Sensorless control of ship propulsion interior permanent magnet synchronous motor based on a new sliding mode observer.

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Sensorless control of ship propulsion interior permanent magnet synchronous motor based on a new sliding mode observer$ Jun-Jie Ren, Yan-Cheng Liu n, Ning Wang, Si-Yuan Liu Marine Engineering College, Dalian Maritime University, No. 1 Linghai Road, Dalian City 116026, Liaoning Province, China

art ic l e i nf o

a b s t r a c t

Article history: Received 3 May 2014 Received in revised form 5 August 2014 Accepted 20 August 2014 This paper was recommended for publication by Dr. Jeff Pieper

This paper proposes a sensorless speed control strategy for ship propulsion interior permanent magnet synchronous motor (IPMSM) based on a new sliding-mode observer (SMO). In the SMO the low-pass filter and the method of arc-tangent calculation of extended electromotive force (EMF) or phase-locked loop (PLL) technique are not used. The calculation of the rotor speed is deduced from the Lyapunov function stability analysis. In order to reduce system chattering, sigmoid functions with switching gains being adaptively updated by fuzzy logic systems are innovatively incorporated into the SMO. Finally, simulation results for a 4.088 MW ship propulsion IPMSM and experimental results from a 7.5 kW IPMSM drive are provided to verify the effectiveness of the proposed SMO method. & 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Keywords: Ship propulsion interior permanent magnet synchronous motor (IPMSM) Sensorless control Sliding-mode observer (SMO) Sigmoid function and fuzzy logic Propeller load characteristic

1. Introduction Recently, the electric ship propulsion system has been a prospective candidate in the marine community due to environmental emission reduction, economic fuel consumption, compactness and superior maneuverability [1].The permanent magnet synchronous motors (PMSMs), having the advantages of high efficiency, high power density and fast dynamic response, are very suitable as the propulsion motor in compact electric propulsion systems. In the PMSM vector control or direct torque control systems, it requires the information of rotor speed for closed-loop control, so the position sensors such as an optical encoder or a resolver are needed to be installed on the shaft [2]. However the ship propulsion motors are located in a harsh environment due to severe moisture, humidity, and vibration and in these conditions the conventional rotor angle sensors often cannot be accommodated because of the reliability concerns and physical constraints [3]. Thus the sensorless control technique of PMSM is necessary in the electric ship propulsion system.

$ This work is supported by National Nature Science Foundation of China (under Grant 51479018) and the Fundamental Research Funds for the Central Universities (under Grant 3132014322). n Corresponding author. Tel.: þ 86 13904282464. E-mail addresses: [email protected] (J.-J. Ren), [email protected] (Y.-C. Liu), [email protected] (N. Wang), [email protected] (S.-Y. Liu).

So far, there have been many methods for estimating the rotor position and the speed of the PMSM, such as the direct estimation method based on the back-electromotive force voltage(EMF) [4,5], the flux linkage estimation method [6], the full-order and reducedorder observers [7,8], the high-frequency (HF) signal injection method [9–14], the sliding-mode observer (SMO) [15–22], the extended Kalman filter (EKF) [22–24], etc. In addition, sliding mode observers combined with HF signal injection have been proposed in [25,26]. Among these techniques the direct estimation method is simple but suffers from the motor parametric uncertainties; in [4,5] a new estimation structure and a constant artificial inductance concept have been proposed to reduce the estimation error. The sliding mode observer is presented to estimate the stator flux linkage for a direct torque controlled interior permanent magnet synchronous motor (IPMSM) drive in [6] and the stability analysis is the utmost important issue in the method of full-order observer [7]. Meanwhile the asymptotic stability of the reduced-order observers that combined position and stator resistance estimation requires careful analysis [8]. Estimation method based on HF signal injection exploits the saliency property of an IPMSM and it offers a solution at standstill and low speeds, but as the speed increases its performance deteriorates drastically [26]. The EKF method can give recursive optimum state estimation when the motor terminal signals are polluted by noise, however it involves vector and matrix operations; this makes it highly computationally intensive and in order to avoid instability, care has to be exercised in selecting the noise covariance matrices and initial values.

http://dx.doi.org/10.1016/j.isatra.2014.08.008 0019-0578/& 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Please cite this article as: Ren J-J, et al. Sensorless control of ship propulsion interior permanent magnet synchronous motor based on a new sliding mode observer. ISA Transactions (2014), http://dx.doi.org/10.1016/j.isatra.2014.08.008i

2

J.-J. Ren et al. / ISA Transactions ∎ (∎∎∎∎) ∎∎∎–∎∎∎

Compared to these methods, the sliding-mode observer has attractive advantages of robustness to disturbances and low sensitivity to the system parameter variations. One obvious disadvantage for SMO is the chattering phenomenon caused by discontinuous control law and frequent switching action near sliding surface. To overcome the problem of chattering, different methods have been studied. In [15] the saturation function is used in the SMO and the technique of feedback of the “equivalent control” is applied, but the introduction of low-pass filter and additional position compensation of the rotor usually causes phase delay and the control requirements of high performance applications cannot be met. Thus a hybrid terminal SMO is proposed in [16] for the rotor position and speed estimation. In [16] the smooth back-EMF signals can be obtained directly from the observer and the lowpass filter can be omitted; however the high-order derivatives in SMO are not desirable for digital signal processor based implementation. In [17] a sigmoid function is used for the switching function instead of the signum function to overcome the time delay caused by the low-pass filter and in [18,19] an iterative SMO and a new SMO which enables the observer to extract the back EMF signals are introduced, respectively. In these papers the lowpass filter and phase compensation part are not include but the arc-tangent method is used to extract the rotor position according to the estimated orthogonal EMF components. However when using the arc-tangent method to calculate the rotor position, the existence of noise and harmonics may influence the accuracy of the position estimation. Especially, during the EMF crossing zero, obvious estimation error may occur due to the noise signals. To improve the accuracy position estimation, the software quadrature phase-locked loop (PLL) is used to extract rotor position according to the estimated EMFs in [27]. Usually, in the SMO the position and velocity of the rotor can be calculated from the estimated back EMF and this method has been extensively applied to sensorless control of surface-mounted PMSMs (SPMSM) [15,17–19,21] and IPMSMs [20,22,25–27]. In the stationary reference frame model, the magnitude of the SPMSM back-EMF is a function of only rotor speed and is not affected by load variations. Meanwhile due to the saliency of the IPMSM, an extended EMF-based IPMSM model is proposed to facilitate the rotor position observation [28]. However the expression of the extended EMF of an IPMSM is much more complex than the back-EMF expression of an SPMSM and the magnitude of the extended EMF is a function of rotor speed, stator current, and derivative of stator current, which means that the load condition will affect the magnitude of the extended EMF. In the electric ship propulsion system, the load of the propulsion IPMSM acts on a propeller and the propeller load conditions will cause significant distortions of the waveforms of the extended EMF components during a state transient. Because of this, the rotor position estimated by an SMO will also have a variable phase shift during the propeller load changes. This problem is proposed in [20] and an adaptive quasi-SMO under stationary reference frame is introduced to estimate the extended EMF signals in an IPMSM and then use a low-pass filter to extract the continuous back-EMF components to estimate the rotor position. This paper proposes a new SMO designed in the synchronous rotating frame to achieve sensorless control of IPMSM for the electric ship propulsion application. The main contributions in this paper are as follows: 1) in the SMO the low-pass filter and the method of arc-tangent calculation of extended EMF or PLL technique are not used; the calculation of the rotor speed is deduced from Lyapunov function stability analysis; 2) in order to reduce the chattering problem in the SMO, not only a sigmoid function is proposed to replace the sign function, but also the observer switching gain is adjusted based on fuzzy logic rules. The rest of this paper is organized as follows. Section 2 presents the mathematical model of the IPMSM. Section 3 proposes the new SMO and

the stability of the observer is verified using the Lyapunov method. The method to reduce the system chattering problem is introduced in Section 4 and the simulation and experimental results are discussed in Section 5. Finally, conclusions are outlined in Section 6.

2. Mathematical model of the IPMSM The voltage model of the IPMSM in the synchronous rotating frame (d q) is shown as follows: " # " #" # " # 0 ud R þ pLd ωre Lq Þ id ¼ þ ð1Þ ωre ψ f uq ωre Ld R þ pLq iq where ud and uq are the d and q axes stator voltage components, id and iq are the d and q axes stator current components, R is the stator resistance, p is the differential operator, Ld and Lq are the d and q axes inductances, ωre is the rotor electrical speed, and ψf is the permanent magnet flux linkage, respectively. From (1), a current model for IPMSMs is described using 0d1 0 1 1 ! 01 ! ! Lq 0 R 0 ud id Ld Ld ωre B id C @ Ld A @ A ψf þ þ @ d A¼ Lq ωre uq iq 0 L1q LLdq ωre LRq iq ð2Þ

3. Design of the new SMO for IPMSM 3.1. Proposed SMO Based on the current model in (2), the structure of the SMO can be expressed as 0d1 0 1 1 ! 01 ! Lq ^ î 0 LRd î ud Ld Ld ωre d d @d A ¼ @ A @ A þ îq uq 0 L1q ^ re LR LLdq ω î q q

þ

0

ψf

^ re Lq ω

! þ K 0 S þ ΦsignðSÞ

ð3Þ

where \widehat denotes the estimated quantities, K0 and Φ are the matrix gains of the observer and sign(x) is the sign function.The gain matrices of K0 and Φ can be expressed as follows: ! ! ϕ11 0 k11 0 K0 ¼ ; Φ¼ ϕ22 0 0 k22 The sliding hyperplane S is defined upon the stator current errors ! ! S1 id îd ¼ ð4Þ S¼ S2 iq îq The observer contains both linear and nonlinear feedback terms and these two parts help the system in quick tracking of the current values. 3.2. Stability analysis When the sliding mode is reached and the estimation errors are on the sliding surface, the estimation errors will become zero. At that moment, the sliding hyperplane surface S ¼0 and the observer becomes robust against the system parameters and disturbances. In order to determine the stability of the designated observer, the Lyapunov function used to find the sliding condition can be



defined as V ¼ 1=2 ST S þ ω2re =γ 1

ð5Þ

^ re . where γ 1 40 and ωre ¼ ωre ω From the Lyapunov stability theorem, the sliding mode condition can be derived to satisfy the condition V_ o 0

ð6Þ

Assuming that the rotor angular velocity is constant within a small sampling interval, from (5) d d ^ \ t\\hskip\ tdre =γ 1 ωre ð7Þ V ¼ ST S ω In equation (7) 0 1 ! Lq ^ d Ld iq d id îd 0 ¼ ðA K ÞS þ ωre @ Ld ^ ψ f A ΦsignðSÞ S¼ dt iq îq Lq id Lq where 0 A¼@

LRd LLdq

Lq Ld

ωre

ωre

LRq

ð8Þ

A

Hence substituting (8) into (7), we can get d ψf Lq ^ L ω^ \ t\\hskip\ tdre iq id d îd iq iq V ¼ ST ðA K 0 ÞS ωre Ld Lq Lq γ1 ð9Þ

From the stability condition of (6), we obtain ST ðA K 0 ÞS o 0

ð10Þ

ψf Lq ^ L ω^ dre iq i d î iq iq ¼0 Ld d Lq d Lq γ1

ð11Þ

ST ΦsignðSÞ 4 0

parts as those of the motor poles, but shifted to the left in the complex plane [30]. In the shifted poles method, the observer still possesses faster dynamics than that of the machine but the noise immunity of the observer is improved because the large values of the imaginary parts in the motor poles are not amplified. This approach is also adopted in [31] to estimate the stator flux for direct torque control of an IPMSM. From (1), we can know that the eigenvalues of matrix A will be the motor poles and the poles of the machine as a function of rotor speed are given by

λm1;2 ¼

ða þbÞ 7

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ða bÞ2 4ω2re

ð16Þ

2

where a ¼ R=Ld , b ¼ R=Lq and λm1;2 are the motor poles. From (16), we can obtain the following: 1) when ωre ¼0, λm1 ¼ 3.42, λm2 ¼ 7.13; 2) ωre ¼1.945, λm1 ¼ λm2 ¼ 5.275; 3) ωre ¼167.67, λm1 ¼ 5.275þ167.66i, λm2 ¼ 5.275 167.66i.

1

ST ΦsignðSÞ

3

The parameter values of R, Ld and Lq are shown in Table 1 and the machine poles as a function of rotor speed are shown in Fig. 1. Fig. 1 shows the machine poles in the complex plane and when the rotor speed increase the values of the imaginary parts in the motor poles become larger. So when the observer poles shift to the left with the motor poles by k0 , the values of the imaginary parts will not amplified. The poles of the observer are governed by the eigenvalues of A K0 and the eigenvalues are

λo1;2 ¼

ða þ b þ 2kgain Þ 7

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ða bÞ2 4ω2re

2

ð17Þ

ð12Þ

Eq. (10) stipulates that the eigenvalues of (A K0 ) should be in the left-half plane. Thus, the individual gains k11 and k22 in the matrix of K0 can be selected by the pole placement method. From (11), the following update laws for rotor-speed can be deduced with Z ψf Lq ^ L ð13Þ iq id d îd iq iq dt ω^ re ¼ γ 1 Ld Lq Lq Typically, a PI mechanism can be used in the speed-adaptation law and the speed estimate is Z ψ ψf L Lq ^ L L ω^ re ¼ K p q îq id d îd iq f iq þ K i iq id d îd iq iq dt Ld Lq Lq Ld Lq Lq

Table 1 Parameters of simulation IPMSM. Rated voltage Rated power Rated speed Flux linkage Stator resistance D-axis inductance Q-axis inductance Pole pairs number

UN ¼ 660 V P¼ 4.088 MW nN ¼ 200 r/min ψf ¼ 3.55 Wb R¼ 1.64 mΩ Ld ¼0.23 mH Lq ¼ 0.48 mH nP ¼ 8

ð14Þ where Kp and Ki are the gains of the PI mechanism. The rotor position estimate is Z θ^ re ¼ ω^ re dt ð15Þ From (12) the switching gains Φ11 and Φ22 in the matrix of Φ should be positive, and larger values of Φ11 and Φ22 will increase the robustness of the observer but may generate unwanted chattering. 3.3. Selection of gains in matrix K0 The classical method of the observer gain selection is to design the observer poles proportional to the motor poles [29]. This method allows the observer to be dynamically faster than the motor, but is susceptible to noise. This problem can be circumvented by designing the observer poles with identical imaginary

Fig. 1. Location of motor poles with ωre changes.



4

where kgain ¼ k11 ¼ k22 and when

λo1 ¼

ð10:55 þ 2kgain Þ þ 3:71 ; 2

ωre ¼ 0

λo2 ¼

ð10:55 þ 2kgain Þ 3:71 2

If the observer poles are shifted to the left by k0 ¼100, then ð10:55 þ 2kgain Þ þ 3:71 ¼ 3:42 100; 2 ð10:55 þ 2kgain Þ 3:71 ¼ 7:13 100 λo2 ¼ 2

λo1 ¼

The gains in the matrix K0 can be obtained as kgain ¼ k11 ¼ k22 ¼ 100.

4. Reducing system chattering Due to the discrete switch control in the SMO, chattering becomes an inherent characteristic of the sliding-mode variable structure system and it cannot be completely eliminated but only reduced. For the traditional SMO the sign function is used as the control function, and due to switch time and space lag the SMO presents serious chattering. In order to reduce the chattering, the sign function can be replaced by the saturation function or sigmoid function. On the other hand larger values of switching gain Φ11 and Φ22 will generate unwanted chattering problem because when the control signal crosses the sliding surface, the larger switching gain will cause bigger and faster switching control components and lead to unexpected chattering in the system. To mitigate this chattering effect, fuzzy logic rules can be adopted for adjusting the switching gains according to the states of the sliding surface.

Fig. 2. Fuzzy input membership functions.

4.1. Sigmoid function In order to reduce the chattering phenomenon, the sign function is replaced by the sigmoid function, which is a continuous function and defined as sigmoidðxÞ ¼

2 1 1þea x

ð18Þ

where a is a positive constant used to regulate the slope of the sigmoid function. Then, the SMO of Eq. (3) can be rewritten as 0 1 0 1 1 ! 01 ! Lq ^ î 0 LRd î \t\\hskip\td ud Ld Ld ωre d d @ A¼@ A @ A þ îq uq 0 L1q ^ re L R LLdq ω îq \t\\hskip\td q ! 0 0 ð19Þ þ ψf ω ^ re þ K S þ Φ sigmoidðSÞ L q

4.2. Adjusting switching gains with fuzzy logic rules The switching gains can be adjusted based on the states of the sliding-mode surface. When the system state trajectories stay far from the sliding surface, which means the value of |S| is large, the switching gains Φ11 and Φ22 should be increased to drive the trajectory back and when the value of |S| is small, the gains should have smaller values. Hence we can adopt fuzzy logic rules to adjust the switching gains according to the value of |S|. In a fuzzy logic inference system, reference inputs need to be converted to fuzzy variables. The universes of input S and output u could be defined, respectively, as n o S ¼ 1 2=3 1=3 0 1=3 2=3 1 ; n o u ¼ 0 1=3 2=3 1

Fig. 3. Fuzzy output membership functions.

The fuzzy sets of S and u can be defined, respectively, as S ¼ NB NM NS ZE PS PM PB ; u ¼ ZE PS PM

PB

where NB represents the negative big, NM represents the negative middle, NS represents the negative small and ZE represents the zero part, PS represents the positive small, PM represents the positive middle and PB represents the positive big. The membership functions of input S and output u are, respectively, shown in Figs. 2 and 3. In the fuzzy logic rules scheme, output u is computed by a mechanism of If–Then rules. Here, the general type of If–Then rules will be used in the following form: Rule (i): If xi is F(xi), then yi is F(yi) where xi are input linguistic variables and yi are output linguistic variables; F(xi) and F(yi) are membership functions. In this paper the fuzzy rules are defined as follows. Rule Rule Rule Rule Rule Rule Rule

1: If S is PB, then u is PB. 2: If S is PM, then u is PM. 3: If S is PS, then u is PS. 4: If S is ZE, then u is ZE. 5: If S is NS, then u is PS. 6: If S is NM, then u is PM. 7: If S is NB, then u is PB.

Finally, the fuzzy outputs need to be converted to precise variables. In this study, the output u can be calculated by the



5

center of area defuzzification and the output u is a scale factor with the gains of Φ11 and Φ22. Therefore the new gains of the observer will be Φ0 11 ¼uΦ11 and Φ0 22 ¼uΦ22.

The resistive drag R is a function of the ship velocity vs and the expression is

5. Simulation and experimental results

and the functional relation is fitted based on the ship experiments data.

Rf ¼ 0:20143–0:059vs þ 0:017 68vs 2

5.1. Simulation results In order to verify the validity of the proposed SMO, the system from Fig. 4 has been implemented in the Matlab/Simulink programming environment and the IPMSM parameters are listed in Table 1. The maximum torque per ampere (MTPA) control is used in the vector control system and a simplified relationship between id and iq can be obtained by taking Taylor's series expansion [20,26] as follows: Ld Lq n2 iq ð20Þ ind ¼

ψf

In the ship electric propulsion system, the load of the propulsion motor is on a propeller as shown in Fig. 4(a); a schematic of the propeller dynamic load mathematical model is showed in Fig. 5 and the parameters values in the model are listed in Table 2. In Fig. 5 J is the propeller advance number, vp is the ship advance speed, Pe is the ship efficient thrust force, Rf is the resistive drag and vs is the ship speed without considering the wake fraction w and it is bigger than vp. In the propeller load model, the torque coefficients Kmj and thrust coefficients Kpj are a function of the advance number J and the function expressions are as follows, which are obtained according to the propeller open-water experimental data: 10K mj ¼ 0:495 43–0:218 32 J–0:209 79 J 2 K pj ¼ 0:38955–0:271 15 J–0:102 56 J 2

Fig. 5. Propeller dynamic load mathematical model.

Table 2 Parameters of propeller model. Propeller diameter Wake fraction Water density Adhesion coefficient Mass of the ship Force reduction factor

Dp ¼3.6 m w¼ 0.1355 ρ ¼1025 kg/m3 k ¼ 1.08 Ms ¼ 15 527 000 kg t ¼0.1548

Fig. 4. Block diagram of sensorless vector control of IPMSM. (a) Overall block diagram of the proposed system. (b) Block diagram of the proposed SMO. (c) Chattering reduced structure of the observer.



6

In the control of speed and current references, the PI control is used to effectively reduce the accumulative errors and using the estimated position and speed of the rotor, the closed sensorless

control of the motor is implemented. The PI parameters of the speed loop are the proportional gain Kps ¼80 and integral gain Kis ¼ 600, the parameters of the q-axis current loop are Kpq ¼0.88

3

120

Motor and Load Torque (N*m)

Motor Estimate speed

Motor Speed (r/min)

100 80 60 40 20 0

0

0.1

0.2

0.3

0.4

x 105 Load Torque Motor Torque

2.5 2 1.5 1 0.5 0

0.5

0

0.1

0.2

time (s)

0

8000

Actual d-axis current Estimate d-axis current

-500

0.5

6000

-1500

5000

-2000

iq (A)

id (A)

0.4

Actual q-axis current Estimate q-axis current

7000

-1000

-2500

4000

-3000

3000

-3500

2000

-4000

1000

-4500

0.3

time (s)

0

0.1

0.2

0.3

0.4

0

0.5

0

0.1

0.2

time (s)

0.3

0.4

0.5

time (s)

Fig. 6. Simulation waveforms obtained by the proposed SMO using sign function. (a) Estimated motor speed. (b) Propulsion IPMSM electromagnetic torque and propeller load torque. (c) Actual and estimate id current. (d) Actual and estimate iq current.

120

3


Motor Speed (r/min)


100 80 60 40 20 0

0

0.1

0.2

0.3

0.4

Motor Torque Load Torque

2.5 2 1.5 1 0.5 0

0.5

x 105

0

0.1

0.2

0

6000

-1500

5000

-2000

id (A)

id (A)

0.5


7000

-1000

-2500

4000

-3000

3000

-3500

2000

-4000

1000

-4500

0.4

8000


-500

0.3

time (s)

time (s)

0

0.1

0.2

0.3

time (s)

0.4

0.5

0

0

0.1

0.2

0.3

0.4

0.5

time (s)

Fig. 7. Simulation waveforms obtained by the proposed SMO using sigmoid function and fuzzy logic. (a) Estimated motor speed. (b) Propulsion IPMSM electromagnetic torque and propeller load torque. (c) Actual and estimated id current. (d) Actual and estimated iq current.



and Kiq ¼3, and those of the d-axis current loop are Kpd ¼0.42, and Kid ¼3. The parameters of the proposed SMO are chosen as follows: k11 ¼k22 ¼ 100, Φ11 ¼ Φ22 ¼2,70,000, Kp ¼0.08, Ki ¼1 and in the sigmoid function a ¼2. Figs. 6 and 7 show the two sets of simulation waveforms when the reference speed is a step signal. In the simulation, the reference speed is changed from 0 to 100 r/min. Fig. 6 shows the simulation waveform obtained by the proposed SMO using a sign function. Fig. 7 gives the waveform obtained by the proposed SMO using sigmoid function and fuzzy logic. It can be seen from Figs. 6 and 7 that the motor speed can be estimated from proposed SMO and chattering phenomenon is reduced when the

7

sign function is replaced by a sigmoid function with one use of fuzzy logic. Fig. 8 displays the estimated speed waveforms using the technique of model reference adaptive system (MRAS) and proposed SMO in this paper. It can be seen from Fig. 8(a) and (b) that the system using SMO method has faster convergence speed than the system using the MRAS and because of the discrete switch control in the SMO, the chattering problem in the steady state speed is bigger than that of the system using MRAS. But from Fig. 7(a), it can be seen that the chattering problem will be reduced mostly when using a sigmoid function and fuzzy logic.

120

120


Motor Estimated Speed 100

Motor Speed (r/min)

Motor Speed (r/min)

100 80 60 40

60 40 20

20 0

80

0

0.1

0.2

0.3

0.4

0

0.5

0

0.1

0.2

time (s)

0.3

0.4

0.5

time (s)

Fig. 8. Estimated speed waveforms obtained by the proposed SMO and MRAS. (a) Estimated motor speed using SMO. (b) Estimated motor speed using MRAS.

10

120

x 104

Motor Estimate speed Motor and Load Torque (N*m)

Motor Torque

Motor Speed (r/min)

100 80 60 40 20 0

0

0.5

1

1.5

2

2.5

6

4

2

0

3

Load Torque

8

0

0.5

1

2

2.5

3

2

2.5

3

3500

100


0


3000

-100

2500

iq (A)

-200

id (A)

1.5

time (s)

time (s)

-300

2000 1500

-400 1000

-500

500

-600 -700

0

0.5

1

1.5

time (s)

2

2.5

3

0

0

0.5

1

1.5

time (s)

Fig. 9. Simulation waveforms obtained by the proposed SMO using sigmoid function and fuzzy logic. (a) Estimated motor speed. (b) Propulsion IPMSM electromagnetic torque and propeller load torque. (c) Actual and estimated id current. (d) Actual and estimated iq current.



8

120

120

60 40

100

Motor Speed (r/min)

Motor Speed (r/min)

Motor Speed (r/min)

80

80 60 40

60 40

0

0.2

0.4

0.6

0

0.8

20

0

0.2

0.4

0.6

0

0.8

120

120

60 40 20

80 60 40 20

0.6

0

0.8

0.6

0.8

Motor Estimated Speed

100

Motor Speed (r/min)

Motor Speed (r/min)

80

0.4

0.4

120

100

100

0.2

0.2

time (s)



0

0

time (s)

time (s)

Motor Speed (r/min)

80

20

20

0


100

100

0

120 Motor Estimated Speed


80 60 40 20

0

0.2

0.4

time (s)

0.6

0

0.8

0

0.2

0.4

time (s)

0.6

0.8

time (s)

Fig. 10. Estimated speed results obtained by the proposed SMO when motor parameters changed. (a) Only stator resistance R changed. (b) Only permanent magnet flux linkage ψf changed. (c) Only d axis inductances Ld changed. (d) Only q axis inductances Lq changed. (e) Ld and Lq changed. (f) All motor parameters R, ψf, Ld and Lq changed.

Experiments Data

Host Computer

Control Signal

Experiments Data

Control Signal

+ Inverter

A C

Rectifier

B C

+ DC Voltage Source

Control Signal

C

Inverter

Control Board I

Control Board II Speed Set

-

Torque Set

Speed Control Coupled Connector

DC Bus

Three Phase Voltage Torque Source Control

Load Induction Motor Gear Box Ratio (1:3)

Propulsion IPMSM

Coupled Connector Base of the Induction Motor

Motor Experimental Platform Fig. 11. Schematic of the test platform for the IPMSM drive.

Fig. 9 displays the simulation waveforms when the motor reference speed is changed from 50 to 100 r/min. As can be seen from Fig. 9(a), when the reference speed is changed the proposed SMO can effectively obtain the estimated rotor speed. Fig. 9 (b) shows the electromagnetic torque of the IPMSM and the propeller load torque. The actual and estimated id, iq current are shown in Fig. 9(c) and (d), respectively. In order to verify the robustness of the system, some experiments have been researched with the change of motor parameters. The proposed SMO that based on the sliding mode control theory

and it presents promising features: disturbances rejection and strong robustness to parameter deviations [32]. So the SMO technique helps increase the overall robustness of the system. Fig. 10 shows the estimated speed results when motor parameters used in the SMO have been changed. Fig. 10(a) gives the result when the stator resistance R increases from 1.64 mΩ to 3.28 mΩ at 0.2 s and then decreases from 3.28 mΩ to the initial value 1.64 mΩ at 0.6 s; Fig. 10(b) shows the waveform when the ψf changes from 3.55 Wb to 3.3 Wb at 0.2 s and then increases to 3.55 Wb at 0.6 s; Fig. 10(c) shows the waveform when Ld is



changed from 0.23 mH to 0.345 mH at 0.2 s and then to the initial value 0.23 mH at 0.6 s and Fig. 10(d) displays the result when Lq decreased from 0.48 mH to 0.384 mH at 0.2 s and then increased to the value 0.48 mH at 0.6 s. Finally Fig. 10(e) shows the waveform whenthe Ld and Lq are changed from 0.23 to 0.345 mH, 0.48 to 0.384 mH at 0.2 s and to the initial value at 0.6 s simultaneously. In Fig. 10(f) all parameters R, ψf, Ld and Lq are changed simultaneously and parameters setting values are as the same as in Fig. 10(a)–(d). It can be seen from Fig. 10 that, when the motor parameters changes, the estimated speed can still converge to the actual value, which verifies the robustness of the proposed approach. 5.2. Experimental results To further verify the performance of the proposed SMO for estimating motor speed, in this paper, the vector control platform of IPMSM based on SMO is constructed and the experimental setup is shown in Fig. 11. A Texas Instruments TMS320F2812 DSP is employed as the digital controller, and the space vector modulation algorithm is used as the modulation strategy. An induction motor through a gear box is mechanically coupled with the IPMSM Table 3 Parameters of experiment IPMSM. UN ¼ 148 V P¼ 7.5 kW nN ¼420 r/min ψf ¼ 1.06 Wb R¼ 0.228 Ω Ld ¼1.24 mH Lq ¼1.63 mH nP ¼ 3

Rated voltage Rated power Rated speed Flux linkage Stator resistance D-axis inductance Q-axis inductance Pole pairs number

1) Steady-state performance: Figs. 12 and 13 show the waveforms when the propulsion IPMSM runs with propeller load and the reference speeds are 50 and 100 r/min, respectively. Fig. 12 shows the waveforms of the motor speed at 50 r/min and Fig. 13 displays the waveforms of motor speed at 100 r/min when the SMO method is based on the sign function or sigmoid function and fuzzy logic. As can be seen from Figs. 12 and 13, compared with the sign function used in the SMO, the waveforms of the estimated rotor speed obtained by the new SMO using the sigmoid function and fuzzy logic are smooth, and the chattering is reduced. 2) Dynamic performance: Fig. 14 shows the experimental results of the motor speed and motor torque with the propeller load torque when the mechanical motor is accelerated from 100 to 150 r/min. Fig. 14(a) and (b) shows the speed and torque for the SMO using the sign function and Fig. 14(c) and (d) displays the results for SMO using the sigmoid function and fuzzy logic.


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to produce the load torque. The IPMSM works in the speed control mode while the induction motor works in the torque control mode. The DC voltage that supplies power to the IPMSM is 220 V and the three phases supply voltage for the load induction motor is 380 V. The parameters of the IPMSM are listed in Table 3; in the experimental system the parameters of the current PI regulator are Kpc ¼5 and Kic ¼ 20, and the parameters of the speed loop are Kps1 ¼30 and Kis1 ¼15. The parameters of the proposed SMO are chosen as follows: k0 11 ¼k0 22 ¼100, Φ0 11 ¼ Φ0 22 ¼120, Kp1 ¼0.5, Ki1 ¼ 2 and the sigmoid function a0 ¼2.

It can be seen that during the motor acceleration operation, the estimated speed tracks the reference speed well and the estimated motor speed obtained by the method using sigmoid function and

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Fig. 12. Operating waveforms obtained by the proposed SMO. (a) Estimated motor speed. (b) Motor torque and propeller load torque: motor speed 50 r/min using sign function. (c) Estimated motor speed. (d) Motor torque and propeller load torque: motor speed 50 r/min using sigmoid function and fuzzy logic.



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Fig. 15. Experimental results when the motor accelerated from 150 to 180 r/min. (a) Estimated motor speed. (b) Motor torque and propeller load torque: motor using sign function. (c) Estimated motor speed. (d) Motor torque and propeller load torque: using sigmoid function and fuzzy logic.

fuzzy logic can accurately converge to their actual values. During the acceleration from 100 to 150 r/min, the maximum value of the load torque is 25 N m and the motor torque is 80 N m. Because the ratio of the gear box is 1:3, the motor torque is three times the load torque and the friction torque of the system is 5 N m. Fig. 15 shows the waves of the motor speed and motor torque when the speed increases from 150 to 180 r/min.

6. Conclusion In this paper, a new SMO is proposed to estimate the rotor speed of the electric ship propulsion IPMSM and the model of the propeller load has been established. In the SMO the low-pass filter and the method of arc-tangent calculation of extended EMF or PLL technique are not used and the stability of the new SMO has been proved using the Lyapunov stability analysis. In order to reduce system chattering the sign function is replaced by the sigmoid function and the switching gains are adjusted based on the fuzzy logic rules. The performance of the sensorless control system was verified with steady state velocities (50 and 100 r/min) and dynamic acceleration process (from 100 to 150 r/min and 150 to 180 r/min ) to ensure its fast response characteristics and simulation and experimental results validate the feasibility and effectiveness of the new SMO for estimating the rotor speed of the IPMSM.

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A Practical Torque Estimation Method for Interior Permanent Magnet Synchronous Machine in Electric Vehicles.

Adaptive fuzzy dynamic surface control for the chaotic permanent magnet synchronous motor using Nussbaum gain.

Sliding mode output feedback control based on tracking error observer with disturbance estimator.

Neural network-based adaptive dynamic surface control for permanent magnet synchronous motors.

Current Sensor Fault Diagnosis Based on a Sliding Mode Observer for PMSM Driven Systems.

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A swarm intelligence-based tuning method for the Sliding Mode Generalized Predictive Control.

High-throughput search for new permanent magnet materials.

Optimal second order sliding mode control for linear uncertain systems.

Optimal second order sliding mode control for nonlinear uncertain systems.

A novel adaptive switching function on fault tolerable sliding mode control for uncertain stochastic systems.

Tensor product model transformation based adaptive integral-sliding mode controller: equivalent control method.

Second-order sliding mode control for DFIG-based wind turbines fault ride-through capability enhancement.

An orientation measurement method based on Hall-effect sensors for permanent magnet spherical actuators with 3D magnet array.

A new design of robust H∞ sliding mode control for uncertain stochastic T-S fuzzy time-delay systems.