification model of the stator windings resistance can be expressed as Eq. (8).
Fig. 3. Single step of speed response.
Fig. 4. Block diagram of the control system. 3
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⎧ ψf = ⎨ Rs = ⎩
It can be observed that the identification result is determined by discount factor since the criterion function is obtained by summing a number of terms with discount factor. By minimizing the criterion function, the estimated parameter vector θˆ (k) would satisfy Eq. (17).
uq2 − Rs i q0 ωr 2 uq2 ωr1 − uq1 ωr 2 i q0 ωr1 − i qm ωr 2
(8)
Consequently, according to the identification model shown in Eq. (8) and the acquired data, the resistance of stator windings could be identified online. During the steady-state operation of TMP, the windings' temperature changes relatively slowly, which indicates that the change of stator resistance is also slow. Here, the time interval Δt between the resistance identification is 3 min. Fig. 4 is the block diagram of the control system. It can be observed that the data of the q-axis current and q-axis voltage are collected for calculating the stator windings resistance.
−1 θˆ (k ) = (HkT Γk Hk ) HkT Γk Yk
Define the covariance matrix P(k) as Eq. (18).
P (k ) = [λP −1 (k − 1) + Λ (k ) ϕ (k ) ϕT (k )]−1 1⎡ = λ ⎢I − ⎣
(10)
y (k ) = uq (k )
(11)
T θ (k ) = [ Rs ψf ]
(12)
⎧ θˆ (k ) = θˆ (k − 1) + K (k )[y (k ) − ϕT (k ) θˆ (k − 1)] ⎪ −1 λ (k ) K (k ) = P (k − 1) ϕ (k ) ⎡ Λ (k ) + ϕT (k ) P (k − 1) ϕ (k ) ⎤ ⎣ ⎦ ⎨ ⎪ P (k ) = 1 [I − K (k ) ϕT (k )] P (k − 1) λ (k ) ⎩
ε (k ) = y (k ) − ϕT (k ) θˆ (k − 1)
(14)
(15)
where k is the number of beats of the selected data, Γ(k,i), Λ(i), and λ denote discount factor, weighting factor, and forgetting factor, respectively. The discount factor contains forgetting factor and weighting factor. By introducing the discount factor, the criterion function is defined as Eq. (16).
⎧ 0 ε (k ) ≥ 10−2 y (k ) ⎪ 0.1 10−4 y (k ) ≤ ε (k ) < 10−2 y (k ) ⎨ 0.5 10−5 y (k ) ≤ ε (k ) < 10−4 y (k ) ⎪ −5 ⎩1 ε (k ) < 10 y (k )
k i=1
(20)
(21)
(22)
where ε(k) is the prediction deviation according to the current model, θˆ (k-1) is the parameter estimation at time of k-1. The prediction deviation is a scalar, representing a single step of information during the iteration. The selection of weighting factor is related to the prediction deviation. When the variation of deviation is small and stable, Λ(i) is set to a value with large confidence. However, when the variation of deviation is large due to measured data with large uncertainties, Λ(i) is set to a value with small confidence. Therefore, according to the variation of deviation, the value of Λ(i) is set into 4 segments, which includes untrusted data, low confidence data, high confidence data and fully trusted data. The value of Λ(i) can be expressed as Eq. (23).
(13)
Introducing the discount factor shown as Eq. (15).
∑ Γ (k, i)[y (k ) − ϕT (k ) θ]2
(19)
According to Eq. (19), in order to make the algorithm track timevarying parameters, the covariance matrix P(k) cannot be 0 when the time approaches infinite. Obviously, P(k) does not approach to 0 when the forgetting factor is introduced. Hence, in the process of data accumulation, the forgetting factor could reduce the influence of older data, which achieves the dynamic characteristics of identification model. For the identification model of PMSM, a small change in the forgetting factor may cause a significant change in the identification performance. Therefore, the selection of the forgetting factor is crucial. Usually, λ satisfies 0 < λ ≤ 1 and it should better be set close to 1 [23]. Here, λ is set to 0.9995. The weighting factor is multiplied directly to each term in the criterion function to reduce the weight of values with large uncertainties and achieve the stability characteristics of identification model. The prediction deviation is defined as Eq. (22).
Then, Eq. (9) could be written in the form of a matrix as shown in Eq. (14).
J (θ) =
− 1)
Then, according to Eq. (15), Eq. (17), Eq. (19) and Eq. (20), the DFRLS algorithm model [24–27] can be shown as Eq. (21).
The output matrix Yk, the information matrix Hk, and the noise matrix Vk are defined as shown in Eq. (13).
Γ (k , i) = Λ (i) λk − i
⎤
Define the gain matrix K(k) as Eq. (20).
(9)
ϕT (k ) = [iq (k ) ωr ]
P (k − 1) ϕ (k ) ϕT (k )
⎥ P (k λ + ϕT (k ) P (k − 1) ϕ (k ) Λ (k ) ⎦
K (k ) = Λ (k ) P (k ) ϕ (k )
where ϕT(k), θ(k), y(k) and e(k) denote the input vector, the parameter vector, the output data and the interference noise data, respectively. Moreover, ϕT(k) and θ(k) are 2-dimensional vector. On the basis of Eq. (6), ϕT (k ) , y(k) and θ(k) could be shown as Eq. (10), Eq. (11) and Eq. (12), respectively.
Yk = Hk θ + Vk
(18)
Based on Eq. (15) and matrix inversion lemma [23], Eq. (18) could be written as Eq. (19).
Comparing with the equation-based algorithm using the data of a certain state point, a better approach is to use an efficient iterative identification algorithm, which has more data to ensure the reliabity and accuracy of identification. Among the existing literature, the RLS algorithm is widly used for parameter identification in engeering because of its simplicity. However, serious data saturation problems will exist in RLS algorithm as the observed data grows, making the parameter identification value insensitive to new data and reducing the dynamic accuracy. Therefore, this paper proposes an improved RLS algorithm with discount factor for resistance identification. Considering that noise interference would exist in TMP systems inevitably in the process of operation, the DFRLS identification model based on Eq. (6) could be presented as follows.
T ⎡ ϕ (1) ⎤ ⎡ e (1) ⎤ ⎡ y (1) ⎤ ⎢ ϕT (2) ⎥ ⎢ ⎥ ⎢ y (2) ⎥ YK = ⎢ ,H = , V = e (2) ⋯ ⎥ K ⎢ ⋯ ⎥ K ⎢ ⋯ ⎥ ⎢ T ⎥ ⎢ e (k ) ⎥ ⎢ y (k ) ⎥ ⎣ ⎦ ⎦ ⎣ ⎣ ϕ (k ) ⎦
−1
k
⎤ ⎡ P (k ) = ⎢∑ Γ (k , i) ϕ (i) ϕT (i) ⎥ ⎣ i=1 ⎦
3.3. Resistance online identification method based on DFRLS algorithm
y (k ) = ϕT (k ) θ (k ) + e (k )
(17)
(16)
(23)
Besides, when Λ is taken as 1, the DFRLS algorithm equals to RLS 4
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Table 1 Experimental TMP parameters. TMP Parameters
Value
Inlet flange Number of pole pairs Volume flow rate N2 (L/s) Ultimete pressure (Pa) Rate speed (r/min) Flux Linkage (Wb) Phase resistance (Ω) Phase inductance (mH)
ISO400 1 4100 1 × 10−7 21000 0.0182 0.28 0.24
motor temperature, the TMP system operates continuously for 24 h and the identified resistance used to estimate temperature is recorded every 30 min. The TMP reaches the rated speed of 21000r/min after 8 min of acceleration. During this time, according to Eq. (7), the estimation of PM flux linkage of motor based on equation-based algorithm, RLS algorithm and DFRLS algorithm are 0.0177Wb, 0.0186Wb, 0.0180Wb, respectively. Here, the equation-based algorithm represents Eq. (8) using data only from a single measurement at time k. Fig. 9 shows the identification experiment results of stator resistance Rs based on different identification algorithms. When the motor stopped, the resistance of the winding at room temperature is defined as the static value. It can be observed that the estimated stator resistance is higher than the static value due to the temperature of the stator windings rise. Fig. 9 a) is the identification results of Rs within 24 h. From Fig. 9 a), during the 24 h, the curves of resistance identified by RLS algorithm and DFRLS algorithm converge to a stable value, while the curve based on equation-based algorithm shows no sign of convergence, because the input data are small compared to the inherent noise, resulting in the identified resistance values fluctuate a lot at different time. Besides, the curve of DFRLS algorithm has smaller fluctuation than the other two algorithms. Fig. 9 b) is the identification results of Rs starting at 11:00. When the identification process is close to the convergence state, the fluctuation level of resistance identification is defined as Eq. (24).
Fig. 5. Single step of speed response-data segments.
algorithm with the forgetting factor. Furthermore, when λ and Λ are taken as 1, the DFRLS algorithm equals to standard RLS algorithm. For the sake of iteration convenience, the data segments shown in Fig. 5 are used for DFRLS algorithm identification model. In Fig. 5, L denotes the length of the data segments. Fig. 6 is the diagram of temperature online estimation method based on DFRLS algorithm. The resistance of the stator windings is identified firstly. Then, the temperature could be estimated. 4. Experiments 4.1. Experiment platform setup To confirm the validity of the proposed method, tests are implemented on a self-developed MLTMP testing platform. Table 1 shows its main parameters. The system consists of a power source, a control circuit box, a backing pump, a Pt100 temperature meter and a TMP which is shown in Fig. 7. The Pt100 thermal sensors are also used to monitor the temperature in real-time. In order to minimize measurement error, three Pt100 thermal resistors are embedded in the TMP stator windings every 120 mechanical degrees as shown in Fig. 8. 4.2. Resistance identification result with different identification methods
δR = In order to estimate the temperature of TMP system, three resistance-identification-based temperature estimation methods are implemented on the testing TMP. As described in Section Ⅲ, the data segments at different time are taken out to identify the parameter of motor. The length of the data segment is 2000 and the time between two samples is 10 ms. Additionally, in order to accurately monitor the
R c max − R c × 100% Rc
(24)
where Rc denotes the convergence value of resistance, Rcmax denotes the maximum value of resistance when the identification process is close to the convergence state, and δR denotes the fluctuation level. The results in Fig. 9 show that the fluctuation level of resistance identification based on the RLS algorithm is 2%, while that of the
Fig. 6. Diagram of proposed temperature online estimation method. 5
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Fig. 7. Experimental platform.
range of −70 °C to +500 °C. The temperature coefficient of Pt100 is 0.003851 °C-1, and the tolerance class of Pt100 is F 0.15. Moreover, three Pt100 are exposed to the room temperature 27.2 °C to determine the T0 and R0. Then, in order to calculate the slopes α of Pt100, they are also exposed to 50 °C. Three Pt100 are labeled T1, T2 and T3, respectively, and the testing results of Pt100 are shown in Table 2. According to the testing results of three Pt100, the differences of offsets T0 and slopes α between three Pt100 are small, which is no more than 1%. In addition, when the current flows through the Wheatstone bridge circuit, the connecting wires and the Pt100 will cause additional temperature uncertainties. The uncertainty of the Wheatstone bridge circuit is designed to be no more than 0.2%. However, it can be found that the temperature values measured by three Pt100 are different. In order to minimize measurement error, three temperature values are averaged as shown in Fig. 10. The averaged temperature is used as a reference for testing to verify the feasibility of proposed identification method. Fig. 11 shows that the proposed algorithm could effectively estimate TMP's stator temperature, comparing with the traditional measurement method based on Pt100. Therefore, the resistance-identification-based temperature estimation method is feasible. It can be observed that the value of the TMP's stator temperature changes slowly within 24 h. The fluctuation level of temperature identification is defined as Eq. (25).
Fig. 8. The motor stator of tested TMP with three Pt100 thermal resistors.
DFRLS algorithm is 0.7%. Apparently, the DFRLS algorithm has less fluctuation and better stability. In addition, the convergence time of the RLS algorithm is 0.27s, while that of the DFRLS algorithm is 0.16s, which is nearly 33.3% shorter. It shows that with the forgetting factor, the influence of older data in the fitting algorithm is reduced, making the identification algorithm is sensitive to the new data. Therefore, the DFRLS algorithm has a faster convergence rate and better dynamic characteristics during the convergence process. Combine with the above analysis, discount factor plays a significant role in convergence speed and stability performance for identification system.
δT =
ΔT × 100% TA
(25)
where TA denotes the average temperature of Pt100, ΔT denotes the maximum variation between identification temperature and the average temperature, and δT denotes the fluctuation level. Compared with the average temperature, the estimated temperature fluctuations based on equation-based algorithm are relatively large. Its maximum error reaches 27.5%. Obviously, this method cannot be applied directly. However, the maximum error of the RLS algorithm reduces to 6.2%, which improves the accuracy of temperature estimation. After adopting the DFRLS algorithm with discount factor, the accuracy of the temperature estimation is further improved compared with the RLS, and its maximum error decreases to 2.3%. Therefore, it is evidently demonstrated that the proposed DFRLS algorithm can achieve a
4.3. Temperature estimation results with different estimation methods In order to compare the temperature of the stator windings with different estimation methods, the temperature is recorded every 30 min. The Pt100 used here is M222 A platinum resistance temperature detector produced by Heraeus. It has an operating temperature 6
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Fig. 9. Identification experiment results of stator resistance Rs.
faster convergence capability and less fluctuation, which is in accordance with the theoretical analysis.
Table 2 The testing results of Pt100. Sensors number
Offsets T0 (°C)
R0 (Ω)
Slopes α
T1 T2 T3
27.4 27.2 27.1
109.94 109.67 109.54
0.003848 0.003850 0.003849
5. Conclusion In this paper, the TMP system temperature is investigated with different measurement methods. The following conclusions are obtained through analysis and experiment. 7
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Fig. 10. Average temperature curves of TMP system. According to identified stator resistance previously, the temperature of TMP system can be estimated based on Eq. (3). Fig. 11 provides the comparison results of temperature estimation of TMP system in 24 h.
finite element software to calculate the temperature distribution in the motor and find out the position of the highest temperature point, which could provide more basis for the fault diagnosis of the TMP system.
1) Compared with traditional temperature measurement method used in TMP system, the proposed method based on identification algorithm has the advantages of cheapness, easy installation, high reliability and less signal conditioning circuits. 2) The proposed DFRLS algorithm could improve real-time tracking performance and the stability of the estimation of the temperature, which is suitable for long-term monitoring of the TMP motor temperature. 3) With the proposed method based on resistance identification algorithm, the average temperature of motor stator could be calculated which is suitable for the thermal protection of TMP system. Besides, the thermal model of the TMP system should also be analyzed with
Acknowledgements This work was supported in part by the Supported by Beijing Natural Science Foundation under Grant 4191002, by the National nature science foundation of China under Grant 61573032, by the National Nature Science Foundation of China under Grant 61374029.
Fig. 11. Estimation experiment results of TMP system temperature. 8
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B. Han, et al.
References
55–62. [14] G.D. Demetriades, H.Z.D.L. Parra, E. Andersson, et al., A real-time thermal model of a permanent-magnet synchronous motor, IEEE Trans. Power Electron. 25 (2) (2010) 463–474. [15] K. Lee, D. Jung, I. Ha, An online identification method for both stator resistance and back-EMF coefficient of PMSMs without rotational transducers, IEEE Trans. Ind. Electron. 51 (2) (2004) 507–510. [16] B.C. Han, Z.Y. Huang, Y. Le, Design aspects of a large scale turbomolecular pump with active magnetic bearings, Vacuum 142 (2017) 96–105. [17] N.Z. Popov, S.N. Vukosavic, E. Levi, Motor temperature monitoring based on impedance estimation at PWM frequencies, IEEE Trans. Energy Convers. 29 (1) (2014) 215–223. [18] S.D. Wilson, P. Stewart, B.P. Taylor, Methods of resistance estimation in permanent magnet synchronous motors for real-time thermal management, IEEE Trans. Energy Convers. 25 (3) (2010) 698–707. [19] Y. Xu, U. Vollmer, A. Ebrahimi, et al., Online estimation of the stator resistances of a PMSM with consideration of magnetic saturation, 2012 International Conference and Exposition on Electrical and Power Engineering, EPE, 2012, pp. 360–365. [20] D.D. Reigosa, F. Briz, P. Garcia, et al., Magnet temperature estimation in surface PM machines using high-frequency signal injection, IEEE Trans. Ind. Appl. 46 (4) (2010) 1468–1475. [21] B.N. Jia, P. Yu, A.G. Song, Sensor Technology[M], Southeast University Press, 2007. [22] Electrician Safety technology[M], Shanghai Institute of Safety Production Science Press, 2005. [23] F. Ding, System Identification - Performance Analysis of Identification Methods [M], Science Press, 2014. [24] L. Ljung, System Identification:Theory for the User [M], Tsinghua University Press, 2002. [25] R. Ghazali, Y.M. Sam, M.F. Rahmat, et al., On-line identification of an electro-hydraulic system using recursive least square, Proceedings of 2009 IEEE Student Conference on Research and Development, SCOReD, 2009, pp. 471–474 2009. [26] Y. Li, K.K. Parhi, STAR recursive least square lattice adaptive filters, IEEE Trans. Circuits Syst. II : Analog Digital Signal Process. 44 (12) (2002) 1040–1054. [27] F. Ding, T. Chen, Performance bounds of forgetting factor least-squares algorithms for time-varying systems with finite measurement data, EEE Trans. Circuits Syst. I: Regular Papers 52 (3) (2005) 555–566.
[1] L. Piroddi, A. Leva, F. Casaro, Vibration control of a turbomolecular vacuum pump using piezoelectric actuators, Proceedings of the 45th IEEE Conference on Decision & Control, IEEE, 2006, pp. 6555–6560. [2] F.C. Hsieh, P.H. Lin, D.R. Liu, F.Z. Chen, Pumping performance analysis on turbomolecular pump, Vacuum 86 (7) (2012) 830–832. [3] M. Ganchev, C. Kral, T. Wolbank, Identification of sensorless rotor temperature estimation technique for permanent magnet synchronous motor, Power Electronics, Electrical Drives, Automation and Motion, IEEE, 2012, pp. 38–43. [4] T. Alberto, A survey of state-of-the-art methods to compute rotor eddy-current losses in synchronous permanent magnet machines, Electrical Machines Design, Control & Diagnosis, IEEE, 2017, pp. 12–19. [5] G. Liu, K. Mao, Investigation of the rotor temperature of a turbo-molecular pump with different motor drive methods, Vacuum 146 (2017) 252–258. [6] R. Größle, N. Kernert, S. Riegel, K. Wada, Model of the rotor temperature of turbomolecular pumps in magnetic fields, Vacuum 86 (7) (2012) 985–989. [7] M. Ganchev, B. Kubicek, H. Kappeler, Rotor temperature monitoring system, XIX International Conference on Electrical Machines, ICEM, 2010, pp. 1–5. [8] D. Díaz Reigosa, F. Briz, Degner, et al., Magnet temperature estimation in surface PM machines during six-step operation, IEEE Trans. Ind. Appl. 48 (6) (2012) 2353–2361. [9] A. Mohammed, J.I. Melecio, S. Djurovíc, Open-circuit fault detection in stranded PMSM windings using embedded FBG thermal sensors, IEEE Sens. J. 19 (9) (2019) 3358–3367. [10] D. Díaz Reigosa, D. Fernandez, H. Yoshida, et al., Permanent-magnet temperature estimation in PMSMs using pulsating high-frequency current injection, IEEE Trans. Ind. Appl. 51 (4) (2015) 3159–3168. [11] G.D. Feng, C.Y. Lai, N. Kar, Expectation maximization particle filter and Kalman filter based permanent magnet temperature estimation for PMSM condition monitoring using high-frequency signal injection, IEEE Trans. Ind. Informat. 13 (3) (2017) 1261–1270. [12] J. Wolf, B. Bornschein, G. Drexlin, et al., Investigation of turbo-molecular pumps in strong magnetic fields, Vacuum 86 (4) (2011) 361–369. [13] Z.Y. Huang, B.C. Han, K. Mao, C. Peng, J.C. Fang, Mechanical stress and thermal aspects of the rotor assembly for turbomolecular pumps, Vacuum 129 (2016)
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