Adaptive observer-based sensorless control method for LC-filtered PMSM

Abstract

This invention discloses a sensorless control method for a PMSM (Motor-Mounted Circulator) based on an adaptive observer and LC filter. The designed adaptive observer only needs to feed back the filter inductor current to simultaneously observe the filter capacitor voltage, stator current, and motor back EMF. By introducing a non-singular coordinate transformation, the coupling between the unknown speed and the state to be estimated is eliminated. The observer gain is estimated and corrected online using an adaptive law, ensuring that the observer poles remain constant across the entire speed domain, thereby guaranteeing the consistency of the dynamic performance of the observation system. This invention significantly reduces the system's dependence on sensors, achieving low-cost, high-reliability, and high-performance control.

Description

Technical Field

[0001] This invention relates to the field of LC-filtered permanent magnet motor drive control, and particularly to a sensorless control method for LC-filtered PMSMs based on an adaptive observer. Background Technology

[0002] In submarine long-cable motor drive systems, the reflected waves caused by the long transmission line, combined with the high-frequency switching of power devices, can easily lead to overvoltage problems at the motor terminals. To address this issue, an effective solution is to introduce an LC filter between the inverter and the motor to shape the output voltage into a sine wave. Meanwhile, to reduce system cost and size while improving reliability, sensorless drive schemes are widely used in industrial applications. However, current research on sensorless control strategies for LC-filtered permanent magnet synchronous motors is insufficient. This is because the LC filter introduces a significant voltage phase shift and amplitude attenuation between the inverter output and the motor input, making sensorless schemes designed for traditional (LC-filter-free) systems unsuitable. Early research attempted to compensate for the adverse effects of the LC filter by adding additional voltage or current sensors, but this inevitably increased system cost and size. Therefore, achieving joint estimation of the filter capacitor voltage, stator current, and motor back EMF under the constraint of only feedback inductor current is crucial for developing low-cost, small-size, and highly reliable LC-filtered permanent magnet synchronous motor drivers.

[0003] A search revealed that Chinese invention patent CN110504888A discloses a sensorless permanent magnet synchronous motor control method based on an adaptive sliding mode observer. This method includes the following steps: First, establishing a mathematical model of the permanent magnet synchronous motor; second, designing an adaptive sliding mode observer, using a continuous, smooth, and strictly monotonic sigmoid threshold function to replace the sgn sign function in the traditional sliding mode observer, thus reducing system chattering caused by the traditional sliding mode observer; then, designing an adaptive back-EMF estimation stage to replace the traditional low-pass filter, improving the back-EMF estimation accuracy; finally, using phase-locked loop (PLL) technology to estimate the rotor position and speed, reducing the estimation errors of the motor rotor position angle and speed, ultimately achieving high-precision sensorless control of the permanent magnet synchronous motor.

[0004] The technical comparison between this invention and "a sensorless permanent magnet synchronous motor control method based on an adaptive sliding mode observer" is as follows:

[0005] 1. Patent CN110504888A targets conventional permanent magnet synchronous motors and estimates back electromotive force by collecting stator current and combining it with a designed adaptive sliding mode observer. The system to be estimated is a third-order model.

[0006] The core objective of this patent is to achieve sensorless control of a permanent magnet synchronous motor with an LC filter. The entire system is a fifth-order model, and the only measurable signal is the filter inductor current. Therefore, this solution employs an adaptive observer to simultaneously estimate the filter capacitor voltage, stator current, and motor back electromotive force. Due to the higher system order and the increased number of variables to be estimated, the observer design becomes significantly more challenging.

[0007] The two are fundamentally different in terms of their research subjects and the difficulty of designing the observers.

[0008] 2. The sliding mode observer used in patent CN110504888A relies on the upper bound of the back electromotive force for gain selection. This reliance can easily lead to overly conservative gain selection, resulting in performance degradation of the system at low speeds.

[0009] This patent avoids dependence on high gain by establishing a back-EMF model and employing a full-order adaptive observer. The observer gain is estimated and corrected online through an adaptive law, ensuring that its poles remain constant across the entire velocity domain, thereby guaranteeing the consistency of the dynamic performance of the observation system.

[0010] The two differ fundamentally in their choice of observer type and their performance.

[0011] A search revealed Chinese invention patent CN119543729A, which discloses a sensorless control method for a permanent magnet synchronous motor (PMSM) across a wide speed range. The method establishes an extended state observer for the PMSM, using it to obtain the motor's back electromotive force (EMF). An adaptive vector filter is used to remove high-order harmonics from the back EMF obtained by the extended state observer, yielding an estimated back EMF. This estimated back EMF is then used as input, and a phase-locked loop (PLL) position observer is used to demodulate the position information contained within the estimated back EMF, obtaining the motor's speed and position angle. The PMSM is then controlled based on the obtained speed and position angle. By extracting position information from the rotor back EMF using a position observer, a mechanical position sensor is eliminated, simplifying the system structure and reducing costs. The adaptive vector filter removes harmonics from the estimated back EMF, reducing the estimation error of the motor speed and position angle, and improving the efficiency and stability of sensorless control over a wide speed range.

[0012] The technical comparison between this invention and "a sensorless control method for a permanent magnet synchronous motor with a wide speed range" is as follows:

[0013] 1. Patent CN119543729A studies a conventional permanent magnet synchronous motor. It estimates the back electromotive force (EMF) using a designed extended state observer and then uses a phase-locked loop (PLL) position observer to demodulate and estimate the position information contained in the back EMF, thereby obtaining the motor's speed and position angle. The system under study is a third-order model.

[0014] This patent focuses on an LC-filtered permanent magnet synchronous motor, with the system being studied as a fifth-order model. As the system order increases, the number of variables to be estimated in the observer increases, making the design more complex and challenging.

[0015] The two differ fundamentally in their research subjects and the difficulty of designing the observers.

[0016] 2. Patent CN119543729A uses an extended state observer to obtain the back electromotive force (EMF) of the motor and employs an adaptive vector filter to remove high-order harmonics from the back EMF obtained by the extended state observer. This scheme requires the observer to utilize speed information estimated by a phase-locked loop (PLL), resulting in mutual coupling between the observer and the PLL. This coupling makes overall system stability analysis difficult and increases the complexity of observer parameter design.

[0017] The observer proposed in this patent uses an adaptive term to estimate unknown rotational speed information online, eliminating the need for rotational speed information estimated by a phase-locked loop, thus completely eliminating the coupling relationship between the two and significantly simplifying the observer parameter design process.

[0018] The two differ fundamentally in their choice of observer type and their performance. Summary of the Invention

[0019] This invention provides a sensorless control method for an LC-filtered PMSM based on an adaptive observer, which enables joint estimation of the filter capacitor voltage, stator current, and motor back EMF under the constraint of only feedback inductor current, thereby reducing the cost and size of the drive system and improving its reliability.

[0020] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0021] The sensorless control method for PMSM based on adaptive observer LC filter is characterized by the following steps:

[0022] S1. Based on the mathematical model of the LC-filtered permanent magnet synchronous motor, a non-singular coordinate transformation matrix is ​​designed to eliminate the coupling between the back electromotive force to be estimated and the unknown speed.

[0023] S2. Based on the principle of deterministic equivalence of adaptive control, an adaptive observer is designed, and by introducing an auxiliary vector, the observer is ensured to satisfy the strict positive real condition.

[0024] S3. Design an adaptive term update law to achieve online estimation of rotational speed information, and then update the observer gain in real time;

[0025] S4. Combining the non-singular coordinate transformation matrix, the estimated filter capacitor voltage, stator current, and motor back electromotive force are obtained by inverse coordinate transformation.

[0026] As a preferred technical solution of the present invention: In step S1: the mathematical model of the permanent magnet synchronous motor with LC filter is:

[0027] ;

[0028] in , , , and These represent the inverter output voltage, filter inductor current, stator voltage, stator current, and back electromotive force, respectively. and They represent the back electromotive force, respectively. The first and second derivatives; , , and These represent the filter inductor, filter capacitor, stator inductor, and stator resistance, respectively. Indicates the electric rotation speed;

[0029] By defining state variables ,Model It can be rewritten as:

[0030] ;

[0031] in:

[0032] in , , , , , , , ;

[0033] according to It can be seen that the unknown rotational speed information and back electromotive force When they are coupled together, a non-singular coordinate transformation is introduced:

[0034] ;

[0035] in Represents the new variable obtained after coordinate transformation. non-singular matrix for:

[0036] ;

[0037] Will Substitution From this, we can obtain:

[0038] ;

[0039] in:

[0040] , , ;

[0041] Depend on It can be seen that the unknown rotational speed information was eliminated through non-singular coordinate transformation. and back electromotive force Coupled between them.

[0042] As a preferred technical solution of the present invention: [Regarding] Based on the principle of deterministic equivalence in adaptive control, the adaptive observer can be designed as follows:

[0043] ;

[0044] The superscript "^" indicates the estimated value of the variable.

[0045] , , Indicates unknown speed information The estimated value, Represents the auxiliary input vector. Represents the observer gain matrix.

[0046] Among them, auxiliary input vector It can be designed as:

[0047] ;

[0048] in , , ; Represents the Laplace operator; This represents the adaptive update law for the term to be designed; , , , ; Represents the positive real number to be designed; The stable transfer function can be designed as follows:

[0049] .

[0050] As a preferred technical solution of the present invention: observer gain matrix It can be designed as:

[0051] ;

[0052] in , , , , , Represents the positive real number to be designed;

[0053] Adaptive Term Update Law The update law can be designed as follows:

[0054]

[0055] Through the designed adaptive observer It can accurately estimate the new state. And adaptive terms Able to accurately track real rotational speed information .

[0056] As a preferred technical solution of the present invention: [The following is a description of the invention:] Substitution From this, we can obtain:

[0057] ;

[0058] Adaptive observer estimated and adaptive terms Substitution From this, we can obtain estimates of the filter inductor current, stator voltage, stator current, and back electromotive force:

[0059] (12).

[0060] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0061] This invention reconstructs system variables through non-singular coordinate transformation, eliminating the coupling between unknown rotational speed information and the back EMF to be estimated. Based on this, an adaptive observer is designed according to the deterministic equivalence principle of adaptive control, and an auxiliary input vector is introduced to ensure that the observer satisfies the strictly positive-real condition. Furthermore, an adaptive term is designed for online estimation of rotational speed information, and this estimate is used to correct the observer gain in real time, ensuring that the observer poles remain constant across the entire speed domain, thereby guaranteeing the consistency of the dynamic performance of the observation system. Compared with existing technologies, the proposed scheme does not require additional sensors; it only needs to feed back the filter inductor current to simultaneously observe the filter capacitor voltage (stator voltage), stator current, and motor back EMF information, effectively reducing the cost and size of the drive system and improving its reliability.

[0062] Other beneficial effects of the present invention will be described in detail in the following detailed description section. Attached Figure Description

[0063] Figure 1 This is a topology diagram of the LC-filtered permanent magnet synchronous motor drive system in an embodiment of the present invention;

[0064] Figure 2 This is a block diagram of the adaptive observer implementation proposed in the embodiments of the present invention;

[0065] Figure 3 The above is an experimental waveform diagram of the rotor position and back electromotive force estimation results obtained by the adaptive observer proposed in this embodiment of the invention.

[0066] Figure 4 The above are experimental waveforms of the stator voltage and stator current estimation results obtained by the adaptive observer proposed in this embodiment of the invention.

[0067] Figure 5 The waveform diagram shows the experimental results of the adaptive observer proposed in this embodiment of the invention under the condition of rotating speed reference change. Detailed Implementation

[0068] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0069] The sensorless control method for PMSM based on adaptive observer LC filter proposed in this invention includes the following steps:

[0070] S1. Based on the mathematical model of the LC-filtered permanent magnet synchronous motor, a non-singular coordinate transformation matrix is ​​designed to eliminate the coupling between the back electromotive force to be estimated and the unknown speed.

[0071] Specifically, the mathematical model of a permanent magnet synchronous motor with an LC filter is as follows:

[0072] ;

[0073] in , , , and These represent the inverter output voltage, filter inductor current, stator voltage, stator current, and back electromotive force, respectively. and They represent the back electromotive force, respectively. The first and second derivatives; , , and These represent the filter inductor, filter capacitor, stator inductor, and stator resistance, respectively. Indicates the electric rotation speed;

[0074] By defining state variables ,Model It can be rewritten as:

[0075] ;

[0076] in:

[0077] , , , , , , , ;

[0078] according to It can be seen that the unknown rotational speed information and back electromotive force The mutual coupling leads to complexity in observer design. To address this issue, a non-singular coordinate transformation is introduced:

[0079] ;

[0080] in Represents the new variable obtained after coordinate transformation. non-singular matrix for ;

[0081] Will Substitution From this, we can obtain:

[0082] ;

[0083] in:

[0084] , , ,

[0085] Depend on It can be seen that the unknown rotational speed information was eliminated through non-singular coordinate transformation. and back electromotive force The coupling between them simplifies the observer design.

[0086] S2. Based on the principle of deterministic equivalence of adaptive control, an adaptive observer is designed, and by introducing an auxiliary vector, the observer is ensured to meet the strict positive real condition.

[0087] For the system Based on the principle of deterministic equivalence in adaptive control, the adaptive observer can be designed as follows:

[0088] ;

[0089] The superscript "^" indicates the estimated value of the variable.

[0090] , , Indicates unknown speed information The estimated value, Represents the auxiliary input vector. The observer gain matrix is ​​represented by the auxiliary input vector. To ensure that the designed adaptive observer satisfies the strictly positive real condition, the auxiliary input vector is used. Designed as:

[0091] ;

[0092] in , , ; Represents the Laplace operator; This represents the adaptive update law for the term to be designed; , , , ; Represents the positive real number to be designed; The stable transfer function can be designed as follows:

[0093] .

[0094] S3. Design an adaptive term update law to achieve online estimation of rotational speed information, and then update the observer gain in real time.

[0095] Specifically, to ensure that the observer's poles are unaffected by changes in rotational speed, the observer gain matrix... It can be designed as:

[0096] ;

[0097] in , , , , , Represents the positive real numbers to be designed; Adaptive term update law The update law can be designed as follows:

[0098] Adaptive Term Update Law The update law can be designed as follows:

[0099]

[0100] Through the designed adaptive observer It can accurately estimate the new state. And adaptive terms Able to accurately track real rotational speed information .

[0101] S4. Combining the non-singular coordinate transformation matrix, the estimated filter capacitor voltage, stator current, and motor back electromotive force are obtained by inverse coordinate transformation.

[0102] Specifically as follows: Substitution From this, we can obtain:

[0103] ;

[0104] Adaptive observer estimated and adaptive terms Substitution From this, we can obtain estimates of the filter inductor current, stator voltage, stator current, and back electromotive force:

[0105] (12).

[0106] like Figure 1As shown in the figure, the topology of the LC-filtered permanent magnet synchronous motor drive system provided in the embodiment of the present invention mainly consists of a DC power supply, a DC-side capacitor, a three-phase inverter, a filter inductor, a filter capacitor, and a permanent magnet synchronous motor.

[0107] like Figure 2 The diagram shown is a block diagram of the adaptive observer implementation in the embodiment of the invention. The specific steps are as follows:

[0108] By collecting the filter inductor currents of phase a and phase b ( and The filter inductor current in the orthogonal stationary coordinate system is obtained through Clark transformation. and :

[0109]

[0110] The filter inductor current in the orthogonal stationary coordinate system Substitute the designed adaptive observer From this, we can obtain:

[0111] (6)

[0112] Where the auxiliary input vector It can be designed as:

[0113] (7)

[0114] in , , ; Represents the Laplace operator; This represents the adaptive update law for the term to be designed; , , , ; Represents the positive real number to be designed; The stable transfer function can be designed as follows:

[0115] (8)

[0116] Observer gain matrix It can be designed as:

[0117] (9)

[0118] in , , , , , Represents the positive real number to be designed;

[0119] Adaptive Term Update Law The update law can be designed as follows:

[0120] (10)

[0121] Adaptive observer estimated and adaptive terms Substituting these values ​​into the coordinate transformation matrix yields estimated values ​​for the filter inductor current, stator voltage, stator current, and back electromotive force:

[0122] (12)

[0123] like Figure 3 The figure shows the experimental waveforms of the rotor position and back EMF estimation results obtained by the proposed adaptive observer. From top to bottom, the figures are: rotor position estimate, rotor position estimation error, back EMF estimate, and back EMF estimation error.

[0124] Experimental results show that the observer can accurately estimate the back electromotive force information, and the maximum error in rotor position estimation is only 0.052 radians.

[0125] like Figure 4 The figure shows the experimental waveforms of the stator voltage and stator current estimation results obtained by the proposed adaptive observer. The experimental results show that the estimated stator voltage and stator current can accurately track the actual values.

[0126] like Figure 5 The figure shows the experimental waveforms of the proposed adaptive observer under varying rotational speed reference conditions. The experimental results demonstrate that the estimated rotational speed consistently tracks the actual rotational speed using the proposed adaptive observer. The maximum rotational speed estimation error is 20 r / min. The maximum rotor position estimation error is 0.087 radians.

[0127] The above description represents the preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A sensorless control method for PMSM based on an adaptive observer using LC filtering, characterized in that, Includes the following steps: S1. Based on the mathematical model of the LC-filtered permanent magnet synchronous motor, a non-singular coordinate transformation matrix is ​​designed to eliminate the coupling between the back electromotive force to be estimated and the unknown speed. S2. Based on the principle of deterministic equivalence of adaptive control, an adaptive observer is designed, and by introducing an auxiliary vector, the observer is ensured to satisfy the strict positive real condition. Based on the principle of deterministic equivalence in adaptive control, the adaptive observer can be designed as follows: ； The superscript "^" indicates the estimated value of the variable. , , Indicates unknown speed information The estimated value, Represents the auxiliary input vector. Represents the observer gain matrix. Among them, auxiliary input vector It can be designed as: ； in , , ; Represents the Laplace operator; This represents the adaptive update law for the term to be designed; , , , ; Represents the positive real number to be designed; The stable transfer function can be designed as follows: ； S3. Design an adaptive term update law to achieve online estimation of rotational speed information, and then update the observer gain in real time; S4. Combining the non-singular coordinate transformation matrix, the estimated filter capacitor voltage, stator current, and motor back electromotive force are obtained by inverse coordinate transformation.

2. The sensorless control method for LC-filtered PMSM based on adaptive observers according to claim 1, characterized in that, In step S1: The mathematical model of the permanent magnet synchronous motor with LC filter is: ; in , , , and These represent the inverter output voltage, filter inductor current, stator voltage, stator current, and back electromotive force, respectively. and They represent the back electromotive force, respectively. The first and second derivatives; , , and These represent the filter inductor, filter capacitor, stator inductor, and stator resistance, respectively. Indicates the electric rotation speed; By defining state variables ,Model It can be rewritten as: ； in: ， ， ， ， ， ， ， ； according to It can be seen that the unknown rotational speed information and back electromotive force When they are coupled together, a non-singular coordinate transformation is introduced: ； in Represents the new variable obtained after coordinate transformation. non-singular matrix for: ； Will Substitution From this, we can obtain: ； in: ， ， ； Depend on It can be seen that the unknown rotational speed information was eliminated through non-singular coordinate transformation. and back electromotive force Coupled between them.

3. The sensorless control method for LC-filtered PMSM based on adaptive observers according to claim 2, characterized in that, Observer gain matrix It can be designed as: ； in , , , , , Represents the positive real number to be designed; Adaptive Term Update Law The update law can be designed as follows: ； Through the designed adaptive observer It can accurately estimate the new state. And adaptive terms Able to accurately track real rotational speed information .

4. The sensorless control method for LC-filtered PMSM based on an adaptive observer according to claim 2 or 3, characterized in that, Will Substitution From this, we can obtain: （11）； Adaptive observer estimated and adaptive terms Substitution From this, we can obtain estimates of the filter inductor current, stator voltage, stator current, and back electromotive force: （12）。

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