Permanent magnet synchronous motor driving system robust current observer based on single direct current bus current sensor and design method

Abstract

The invention discloses a permanent magnet synchronous motor driving system robust current observer based on a single direct current bus current sensor and a design method, and belongs to the technical field of permanent magnet synchronous motor driving. In order to solve the problems that an existing single direct-current bus current sensor control strategy is low in current reconstruction precision and an existing observer is reduced in performance during dynamic response and parameter change, a dq-axis current observer is introduced into a pulse shift method to filter reconstructed current so as to suppress current harmonics and distortion, and the current reconstruction precision is improved. According to the method, the optimal correction gain of the observer is deduced according to the theory of a Lipschitz nonlinear system, the gain is obtained through a gradient method, meanwhile, the influence of the rotating speed of the motor is eliminated through a rotating speed decoupling item, so that the performance of the needed observer is guaranteed, and on the basis, the robustness of the current observer is enhanced through a disturbance compensation item.

Description

Technical Field

[0001] The present invention belongs to the technical field of permanent magnet synchronous motor drives, and particularly relates to a robust current observer for a permanent magnet synchronous motor drive system and a design method thereof. Background Art

[0002] Due to advantages such as fast dynamic response, high power density, and high efficiency, permanent magnet synchronous motors (PMSMs) have been widely used in many fields such as electric vehicles, household appliances, and aerospace. Usually, two or three current sensors are used at the three-phase output to achieve closed-loop current control, and a current sensor is installed at the DC bus for protection. Current sensors (such as Hall effect sensors and shunt resistors and their peripheral circuits) account for 9.7% of the total cost of the motor drive system. Therefore, current sensors will inevitably increase the cost, volume, and complexity of the motor drive system. In addition, due to environmental conditions or physical damage, current sensors may malfunction during operation, which will affect the current control performance and even cause the motor to stop. To improve the reliability of the permanent magnet synchronous motor drive system and reduce costs, control strategies for reducing current sensors have been widely studied.

[0003] Control methods for reducing current sensors mainly focus on two categories: sensorless control and single current sensor control. In sensorless control, the current is simulated based on the motor model. Chaoui et al. proposed a direct voltage control method that does not use a current loop, thus eliminating the current sensor. However, current sensorless control is sensitive to parameter changes and has potential risks due to the lack of actual motor current feedback. In single current sensor control, the method of reconstructing three-phase currents by measuring a specific current is called the phase current reconstruction (PCR) strategy, and this strategy has been widely studied.

[0004] Based on the relationship between the DC bus current and the phase current under the effective voltage vector, the three-phase current can be reconstructed by only measuring the DC bus current, which is called single DC bus current sensor control. However, when the period of the effective voltage vector is not sufficient to accurately measure the DC bus current, current reconstruction dead zones (CRDZs) will appear in the sector boundary region and low modulation ratio region, resulting in a decrease in the accuracy of the reconstructed current. Some researchers extend the duration of the effective voltage vector by modifying the pulse width modulation (PWM) waveform. The measurement vector insertion method is proposed in "Phase Current Reconstruction for AC Motor Drives Using a DC Link Single Current Sensor and Measurement Voltage Vectors", that is, a measurement vector is inserted at the end of each PWM period. However, the amplitude of the synthesized voltage vector will decrease, and the DC bus voltage needs to be increased. Without changing the duty cycle, the pulse shift method (SSPS) extends the action time of the effective voltage vector by shifting one or two PWM waveforms. However, the upper limit of the PCR range allowed by the SSPS method is only about 3.5% of the sampling period. Based on fixed sampling points, a three-state PWM technique is proposed in "A Three-Phase Current Reconstruction Technique Using Single DC Current Sensor Based on TSPWM", and the current reconstruction error is reduced. A random PWM strategy is proposed by double sampling the current values of complementary non-zero vectors within one PWM period. "Saliency-Based Sensorless Control Using Current Derivative in IPM SM Drives With Single DC-Link Current Sensor" proposes three effective vector PWM, in which three effective vectors are used for voltage synthesis to eliminate the CRDZ. However, the PWM waveforms of these methods are asymmetric, which will introduce additional current harmonics and increase the total harmonic distortion (THD). To ensure the symmetry of the PWM waveform, some hybrid PWM methods replace the zero voltage vector with the effective voltage vector and compensate for the duration. Due to the absence of the zero voltage vector, the fluctuations of the DC bus current, THD, and switching losses will increase.

[0005] The multi-branch sampling method can eliminate CRDZ by using a current sensor that simultaneously samples the sum of currents in multiple branches. After placing the current sensor at a specific location, Xu et al. proposed a zero-voltage vector sampling method, which can eliminate CRDZ in the sector boundary region and the low modulation ratio region. However, since this method samples the current at the zero-voltage vector, CRDZ still exists in the high modulation ratio region of the space vector hexagon. "Single-Current-Sensor Control for PMSM Driven by Quasi-Z-Source Inverter" introduced a quasi-Z-source inverter and achieved PCR in the high modulation ratio region. However, the circuit structure of this method is too complex. Some scholars have also proposed a multi-position coupled sampling method, which can shift CRDZ to the six corner regions of the space vector hexagon. However, these methods are only applicable to discrete switching devices and not to intelligent power modules (IPM), which limits the application of the multi-branch sampling method.

[0006] The observer method can filter (estimate) the reconstructed current without changing the PWM waveform and can maintain the symmetry of the three-phase PWM waveform. The Luenberger-based αβ-axis observer can effectively reduce the total harmonic distortion of the input current compared to the improved PWM method. However, it is sensitive to parameter changes. Wolbank and Macheiner proposed an adaptive phase current observer for induction motors, and Saritha et al. proposed an asymptotic observer. Although the observer method can ensure the symmetry of the PWM waveform, minimize current harmonics, and thus achieve excellent steady-state performance, its performance may degrade during dynamic response and parameter changes. Summary of the Invention

[0007] The present invention aims to solve the problems of low accuracy of the reconstructed current in the existing single DC bus current sensor control strategy and the performance degradation of the existing observer during dynamic response and parameter changes.

[0008] A robust current observer for a permanent magnet synchronous motor drive system based on a single DC bus current sensor, the observer is as follows:

[0009]

[0010]

[0011] Wherein, represents the differentiation with respect to time t; represents the estimated current on the dq axis; L opt is the correction gain of the dq axis current observer; i dq_rec is the three-phase reconstructed current i abc_recThe current calculated through the Clarke transformation T under the constant amplitude constraint 3s / 2s and through the Park transformation T 2s / 2r ; k d1 and k d2 are the correction coefficients of the disturbance compensation term; k de1 and k de2 represent the decoupling coefficients of the dq-axis decoupling term; ω e represents the electrical angular velocity; L d , L q are the stator inductances of the d-axis and q-axis; R s is the stator resistance; the subscript o represents the rated value of the corresponding parameter.

[0012] Furthermore, the process of calculating the three-phase reconstructed current i abc_rec through the Clarke transformation T under the constant amplitude constraint 3s / 2s and through the Park transformation T 2s / 2r to obtain the current i dq_rec includes:

[0013] First, the three-phase reconstructed current i abc_rec obtained by controlling through a single DC bus current sensor, and then through the Clarke transformation T under the constant amplitude constraint 3s / 2s and through the Park transformation T 2s / 2r is calculated as follows:

[0014]

[0015] where θ e is the electrical angular position of the rotor.

[0016] Furthermore, the electrical angular position θ e = P n θ m , where θ m is the mechanical position of the rotor, and P n is the number of pole pairs.

[0017] Furthermore, the electrical angular velocity ω e = P n ω m， , where P n is the number of pole pairs, and ω m is the mechanical angular velocity of the rotor.

[0018] Furthermore, the correction gain L opt of the dq-axis current observer is obtained as follows:

[0019] First, the error dynamic equation considering concentrated disturbance is determined as:

[0020]

[0021] Among them, d dq (i dq ) = d dq (t) represents the actual concentrated disturbance, and d dq (i dq ) satisfies the Lipschitz property with a Lipschitz constant γ; L is the correction gain of the linear dq-axis current observer, represents the estimated current on the dq-axis;

[0022] Construct a Lyapunov function with a positive definite matrix P:

[0023]

[0024] Take the derivative of V and combine the Lipschitz property to obtain the upper bound form of; Based on the upper bound form of, obtain:

[0025]

[0026] When the eigenvalues λ of (A o - L) satisfy the formula , where represents the real part of the corresponding eigenvalue, κ(Q) is the condition number of the matrix Q, and Q is the eigenvector matrix of the matrix (A o - L); then there exists a positive definite matrix P = P T satisfying the following Riccati equation:

[0027]

[0028] where ∈ represents a constant greater than 0, and I represents the identity matrix;

[0029] Therefore, this indicates that the dq-axis current observer is asymptotically stable;

[0030] Obtain the optimal L by minimizing κ(Q), that is, L opt .

[0031] Furthermore, the process of obtaining the optimal L by minimizing κ(Q), that is, L opt includes:

[0032] First, use the gradient-based method to maximize the following formula

[0033]

[0034] where λ l represents the smallest corresponding eigenvalue;

[0035] For the process of maximizing based on the gradient method of L opt for tuning, during the process of tuning L opt for tuning, set the non - diagonal elements of L opt to be exactly equal to the corresponding non - diagonal elements of A o , that is, introduce the speed decoupling term, and represent L opt as:

[0036]

[0037] where l1 and l2 are obtained through tuning.

[0038] A design method of a robust current observer for a permanent magnet synchronous motor drive system based on a single DC - bus current sensor includes the following steps:

[0039] S1. Modeling of a permanent magnet synchronous motor with uncertainties:

[0040] Represent the current dynamic characteristics of the PMSM in the dq rotor reference frame as:

[0041]

[0042] where represents the differentiation with respect to time t; i d (t), i q (t) and u d (t), u q (t) represent the stator currents and voltages of the d - axis and q - axis respectively; R s is the stator resistance, L d , L q are the stator inductances of the d - axis and q - axis, and the subscript o represents the rated value of the corresponding parameter; ψ f is the permanent - magnet flux linkage; ω e represents the electrical angular velocity; d d (t), d q (t) are the concentrated disturbances on the d - axis and q - axis,

[0043] Define the state vector i dq (t) = [i d (t) i q (t)] T , the input vector u dq (t) = [u d (t) u q (t) - ω e ψ fo T and the concentrated disturbance d​dq (t) = [d d (t)d q (t)] T ;

[0044] S2. Design a new robust current observer based on single DC bus current sensor control:

[0045] S201. Design the correction gain of the current observer with concentrated disturbance prediction:

[0046] Estimate the current on the dq axes Estimate the concentrated disturbance, and combine the estimated concentrated disturbance to obtain the dq-axis current observer:

[0047]

[0048] where, represents the estimated current on the dq axes; L is the correction gain of the linear dq-axis current observer;

[0049] Combine the dq-axis current dynamics and convert them into the vector form of the permanent magnet synchronous motor state space, and the error dynamics equation considering the concentrated disturbance is:

[0050]

[0051] where, d dq (i dq ) = d dq (t) represents the actual concentrated disturbance; d dq (i dq ) satisfies the Lipschitz property and has a Lipschitz constant γ;

[0052] Construct a Lyapunov function with a positive definite matrix P Take the derivative of V and combine the Lipschitz property to obtain the upper bound form of; Based on the upper bound form of obtain:

[0053]

[0054] When the eigenvalues λ of (A o -L) satisfy the equation where represents the real part of the corresponding eigenvalue, κ(Q) is the condition number of the matrix Q, and Q is the eigenvector matrix of the matrix (A o -L); then there exists a positive definite matrix P = P T satisfying the following Riccati equation:

[0055]

[0056] Among them, ∈ represents a constant greater than 0, and I represents the identity matrix;

[0057] Therefore, This indicates that the dq-axis current observer is asymptotically stable;

[0058] The optimal L is obtained by minimizing κ(Q), that is, L opt ;

[0059] S202. Design the disturbance compensation term and design the current observer:

[0060] Design the disturbance compensation term:

[0061]

[0062] Among them, k de1 and k de2 represent the decoupling coefficients of the dq-axis decoupling terms;

[0063] Finally, the current observer is designed as:

[0064]

[0065] Among them, i dq_rec is the three-phase reconstructed current i obtained by controlling through a single DC bus current sensor abc_rec under the constant amplitude constraint through the Clarke transformation T 3s / 2s and the current calculated through the Park transformation T 2s / 2r ;

[0066] Furthermore, the concentrated disturbances d d (t), d q (t) on the d-axis and q-axis are as follows:

[0067]

[0068] Among them, R s =R so +ΔR s , L d =L do +ΔL d , L q =L qo +ΔL q , ψ f =ψ fo +Δψ f , Δ represents the change in the corresponding parameters of the PMSM; ε d , ε q represent the unmodeled slow-varying disturbances;

[0069] Furthermore, the state space of the permanent magnet synchronous motor in the vector form obtained by dynamically converting the dq-axis current is as follows:

[0070]

[0071] Among them,

[0072] Furthermore, the concentrated disturbance estimated by the dq-axis estimated current is as follows:

[0073]

[0074] where p is a differential operator.

[0075] Beneficial effects:

[0076] The current observer proposed by the present invention filters the current reconstructed by the single DC bus current sensor control reconstruction without delay, improving the accuracy of the reconstructed current after the pulse shift method; moreover, the present invention derives the optimal correction gain of the proposed current observer, which can be obtained by the gradient method, and by introducing a speed decoupling term, the optimal performance of the observer is ensured in a wide speed operation range. In addition, the present invention improves the robustness of the proposed current observer by designing a disturbance compensation term, and can resist the influence of permanent magnet synchronous motor parameter changes and other interferences. The present invention can still ensure good performance during the transient process and parameter changes. Description of the drawings

[0077] Figure 1 is the topology diagram of the three-phase two-level permanent magnet synchronous motor drive system.

[0078] Figure 2 is the curve of the bus current establishment process.

[0079] Figure 3 is the current reconstruction blind area diagram.

[0080] Figure 4 is the PWM waveform diagram under the pulse width shift method.

[0081] Figure 5 is ω e Comparison diagram with and without speed decoupling term when increasing from 0 to 1000π rad / s.

[0082] Figure 6 is the system block diagram of the robust current observer proposed by the present invention.

[0083] Figure 7 is the experimental platform in the embodiment.

[0084] Figure 8 Phase current comparison diagram at a load torque of 2.39 N·m and a speed of 1000 r / min.

[0085] Figure 9 Experimental results of the actual and reconstructed phase-a current before and after applying the proposed RCO method at a speed of 1000 r / min and a load of 0.5 N·m.

[0086] Figure 10 Phase current comparison diagram in the low modulation ratio region at a speed of 300 r / min and a load of 0.5 N·m.

[0087] Figure 11 Phase current comparison diagram of the reconstructed phase-a current when the PMSM suddenly decelerates from 1000 r / min to 0 under a load of 2.39 N·m.

[0088] Figure 12 Phase current comparison diagram of the reconstructed phase-a current when the load torque rapidly increases from 0 to 2.39 N·m at 1000 r / min.

[0089] Figure 13 Robustness comparison diagram of the dq-axis inductance variation at a speed of 1000 r / min and a load of 2.39 N·m.

[0090] Figure 14 Robustness comparison diagram of the stator resistance and the permanent magnet flux linkage at a speed of 1000 r / min and a load of 2.39 N·m.

[0091] Figure 15 Experimental results with and without the speed decoupling term at a speed of 2000 r / min and a load of 1.26 N·m. Detailed implementation

[0092] Before explaining the robust current observer of the permanent magnet synchronous motor drive system based on a single DC bus current sensor of the present invention in combination with this implementation, first explain the basic principle of the single DC bus current sensor control. Figure 1 Shows the topology of a permanent magnet synchronous motor drive system using a three-phase two-level voltage source inverter, where the current sensor is installed at the positive end of the DC bus. The switching states of the two switching devices in a specific leg of the abc three phases are defined as S y (y = a, b, c). S y = 1 indicates that the upper switching device of the y phase is conducting and the lower switching device is off, and S y = 0 is the opposite. As shown in Table 1, according to the space vector pulse width modulation (SVPWM) method, Figure 1 The six switching devices in can generate eight switching states and the corresponding voltage vectors It contains two zero-voltage vectors and six effective voltage vectors After defining the positive reference direction of the current in Figure 1 there is a specific relationship between the DC bus current and the three-phase currents under the eight voltage vectors, as shown in Equation (1) and summarized in Table 1.

[0093] i dc = S a i a + S b i b + S c i c (1)

[0094] where, i dc is the DC bus current, i a , i b , i c are the three-phase currents;

[0095] Table 1 Relationship between eight switching states and the reconstructed current

[0096] <![CDATA[V x > <![CDATA[V0]]> <![CDATA[V1]]> <![CDATA[V2]]> <![CDATA[V3]]> <![CDATA[V4]]> <![CDATA[V5]]> <![CDATA[V6]]> <![CDATA[V7]]> <![CDATA[S a S b S c > 000 100 110 010 011 001 101 111 <![CDATA[i dc > 0 <![CDATA[+i a > <![CDATA[-i c > <![CDATA[+i b > <![CDATA[-i a > <![CDATA[+i c > <![CDATA[-i b > 0

[0097] In the SVPWM method, each switching cycle contains two different effective voltage vectors, from which the corresponding two-phase currents can be reconstructed. Assuming a balanced three-phase system, i.e., the zero-sequence current is zero, then the third-phase current can be obtained from i a + i b + i c = 0. In practical applications, since the turn-on and turn-off of the switching devices and the current sampling are not instantaneous, a minimum current sampling time T min (as shown in Equation (2)) is required to ensure reliable sampling of the DC bus current.

[0098] T min = T dead + T sett + T adc (2)

[0099] where, T dead is the dead time to prevent short-circuit between the upper and lower arms of the inverter; T sett is the stabilization time of the switching device, including the turn-on delay time t d(on) , the commutation time t rI , the voltage drop time t fV , the overshoot time t o ; T adc is the analog-to-digital conversion (ADC) time.

[0100] The establishment process of the DC bus current is as Figure 2 shown, where ug Represents the gate signal of the switching device.

[0101] If the duration of the effective voltage vector is less than T min , the DC bus current sensor cannot accurately sample, nor can it reconstruct the corresponding phase current, resulting in distorted reconstructed current. Therefore, these regions are called current reconstruction blind zones, located in the low modulation ratio regions and sector boundary regions of the space vector hexagon, as Figure 3 shown.

[0102] The pulse shift method (SSPS) can extend the duration of the effective voltage vector by shifting the two phases with the highest and lowest duty cycles in the SVPWM waveform, thus eliminating the current reconstruction blind zone. Taking the first sector as an example, as shown by the black line in Figure 4 , the PWM waveform duration is less than T min , resulting in reconstruction failure. By advancing the S with the highest duty cycle a and delaying the S with the lowest duty cycle c , as shown by the red line waveform in Figure 4 , it can ensure effective sampling, and three-phase currents can be reconstructed even in the current reconstruction blind zone. Note: Generally, the turn-on time of IGBT and MOSFET devices is shorter than the turn-off time. Therefore, it is recommended to sample in the turn-on half cycle of the switching period, that is, Figure 4 the left half cycle in.

[0103] However, under the pulse shift method, the three-phase PWM waveforms will become asymmetric, resulting in distorted phase currents and increasing the total harmonic distortion (THD) of the reconstructed current, which may even cause noise and reduce the motor control performance. Therefore, this problem must be solved through strategies such as observers and current prediction to improve the accuracy of the reconstructed current under single DC bus current sensor control.

[0104] Based on the above basic principle of single DC bus current sensor control, the following will be described in detail in combination with specific embodiments. Specific Embodiment 1:

[0106] This embodiment is a robust current observer for a permanent magnet synchronous motor drive system based on a single DC bus current sensor and its design process, as follows:

[0107] S1. Modeling of the permanent magnet synchronous motor with uncertainties:

[0108] The linear dq-axis current observer has a simple structure and can filter the current without delay. However, the traditional linear dq-axis current observer is vulnerable to the influence of parameter variations and other disturbances in the permanent magnet synchronous motor drive system. Therefore, based on the traditional linear dq-axis current observer, this invention analyzes the impact of system uncertainties.

[0109] Assuming that the high-order harmonic components in the inductance and magnetic flux of the permanent magnet synchronous motor (PMSM) can be neglected, the current dynamic characteristics of the PMSM in the dq rotor reference coordinate system can be expressed as:

[0110]

[0111] Where, represents the differentiation with respect to time t; i d (t), i q (t) and u d (t), u q (t) represent the stator currents and voltages on the d-axis and q-axis respectively; R s is the stator resistance, L d , L q are the stator inductances on the d-axis and q-axis, and the subscript o represents the rated value of the corresponding parameter; ψ f is the permanent magnet flux linkage; ω e represents the electrical angular velocity; d d (t), d q (t) are the concentrated disturbances on the d-axis and q-axis, and these disturbances may be caused by parameter variations and slowly varying disturbances, and the specific forms are as follows:

[0112]

[0113] Where, R s = R so + ΔR s , L d = L do + ΔL d , L q = L qo + ΔL q , ψ f = ψ fo + Δψ f , Δ represents the change in the corresponding parameter of the PMSM; ε d , ε q represent the unmodeled slow-varying disturbances.

[0114] According to Equation (3), by defining the state vector i dq (t) = [i d (t) i q (t)] T and the input vector u dqi(t) = [u d i(t)u q (t) - ω e ψ fo T and the concentrated disturbance d dq d(t) = [d d d(t)d q (t)] T After that, the dq-axis current dynamics can be transformed into the vector form of the permanent magnet synchronous motor state space (5):

[0115]

[0116] Among them,

[0117]

[0118] Without considering the concentrated disturbance, the linear dq-axis current observer can be established as follows:

[0119]

[0120] Among them, represents the estimated current on the dq-axis; L is the correction gain of the linear dq-axis current observer.

[0121] Subtracting Equation (6) from Equation (5), the error dynamic equation of this current state observer can be obtained as follows:

[0122]

[0123] Among them, is the dq-axis current estimation error.

[0124] Since it has been assumed previously that the concentrated disturbance consists of parameter variations and slowly varying disturbances, these disturbances are continuous and slowly varying compared with the control period, that is So d dq (t) can be regarded as a constant D.

[0125] Taking the Laplace transform of Equation (7) gives:

[0126]

[0127] Among them, represents the Laplace transform, s represents the complex variable in the Laplace transform;

[0128]

[0129] According to Equation (8) and the final value theorem, the steady-state current error can be deduced as follows:

[0130] ​

[0131] It can be inferred from the above equations that if the concentrated disturbance is not considered in the current state observer, when disturbances such as parameter variations occur, there will be a steady-state error between the estimated dq-axis currents and the actual dq-axis currents. This steady-state error will cause an undesired change in the estimated phase current amplitude, thereby triggering torque fluctuations at twice the electrical frequency and affecting the control performance of the motor.

[0132] S2. Design of a novel robust current observer based on single DC-bus current sensor control:

[0133] To improve the accuracy of the reconstructed current and the robustness of the current observer, a novel robust dq-axis current observer for single DC-bus current sensor control is proposed here. The optimal correction gain tuning principle and speed decoupling design of the proposed observer are given in this embodiment. In addition, a disturbance compensation term is proposed to improve the robustness of the proposed observer.

[0134] S201. Correction gain design of the current observer with concentrated disturbance prediction:

[0135] According to Equation (4), the concentrated disturbance can be estimated through the dq-axis estimated current as follows:

[0136]

[0137] where p is a differential operator.

[0138] Combining the estimated concentrated disturbance the dq-axis current observer can be expressed as follows:

[0139]

[0140] Subtracting Equation (11) from Equation (5), the error dynamic equation considering the concentrated disturbance can be obtained as:

[0141]

[0142] where d dq (i dq ) = d dq (t) represents the actual concentrated disturbance.

[0143] Since d dq (i dq ) is assumed to be continuous and slowly varying, d dq (i dq ) is differentiable, its derivative is bounded, and it can be regarded as satisfying the Lipschitz condition. d dq (i dq) has a Lipschitz constant γ and satisfies:

[0144]

[0145] Construct a Lyapunov function with a positive definite matrix P:

[0146]

[0147] Taking the derivative of it gives:

[0148]

[0149] where,

[0150]

[0151] Using the Lipschitz property of Equation (13), we can obtain The upper bound of is:

[0152]

[0153] From the properties of the Euclidean norm and using

[0154]

[0155] Deriving from Equation (16) gives:

[0156]

[0157] When the eigenvalue λ of (A o -L) satisfies Equation (18), then there exists a positive definite matrix P = P T Satisfying the Riccati equation shown in Equation (19):

[0158]

[0159] where, represents the real part of the corresponding eigenvalue, κ(Q) is the condition number of matrix Q, and Q is the eigenvector matrix of matrix (A o -L);

[0160]

[0161] where, ∈ represents a constant greater than 0, and I represents the identity matrix;

[0162] Therefore, This shows that the dq-axis current observer of Equation (11) is asymptotically stable.

[0163] Generally, the smaller the condition number, the greater the distance from non - observability, which means that the optimal L can be obtained by minimizing κ(Q), that is, L opt . A gradient - based method can be designed to maximize Equation (20). Since the analytical gradient of L opt is relatively complex, numerical methods such as the central difference method can be used to approximate the gradient.

[0164]

[0165] Among them, λ l represents the eigenvalue that minimizes Equation (20);

[0166] The off - diagonal elements of A o contain ω e , but in practical applications, ω e is not constant. Therefore, during the tuning process of L opt , we can assume ω e = 0, and then obtain the optimal diagonal matrix L opt through Equation (20). At this time, L opt is a constant matrix, while (A o - L opt ) changes with ω e , resulting in the observer being affected by ω e , and it is impossible to ensure that the observer performance reaches the optimal. To eliminate the influence of ω e on the observer, the off - diagonal elements of L opt can be set to be exactly equal to the corresponding off - diagonal elements of A o , that is, the speed decoupling term is introduced. In this case, L opt can be expressed as:

[0167]

[0168] Among them, l1 and l2 are obtained by tuning through Equation (20).

[0169] Assume l1 = l2 = 500, L do = L qo and ω e increases from 0 to 1000π rad / s. The comparison of the pole distributions of (A o - L opt ) without and with the speed decoupling term is shown as Figure 5 . It can be seen that without the speed decoupling term, as ω e increases, the imaginary part of the pole increases monotonically, which will cause serious oscillations in the current observer and deteriorate the system performance. In contrast, the poles with the speed decoupling term are not affected by ω eThe influence can maintain the optimal observer performance tuned by Equation (20).

[0170] S202. Design of the disturbance compensation term:

[0171] In Equation (10), it is difficult to measure the amplitude of parameter variation, which makes it difficult to accurately obtain the total disturbance. As analyzed above, the total disturbance will cause the actual dq-axis current i dq and the estimated dq-axis current to have a steady-state error. These errors will cause torque fluctuations at twice ω e and, when the steady-state error is large enough, will cause the motor to stop running. To eliminate the steady-state error, an integral-form disturbance compensation term is proposed, as shown in Equation (22):

[0172]

[0173] However, there is a cross-coupling component between the d-axis and q-axis in Equation (10), as shown in Equation (23), which will reduce the estimation accuracy and dynamic performance of the dq-axis current observer after introducing the disturbance compensation component:

[0174]

[0175] To eliminate the cross-coupling term, a d-axis decoupling term and a q-axis decoupling term are respectively substituted into Equation (22). The disturbance compensation term proposed in the present invention is as follows:

[0176]

[0177] where k d1 and k d2 are the correction coefficients of the disturbance compensation term; k de1 and k de2 represent the decoupling coefficients of the dq-axis decoupling terms and can be adjusted according to ΔL q and ΔL d respectively.

[0178] Finally, the robust current observer (RCO) proposed for single DC bus current sensor control can be summarized as follows:

[0179]

[0180] where

[0181] i dq_rec is determined through the following steps:

[0182] Firstly, the three-phase reconstructed current \(i\) obtained by controlling with a single DC bus current sensor abc_rec , and then under the constant amplitude constraint, through the Clarke transform \(T\) 3s / 2s and the Park transform \(T\) 2s / 2r is calculated as follows:

[0183]

[0184] where, \(\theta\) e is the electrical angular position of the rotor.

[0185] The block diagram of the proposed robust current observer is as shown in Figure 6 , where \(\theta\) m and \(\omega\) m represent the mechanical position and mechanical angular velocity of the rotor respectively, and the number of pole pairs is \(P\) n : \(\theta\) e = \(P\) n \(\theta\) m , and \(\omega\) e = \(P\) n \(\omega\) m . The three-phase reconstructed current obtained by the single DC bus current sensor and the SSPS method may cause current distortion, and these currents will then be filtered by the proposed robust current observer. This observer is not affected by the motor speed, can not only optimize the estimated reconstructed current, reduce the total harmonic distortion (THD) of the three-phase current, but also enhance the robustness of the observer by introducing a disturbance compensation term.

[0186] Example:

[0187] To verify the effectiveness of the proposed robust current observer, an experimental platform was built, as shown in Figure 7 . Figure 7 The specifications of the permanent magnet synchronous motor (PMSM) tested in it are shown in Table 2, and the parameters of the loaded PMSM are similar to those of the tested PMSM. An incremental optical encoder with 2500 pulses per revolution is coaxially installed with the tested PMSM to provide the rotor position. The field-oriented control algorithm and the single DC bus current sensor control algorithm based on the proposed robust current observer are implemented in the digital signal processor (DSP) TMS320F28377D Delfino (Texas Instruments). The DC bus current is measured using a Hall effect linear current sensor (ACS758, Allegro) with a bandwidth of 120 kHz. The drive unit, that is, the three-phase inverter of the tested PMSM, uses an intelligent power module (FSS0R12W1T7, Infineon). Multiple waveforms are displayed on the oscilloscope through the 12-bit three-channel digital-to-analog converter (DAC) inside the DSP. The switching frequency and the sampling frequency are both selected as 10 kHz, and the current loop bandwidth is set to 400 Hz. The dead time is set to 1.5 μs. The minimum current sampling time \(T\)min Set to 5 μs.

[0188] Table 2 Parameters for testing the PMSM and control system

[0189] Physical quantity Symbol Value Nominal stator resistance <![CDATA[R so > 0.87 Ω Nominal d-axis inductance <![CDATA[L do > 4 mH Nominal q-axis inductance <![CDATA[L qo > 4 mH Nominal permanent magnet flux linkage <![CDATA[ψ fo > 0.0593 Wb Number of pole pairs <![CDATA[P n > 5 Rated torque <![CDATA[T rate > 2.39 N·m Rated speed <![CDATA[n rate > 3000 r / min Bus voltage <![CDATA[U dc > 150V Sampling / switching frequency <![CDATA[f s > 10 kHz

[0190] According to the parameters of the tested PMSM in Table 2, the formula (20) is iterated 100,000 times using the gradient-based method with a learning rate of 0.01 to obtain and l1 = l2 = 500. The parameters of the disturbance compensation term are tuned to k d1 = k d2 = 10 6 , and the dq-axis decoupling term is tuned to k de1 = L qo = 4 mH, k de2 = L do = 4 mH.

[0191] To verify the estimation accuracy of the proposed robust current observer, steady-state experiments were conducted on three phase current reconstruction (PCR) methods, namely the ordinary PCR method, the pulse shift method (SSPS) in "Switching-State Phase Shift Method for Three-Phase-Current Reconstruction With a Single DC-Link Current Sensor", and the proposed robust current observer (RCO) method. The tested PMSM operates at a speed of 1000 r / min with a load torque of 2.39 N·m, as Figure 8 shown, Figure 8 is the comparison diagram of phase currents at a load torque of 2.39 N·m and a speed of 1000 r / min, where (a) is the actual phase current, (b) is the result reconstructed by the ordinary PCR method, (c) is the result reconstructed by the SSPS method, and (d) is the result reconstructed by the RCO method proposed in the present invention. Figure 8 In abc_A , the actual phase current i abc_PCR is measured by two current sensors, the phase current reconstructed by the ordinary PCR method is i abc_SSPS , the phase current reconstructed by the SSPS method is i abc_RCO , and the phase current estimated by the proposed robust current observer is i a_PCR , e a_SSPS , e a_RCO are the reconstruction errors between the actual phase-a current and the corresponding reconstructed phase-a current, respectively.

[0192] Table 3 Current error statistics of three reconstruction methods at a torque of 2.39 N·m and a speed of 1000 r / min

[0193] Case Ordinary PCR SSPS Proposed RCO Standard deviation 1.731A 0.985A 0.500A Peak-to-peak value 10.613A 11.893A 3.413A

[0194] From Figure 8 it can be seen from (b) that, compared with i Figure 8 in (a), abc_A the sine wave of i abc_PCR is distorted and contains a large amount of harmonics. After a phase shift of about 5 μs, Figure 8 i abc_SSPS in (c) becomes more sinusoidal, but there are still obvious current spikes when the voltage vector passes through some sector boundary regions. As shown in (d) of Figure 8 , after filtering by the proposed observer, i abc_RCO does not contain current spikes, and e a_RCO is significantly reduced. The statistical results in Table 3 show the standard deviation and peak-to-peak value of the reconstruction error under different reconstruction methods, and the RCO method proposed by the present invention has the lowest standard deviation and peak-to-peak value.

[0195] Figure 9 shows the experimental results of the actual and reconstructed phase-a current and the Fourier analysis of the reconstructed phase-a current at a speed of 1000 r / min and a load of 0.5 N·m before and after applying the RCO method proposed by the present invention. In the first 0.1 s, the total harmonic distortion (THD) of i abc_SSPS reaches 33.07%, and there are occasional large current errors, as shown by the red dashed box in Figure 9 , resulting in motor stall. Thanks to the application of the RCO method proposed by the present invention, the THD of i a_RCO after 0.1 s drops to 6.17%, and the tested PMSM can always maintain stable operation. Therefore, the steady-state experiment verifies that the RCO method proposed by the present invention can effectively improve the accuracy of the reconstructed current, reduce current harmonics, and enhance the stability of the PMSM drive system.

[0196] Figure 10 is a comparison diagram of the phase current in the low modulation ratio region at a speed of 300 r / min and a load of 0.5 N·m, where (a) is the actual phase current, (b) is the result reconstructed by the ordinary PCR method. (c) is the result reconstructed by the SSPS method. (d) is the result reconstructed by the proposed RCO method. Figure 10 and Table 4 show the experimental results of the PMSM operating in the low modulation ratio region at a speed of 300 r / min and a load of 0.5 N·m. Although the standard deviation of e a_RCO is greater than that of e a_SSPS , that is, the proposed method has larger current fluctuations, but e a_RCOThe peak-to-peak error is relatively small. When the motor operates in the low modulation ratio region, the three-phase current is small, and current accuracy is not the main consideration. Therefore, the RCO method proposed in the present invention can effectively improve the stability of the motor and is beneficial to the operation of the motor in the low modulation ratio region.

[0197] Table 4 Current error statistics of three reconstruction methods in the low modulation ratio region

[0198] Case Ordinary PCR SSPS Proposed RCO Standard deviation 0.376A 0.242A 0.291A Peak-to-peak value 4.030A 2.760A 2.307A

[0199] Figure 11 Fig. is a comparison diagram of the reconstructed phase-a current when the PMSM suddenly decelerates from 1000 r / min to 0 under a 2.39 N·m load, where (a) is the result reconstructed by the SSPS method and (b) is the result reconstructed by the proposed RCO method. Figure 11 Shows the experimental results of the SSPS method and the RCO method proposed in the present invention when the PMSM suddenly decelerates from 1000 r / min to 0 under a 2.39 N·m load, where n is the actual speed of the PMSM. As Figure 11 shown, at the moment when the motor decelerates to 0 r / min, both the SSPS method and the RCO method have large dynamic current errors, but e a_RCO is smaller. In addition, the current harmonic of i a_RCO is less than that of i a_SSPS , which indicates that the RCO method proposed in the present invention can effectively improve the performance of the reconstructed current in the low modulation ratio region.

[0200] Figure 12 Fig. is a comparison diagram of the reconstructed phase-a current when the load torque rapidly increases from 0 to 2.39 N·m at 1000 r / min, where (a) is the result reconstructed by the SSPS method and (b) is the result reconstructed by the proposed RCO method. Figure 12 Shows the experimental results when the load torque rapidly increases from 0 to 2.39 N·m at a speed of 1000 r / min. It can be seen that at the moment of sudden change of the load torque, neither the SSPS method nor the RCO method proposed in the present invention produces significant reconstructed current errors, and the RCO method always maintains a low error. Generally speaking, through the experiments of speed sudden change and load torque sudden change, the dynamic performance of the RCO method proposed in the present invention is verified.

[0201] To verify the robustness of the proposed RCO method of the present invention, a comparative experiment was carried out at a rotational speed of 1000 r / min and a rated torque of 2.39 N·m. The proposed method was compared with the current prediction method in "Improved Saliency-Based Position Sensorless Control of Interior Permanent-Magnet Synchronous Machines With Single DC-Link Current Sensor Using Current Prediction Method" (hereinafter referred to as "current prediction method") as Figure 13 and Figure 14 shown. Figure 13 Fig. is a robustness comparison diagram of the dq-axis inductance change under a rotational speed of 1000 r / min and a load of 2.39 N·m, where (a) is the current prediction method and (b) is the proposed RCO method; Figure 14 Fig. is a robustness comparison diagram of the stator resistance and permanent magnet flux linkage under a rotational speed of 1000 r / min and a load of 2.39 N·m, where (a) is the current prediction method and (b) is the proposed RCO method.

[0202] Figure 13 shows the change of the dq-axis inductance, Figure 14 shows the change of the stator resistance and permanent magnet flux linkage, where i dq_CP and i dq_RCO are the dq-axis currents estimated by the "current prediction method" and the proposed RCO method of the present invention respectively. From Figure 13 it can be seen that the change of the q-axis inductance has a significant impact on the current prediction method in the "current prediction method", resulting in a speed fluctuation of 500 r / min and a significant error in the q-axis current. However, the proposed method only experiences a dynamic process after the sudden change of the dq-axis inductance and converges to the correct dq-axis current. In Figure 14 of (a), the change of the stator resistance and permanent magnet flux linkage causes speed fluctuation and q-axis current error under the current prediction method in the "current prediction method". However, the proposed RCO method of the present invention effectively resists parameter fluctuation and accurately estimates the dq-axis current. These experiments verify the effectiveness of the disturbance compensation term and the robustness of the proposed RCO method of the present invention.

[0203] To verify the effectiveness of the speed decoupling term, the PMSM was set to operate at a rotational speed of 2000 r / min and a load torque of 1.26 N·m, and a comparative experiment with and without the speed decoupling term was carried out, as Figure 15 shown, where Figure 15 (a) is the normal waveform diagram and (b) is the enlarged diagram at the switching moment, edq_RCO is the actual dq-axis current i dq and the dq-axis current i estimated by the RCO method proposed by the present invention dq_RCO The reconstruction error between them. It can be seen that when the speed decoupling term is added to the current observer, all three current errors e q_RCO , e d_RCO and e a_RCO all slightly decrease. Table 5 summarizes the standard deviation (STD) and peak-to-peak value (P-P) of e q_RCO , e d_RCO and e a_RCO without and with the speed decoupling term. e q_RCO , e d_RCO and e a_RCO with the speed decoupling term have smaller peak-to-peak values and standard deviations, which means that introducing the speed decoupling term can improve the accuracy of the reconstructed current, and this phenomenon will be more obvious as the speed increases.

[0204] Table 5 Statistical results of the reconstructed current error without and with the speed decoupling term at a torque of 2.39 N·m and a speed of 1000 r / min

[0205]

[0206] The present invention proposes a novel robust current observer for PMSM based on single DC bus current sensor control. The SSPS method cannot completely eliminate the current reconstruction dead zone (CRDZ), and due to the asymmetry of the three-phase PWM waveform, the harmonics of the phase current increase. By introducing a dq-axis current observer in the SSPS method to filter the reconstructed current, current harmonics and distortion can be suppressed. Based on the Lipschitz nonlinear system theory, the tuning principle of the observer correction gain is derived, and the optimal correction gain is obtained by the gradient method. A speed decoupling term is proposed to ensure the performance of this optimal observer. In addition, since the current observer is sensitive to motor parameter changes and unmodeled disturbances, a disturbance compensation term is proposed to improve the robustness of the current observer.

[0207] Experimental results show that the proposed robust current observer can effectively improve the accuracy of the reconstructed current and reduce the THD, including in the low modulation ratio region; and shows strong robustness to the parameter changes of PMSM. Since many parameters of the proposed method can be tuned offline, this method is easy to implement and can be practically applied in systems such as embedded systems.

[0208] The above numerical examples of the present invention are only for explaining in detail the calculation model and calculation process of the present invention, rather than limiting the implementation manners of the present invention. For those of ordinary skill in the art, other different forms of changes or variations can be made on the basis of the above description. It is impossible to list all the implementation manners here. Any obvious changes or variations derived from the technical solutions of the present invention still fall within the protection scope of the present invention.

Claims

1. A robust current observer for a permanent magnet synchronous motor drive system based on a single DC bus current sensor, characterized in that: The observer is as follows: in, represents the differential with respect to time t; represents the estimated current on the dq axis; L opt is the correction gain of the dq-axis current observer; i dq_rec is the three-phase reconstructed current i abc_rec By using Clarke transformation T under constant amplitude constraint 3s / 2s and through the Park transformation T 2s / 2r Calculated current; k d1 and k d2 is the correction coefficient of the disturbance compensation term; k de1 and k de2 represents the decoupling coefficient of the dq axis decoupling term; ω e Indicates electrical angular velocity; L d , L q is the stator inductance of the d-axis and q-axis; R s is the stator resistance; the subscript o represents the rated value of the corresponding parameter.

2. The robust current observer of a permanent magnet synchronous motor drive system based on a single DC bus current sensor according to claim 1, characterized in that: Three-phase reconstruction current i abc_rec By using Clarke transformation T under constant amplitude constraint 3s / 2s and through the Park transformation T 2s / 2r Calculate the current i dq_rec The process includes: First, the three-phase reconstructed current i is obtained by controlling the single DC bus current sensor abc_rec , and then by Clarke transformation T under constant amplitude constraint 3s / 2s and through the Park transformation T 2s / 2r The calculation is as follows: Among them, θ e is the electrical angle position of the rotor.

3. The robust current observer of a permanent magnet synchronous motor drive system based on a single DC bus current sensor according to claim 2, characterized in that: Electrical angle position θ e =P n θ m , where θ m is the rotor mechanical position, P n is the pole pair number.

4. The robust current observer of a permanent magnet synchronous motor drive system based on a single DC bus current sensor according to claim 1, characterized in that: Electrical angular velocity ω e =P n ω m， , where P n is the pole pair number, ω m is the rotor mechanical angular velocity.

5. The robust current observer of a permanent magnet synchronous motor drive system based on a single DC bus current sensor according to any one of claims 1 to 4, characterized in that: Correction gain L of dq axis current observer opt Obtained by: First, the error dynamic equation considering concentrated disturbance is determined as: Among them, d dq (i dq ) = d dq (t) represents the actual concentrated disturbance, d dq (i dq ) satisfies the Lipschitz property and has a Lipschitz constant γ; L is the correction gain of the linear dq axis current observer, represents the estimated current on the dq axis; Construct a Lyapunov function with a positive definite matrix P: Taking the derivative of V and combining it with the Lipschitz property, we get The upper bound form of The upper bound form of is: When(A o -L) satisfies the eigenvalue λ of When represents the real part of the corresponding eigenvalue, κ(Q) is the condition number of the matrix Q, and Q is the matrix (A o -L) eigenvector matrix; then there exists a positive definite matrix P = P T Satisfies the Riccati equation as shown below: Among them, ∈ represents a constant greater than 0, and I represents the identity matrix; therefore, This shows that the dq-axis current observer is asymptotically stable; The optimal L is obtained by minimizing κ(Q), i.e., L opt .

6. The robust current observer of a permanent magnet synchronous motor drive system based on a single DC bus current sensor according to claim 5, characterized in that: The optimal L is obtained by minimizing κ(Q), i.e., L opt The process includes: First, based on the gradient method, we maximize the following formula Among them, λ l express The minimum corresponding eigenvalue; For gradient-based methods to maximize The process of L opt Adjust the L opt During the adjustment process, L opt The off-diagonal elements of A are set to o The corresponding non-diagonal elements of are completely equal, that is, the speed decoupling term is introduced, and L opt It is expressed as: Among them, l1 and l2 are obtained by Adjusted to obtain.

7. A design method for a robust current observer of a permanent magnet synchronous motor drive system based on a single DC bus current sensor, characterized in that: The following steps are involved: S1. Modeling of permanent magnet synchronous motor with uncertainty: The dynamic characteristics of the PMSM current in the dq rotor reference frame are expressed as: in, represents the differential with respect to time t; i d (t), i q (t) and u d (t),u q (t) represents the stator current and voltage of the d-axis and q-axis respectively; R s is the stator resistance, L d , L q is the stator inductance of the d-axis and q-axis, the subscript o represents the rated value of the corresponding parameter; ψ f is the permanent magnet flux; ω e Represents electrical angular velocity; d d (t), d q (t) is the concentrated disturbance on the d-axis and q-axis, Define the state vector i dq (t) = [i d (t)i q (t)] T , input vector u dq (t)=[u d (t)u q (t)-ω e ψ fo ] T and the concentrated disturbance d dq (t) = [d d (t)d q (t)] T ; S2. Design of a new robust current observer based on single DC bus current sensor control: S201. Design the correction gain of the current observer with centralized disturbance estimation: Estimation of current through dq axis Estimate the concentrated disturbance, combine the estimated concentrated disturbance The dq axis current observer is obtained: in, represents the estimated current on the dq axis; L is the correction gain of the linear dq axis current observer; Combined with the dynamic conversion of the dq axis current into the permanent magnet synchronous motor state space in vector form, the error dynamic equation considering the concentrated disturbance is: Among them, d dq (i dq ) = d dq (t) represents the actual concentrated disturbance; d dq (i dq ) satisfies the Lipschitz property and has a Lipschitz constant γ; Constructing Lyapunov functions with positive definite matrix P Taking the derivative of V and combining it with the Lipschitz property, we get The upper bound form of The upper bound form of is: When(A o -L) satisfies the eigenvalue λ of When represents the real part of the corresponding eigenvalue, κ(Q) is the condition number of the matrix Q, and Q is the matrix (A o -L) eigenvector matrix; then there exists a positive definite matrix P = P T Satisfies the Riccati equation as shown below: Among them, ∈ represents a constant greater than 0, and I represents the identity matrix; therefore, This shows that the dq-axis current observer is asymptotically stable; The optimal L is obtained by minimizing κ(Q), i.e., L opt ; S202. Design disturbance compensation items and current observer: Design disturbance compensation term: Among them, k de1 and k de2 represents the decoupling coefficient of the dq-axis decoupling term; The final design of the current observer is: in, i dq_rec is the three-phase reconstructed current i obtained by controlling the single DC bus current sensor abc_rec By using Clarke transformation T under constant amplitude constraint 3s / 2s and through the Park transformation T 2s / 2r Calculated current; 8. The design method of a robust current observer for a permanent magnet synchronous motor drive system based on a single DC bus current sensor according to claim 7, characterized in that: The concentrated disturbance d on the d-axis and q-axis d (t), d q (t) are as follows: Among them, R s =R so +ΔR s , L d =L do +ΔL d , L q =L qo +ΔL q , ψ f =ψ fo +Δψ f , Δ represents the change of the corresponding parameter of PMSM; ε d , ε q represents the unmodeled slowly varying disturbance; 9. The design method of a robust current observer for a permanent magnet synchronous motor drive system based on a single DC bus current sensor according to claim 8, characterized in that: The dq axis current is dynamically converted into a permanent magnet synchronous motor state space in vector form as follows: in, 10. The design method of a robust current observer for a permanent magnet synchronous motor drive system based on a single DC bus current sensor according to claim 9, characterized in that: Estimation of current through dq axis The estimated concentrated disturbance is as follows: Here, p is a differential operator.

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