Adaptive back-EMF observer method for permanent magnet synchronous motor based on coordinate transformation

Abstract

The present invention proposes a method for adaptive back-electromotive force observer of permanent magnet synchronous motor based on coordinate transformation. First, coordinate transformation is used to ensure that the observation system to be designed satisfies the strict positive real condition. Secondly, an intermediate variable is constructed to reduce the order of the observation system and eliminate the dependence on the current derivative information. The disclosed adaptive back-electromotive force observer algorithm based on coordinate transformation eliminates the dependence of the observer on the information in the phase-locked loop, and can design the observer and the phase-locked loop separately, which greatly reduces the design difficulty of the observer and improves the reliability and dynamic response of the observation system.

Description

Technical Field

[0001] The invention belongs to the field of speed sensorless control of permanent magnet synchronous motors, and in particular to an adaptive back electromotive force observer method of permanent magnet synchronous motors based on coordinate transformation. Background Art

[0002] With the development of society and the advancement of technology, people have higher and higher requirements on the performance of household appliances, and energy-saving and environmentally friendly household appliances are becoming more and more popular among consumers. Compared with traditional motors, permanent magnet synchronous motors have been more and more widely used and promoted due to their compact structure, high power density and power factor, large electromagnetic torque, and low noise. In order to reduce production costs, reduce the size of equipment, and improve system reliability, a large number of permanent magnet synchronous motors adopt speed sensorless control strategies.

[0003] The speed sensorless control strategy of permanent magnet synchronous motor mainly includes the model-based medium and high speed control method and the low speed control method based on high frequency injection method. The model-based method can be further divided into the method of estimating flux linkage and the method of estimating back electromotive force. The existing back electromotive force observer often needs to use the estimated speed information in the phase-locked loop, which will lead to mutual coupling between the observer and the phase-locked loop. When performing stability analysis on the observer system, many existing studies often directly ignore this coupling, thereby simplifying the stability analysis and posing a potential risk to the stability of the system; secondly, in order to ensure the overall stability of the system, the bandwidth frequency of the observer should be much lower than the bandwidth frequency of the phase-locked loop, which will limit the dynamic performance of the observer and make its parameter design more complicated.

[0004] The comparison with the existing technology is as follows:

[0005] Publication number: CN113037160A, patent name: Sensorless control method and system of permanent magnet synchronous motor based on nonlinear disturbance observer, the present invention discloses a sensorless control method and system of permanent magnet synchronous motor based on nonlinear disturbance observer, belonging to the field of permanent magnet synchronous motor control. The current and voltage of the permanent magnet synchronous motor in the α-β coordinate system of the present invention are combined with the total disturbance value to obtain the estimated value e of the back electromotive force of the permanent magnet synchronous motor α and e β ; Based on the estimated value of the back electromotive force of the permanent magnet synchronous motor e α and e β , and obtain the rotor position angle and speed of the permanent magnet synchronous motor; the present invention observes and compensates for the load and external disturbances, improves the anti-interference ability of the motor speed regulation system, and introduces an adaptive law to further improve the accuracy of rotor position observation.

[0006] The differences are as follows:

[0007] 1. The designed observer is different: the patent uses a nonlinear disturbance observer;

[0008] 2. The observer design is based on different assumptions: This patent assumes that the back EMF of the system is a constant and uses a nonlinear disturbance observer to estimate the back EMF information;

[0009] 3. Different stability guarantees of the observer: This patent uses speed information when designing the observer. However, during the stability analysis, it ignores the impact of unknown speed information on the overall system, increasing the risk of system instability.

[0010] Publication number: CN115800843A, patent name: A permanent magnet synchronous motor position estimation method based on complex coefficient sliding mode observer, the present invention belongs to the technical field of permanent magnet synchronous motor position estimation, and is a permanent magnet synchronous motor position estimation method based on complex coefficient sliding mode observer. The method comprises the following steps: Step 1, according to the voltage information u in the αβ coordinate system, α,β and current information i α,β , the αβ axis back electromotive force is estimated by a complex coefficient sliding mode observer to obtain the αβ axis estimated back electromotive force step 2, the αβ axis estimated back electromotive force obtained in step 1 is input into a phase-locked loop to obtain an estimated angular velocity and an estimated position step 3, the estimated angular velocity and the estimated position obtained in step 2 are used to perform a speed closed loop and coordinate transformation, so that the position sensorless control of the permanent magnet synchronous motor can be realized, and the position estimation accuracy is improved, and the position sensorless control performance is better. The present invention can realize accurate estimation of the back electromotive force, improve the estimation accuracy of the rotor position, and has a simple structure, is easy to implement, and has a low amount of calculation.

[0011] The differences are as follows:

[0012] 1. The designed observer is different: the patent uses a sliding mode observer;

[0013] 2. The observer design is based on different assumptions: This patent assumes that the back EMF of the system is bounded and uses the deterministic equivalence principle of the sliding film observer to estimate the information of the back EMF;

[0014] 3. The dynamic performance of the observer is different: The observer proposed in this patent needs to use a low-pass filter to extract the back-electromotive force information from the high-frequency switching signal, and the use of the filter will inevitably bring delay to the system, deteriorating the dynamic performance of the system.

[0015] Publication number: CN110572091A, patent name: A sensorless control method for optimizing permanent magnet synchronous motors. The present invention discloses a sensorless control method for optimizing permanent magnet synchronous motors. The present invention performs Clark coordinate transformation on the three-phase current and three-phase voltage collected by the sensor to obtain the voltage and current in a two-phase stationary coordinate system, and then inputs the voltage in the two-phase stationary coordinate system to a sliding mode current observer to obtain an observed current; the difference between the observed current and the actual current is input to a back-electromotive force observer based on a saturation function to obtain an initial value of the back-electromotive force estimation, and a variable domain fuzzy control algorithm is used to adjust the sliding mode gain k in the back-electromotive force observer based on a saturation function. smo ; Then the estimated initial value of the back electromotive force is filtered through a variable cutoff frequency filter to obtain a relatively smooth back electromotive force estimation value; Then the variable hysteresis compensation design is performed on the reverse sub-position after filtering to calculate the motor rotor speed and rotor position value. The present invention can effectively weaken the vibration phenomenon, improve the accuracy of rotor speed and position information estimation, and has good dynamic characteristics.

[0016] The differences are as follows:

[0017] 1. The designed observer is different: the patent uses a sliding mode observer;

[0018] 2. The observer design is based on different assumptions: This patent assumes that the back EMF of the system is bounded and uses the deterministic equivalence principle of the sliding film observer to estimate the information of the back EMF;

[0019] 3. The dynamic performance of the observer is different: The observer proposed in this patent needs to use a low-pass filter to extract the back-electromotive force information from the high-frequency switching signal, and the use of the filter will inevitably bring delay to the system, deteriorating the dynamic performance of the system. Summary of the invention

[0020] In order to solve the above technical problems, the present invention proposes a permanent magnet synchronous motor adaptive back electromotive force observer method based on coordinate transformation, which does not rely on any information in the phase-locked loop, ensures that the observer and the phase-locked loop can be designed separately, reduces the difficulty of observer design, and improves the reliability of the system. The core of the observation method is to ensure that the observed system meets the strict positive real condition through coordinate transformation, and then design a reduced-order adaptive observer to estimate the back electromotive force information. In addition, the unknown speed information is estimated online by designing a reduced-order adaptive law, which effectively avoids the dependence on the phase-locked loop information when designing the observer.

[0021] To achieve the above object, the technical solution adopted by the present invention is:

[0022] The method for adaptive back electromotive force observer of permanent magnet synchronous motor based on coordinate transformation is characterized by the following specific steps:

[0023] S1, transforms the back electromotive force model to be estimated into a model to be estimated that satisfies strict positive real conditions through coordinate transformation;

[0024] S2, by constructing an intermediate variable, effectively avoids the need to directly use the current derivative information when designing the observer;

[0025] S3, based on the deterministic equivalence principle of adaptive control, an adaptive observer is designed to estimate the intermediate variables, and a reduced-order adaptive term update law is designed to estimate the speed information in real time, eliminating the dependence of the back-electric observer on the information in the phase-locked loop, ensuring that the observer and the phase-locked loop can be designed separately;

[0026] S4, obtaining an estimated back electromotive force according to the intermediate variable estimated in step S3, in combination with the coordinate transformation in step S1 and the intermediate variable defined in step S2.

[0027] As a further improvement of the present invention, the coordinate transformation in step S1 is specifically performed as follows:

[0028] The voltage equation of the permanent magnet synchronous motor in the stationary coordinate system is as follows:

[0029]

[0030] where u α and u β represents the stator voltage of the α-axis and the β-axis, i α and i β represents the stator current of the α-axis and β-axis, R s Indicates stator resistance, L s represents the stator inductance, e α and e β represents the α-axis and β-axis back electromotive force;

[0031] Assuming that the air gap magnetic flux of the motor is uniformly distributed and the high-order harmonics of the back EMF are ignored, then e a and e β It is expressed as:

[0032]

[0033] where ψ f represents the permanent magnet flux, ω e represents the rotor electrical angular velocity, θ e Indicates the rotor electrical position;

[0034] By defining the state variable Then x r The state space model of is expressed as:

[0035]

[0036] in And κ = α, β;

[0037] Whether κ is equal to α or β, the state space equation (3) will not change. When κ = α, the adaptive back-EMF observer algorithm of the permanent magnet synchronous motor based on coordinate transformation is used to estimate the back-EMF e of the α-axis. α Obviously, when κ = β, the same method can be used to estimate the back electromotive force e of the β axis. β ;

[0038] According to (1), the back electromotive force y to be estimated is r Written as:

[0039]

[0040] In order to facilitate the design of adaptive observer, a non-singular transformation is introduced:

[0041] z r =Tx r (5)

[0042] The reversible matrix T is:

[0043]

[0044] Where k1 and k2 are positive real numbers to be designed.

[0045] Substituting (6) into (5) yields:

[0046]

[0047] It should be noted that in (6) and (7), the rotor electrical angular velocity ω e It cannot be used directly. However, according to (7), as long as the new state z is estimated r The estimated value of back electromotive force can be obtained;

[0048] Substituting (6) into (5) we can obtain z r The state space equation is:

[0049]

[0050] in and

[0051] As a further improvement of the present invention, an intermediate variable is constructed in step S2, and the specific process is as follows:

[0052] In order to avoid the need to directly use the information of current derivatives in observer design, a new state variable is defined according to (8):

[0053]

[0054] in k2 is the positive real number to be designed in the coordinate transformation matrix (6), k3 is the positive definite observer gain to be designed;

[0055] According to formula (9), due to the stator inductance L s , observer gain matrix K and stator current i α If the new state ξ is known, the estimated value of the back electromotive force can be obtained;

[0056] According to (4) and (8), the state space equation of ξ is:

[0057]

[0058] As a further improvement of the present invention, in step S3, according to the deterministic equivalence principle of adaptive control, the specific process is as follows:

[0059] Since the system (10) is observable, according to the adaptive control deterministic equivalence principle, the adaptive observer of (10) is designed as:

[0060]

[0061] in The adaptive term represents the estimated value of θ. The adaptive term update law is designed as:

[0062]

[0063] As a further improvement of the present invention, in step S4, the estimated back electromotive force is obtained according to the intermediate variable estimated in (11), combined with the coordinate transformation in (6) and the newly defined state variable in (9), and the specific process is as follows:

[0064] According to (9), the estimated state variable It is expressed as:

[0065]

[0066] According to (7), the estimated back EMF It is expressed as:

[0067]

[0068] in and represents the intermediate variable estimated by (11), represents the estimated back EMF.

[0069] Compared with the prior art, the present invention has the following beneficial effects:

[0070] The adaptive back electromotive force observer algorithm of the permanent magnet synchronous motor based on coordinate transformation described in the present invention does not rely on the information in the phase-locked loop, ensuring that the observer and the phase-locked loop can be designed separately and independently. Since the coupling between the observer and the phase-locked loop is eliminated, the design of the observer is simpler and more reliable. In addition, the bandwidth of the observer is no longer limited by the bandwidth of the phase-locked loop, which effectively improves the dynamic performance of the observer. The present invention is completely implemented inside the controller, does not require additional hardware, is simple to implement, and has good transient steady-state performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 The overall block diagram of the permanent magnet synchronous motor speed sensorless control system based on the adaptive back electromotive force observer according to the embodiment of the present invention;

[0072] Figure 2 A block diagram of an adaptive back-electromotive force observer algorithm for a permanent magnet synchronous motor based on coordinate transformation according to an embodiment of the present invention;

[0073] Figure 3 Simulation results of the embodiment of the present invention under the condition of speed reference and load torque step changes. DETAILED DESCRIPTION

[0074] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments:

[0075] The present invention provides a permanent magnet synchronous motor adaptive back electromotive force observer algorithm based on coordinate transformation, which does not rely on any information in a phase-locked loop, effectively avoids the mutual coupling between the observer and the phase-locked loop, and makes the observer simpler and more reliable. After ensuring that the system to be observed meets the strict positive real condition through coordinate transformation, a reduced-order adaptive observer is designed to estimate the back electromotive force information. In addition, the unknown speed information is estimated online by designing a reduced-order adaptive law, which effectively avoids the dependence on the phase-locked loop information during the observer design, and improves the dynamic performance of the observer.

[0076] like Figure 1 As shown, the overall block diagram of a permanent magnet synchronous motor speed sensorless control system based on an adaptive back electromotive force observer includes a three-phase inverter 1, a permanent magnet synchronous motor 2, a speed loop controller 3, a current loop controller 4, an inverse Park transform 5, an inverse Clark transform 6, a space vector pulse width modulation 7, a Clark transform 8, a Park transform 9, a reduced-order adaptive observer 10, a coordinate transform 11, and a phase-locked loop 12. By collecting the two-phase current i a and i b , the current i in the orthogonal coordinate system is obtained by Clark transformation8 α and i β, and combined with the reduced-order adaptive observer 10, coordinate transformation 11 and phase-locked loop 12 to obtain the estimated rotor speed and the estimated rotor position Using the estimated rotor speed and the estimated rotor position Combine the speed loop controller 3 and the current loop controller 4 to obtain the voltage reference in the rotating coordinate system and Finally, the switching signal S is obtained through inverse Park transformation 5, inverse Clark transformation 6 and space vector pulse width modulation 7. abc Used to control a three-phase inverter 1.

[0077] Figure 2 The block diagram of the adaptive back-EMF observer algorithm for permanent magnet synchronous motor based on coordinate transformation is shown in Figure 2. The specific implementation is as follows:

[0078] By collecting the 2-phase current i a and i b , and the current i in the orthogonal coordinate system is obtained by Clark transformation 8 α and i β :

[0079]

[0080] will i α and i β Substituting into the designed adaptive observer (30) and adaptive term update law (31), the estimated intermediate variable can be obtained

[0081]

[0082]

[0083] According to the definition of variable ξ (32) and the coordinate transformation (33) and (34), the estimated value of back EMF can be obtained (35):

[0084]

[0085] z r =Tx r (33)

[0086]

[0087]

[0088] Figure 3The simulation results of the adaptive back electromotive force observer algorithm of the permanent magnet synchronous motor based on coordinate transformation under the speed reference and load torque step change of the present invention are used to show that the present invention can effectively estimate the back electromotive force of the system.

[0089] The above description is only a preferred embodiment of the present invention and does not constitute any other form of limitation to the present invention. Any modification or equivalent change made based on the technical essence of the present invention still falls within the scope of protection required by the present invention.

Claims

1. A method for adaptive back-electromotive force observer of a permanent magnet synchronous motor based on coordinate transformation, characterized in that: The specific steps are as follows: S1, transforms the back electromotive force model to be estimated into a model to be estimated that satisfies strict positive real conditions through coordinate transformation; The specific process of coordinate transformation in step S1 is as follows: The voltage equation of the permanent magnet synchronous motor in the stationary coordinate system is as follows: where u α and u β represents the stator voltage of the α-axis and the β-axis, i α and i β represents the stator current of the α-axis and β-axis, R s Indicates stator resistance, L s represents the stator inductance, e α and e β represents the α-axis and β-axis back electromotive force; Assuming that the air gap magnetic flux of the motor is uniformly distributed and the high-order harmonics of the back EMF are ignored, then e α and e β It is expressed as: where ψ f represents the permanent magnet flux, ω e represents the rotor electrical angular velocity, θ e Indicates the rotor electrical position; By defining the state variable Then x r The state space model of is expressed as: among them And k = a, b; Whether κ is equal to α or β, the state space equation (3) will not change. When κ = α, the adaptive back-EMF observer algorithm of the permanent magnet synchronous motor based on coordinate transformation is used to estimate the back-EMF e of the α-axis. α Obviously, when κ = β, the same method can be used to estimate the back electromotive force e of the β axis. β ; According to (1), the back electromotive force y to be estimated is r Written as: In order to facilitate the design of adaptive observer, a non-singular transformation is introduced: z r =Tx r (5) The reversible matrix T is: Where k1 and k2 are positive real numbers to be designed; Substituting (6) into (5) yields: It should be noted that in (6) and (7), the rotor electrical angular velocity ω e It cannot be used directly. However, according to (7), as long as the new state z is estimated r The estimated value of back electromotive force can be obtained; Substituting (6) into (5) we can obtain z r The state space equation is: in and S2, by constructing an intermediate variable, effectively avoids the need to directly use the current derivative information when designing the observer; In step S2, an intermediate variable is constructed, and the specific process is as follows: In order to avoid the need to directly use the information of current derivatives in observer design, a new state variable is defined according to (8): in k2 is the positive real number to be designed in the coordinate transformation matrix (6), k3 is the positive definite observer gain to be designed; According to formula (9), due to the stator inductance L s , observer gain matrix K and stator current i α If the new state ξ is known, the estimated value of the back electromotive force can be obtained; According to (4) and (8), the state space equation of ξ is: S3, based on the deterministic equivalence principle of adaptive control, an adaptive observer is designed to estimate the intermediate variables, and a reduced-order adaptive term update law is designed to estimate the speed information in real time, eliminating the dependence of the back-electromotive force observer on the information in the phase-locked loop, ensuring that the observer and the phase-locked loop can be designed separately; In step S3, according to the deterministic equivalence principle of adaptive control, the specific process is as follows: Since the system (10) is observable, according to the adaptive control deterministic equivalence principle, the adaptive observer of (10) is designed as: in The adaptive term represents the estimated value of θ, and the adaptive term update law is designed as: S4, obtaining an estimated back electromotive force according to the intermediate variable estimated in step S3, in combination with the coordinate transformation in step S1 and the intermediate variable defined in step S2; In step S4, the estimated back electromotive force is obtained according to the intermediate variable estimated in (11), combined with the coordinate transformation in (6) and the newly defined state variable in (9). The specific process is as follows: According to (9), the estimated state variable It is expressed as: According to (7), the estimated back EMF It is expressed as: in and represents the intermediate variable estimated by (11), represents the estimated back EMF.

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