Pmsm sensorless control method and system based on polynomial saturation function sliding mode observer

Abstract

The present application relates to permanent magnet synchronous motor control technology field, specifically relates to a kind of polynomial saturation function sliding mode observer PMSM sensorless control method and system, including establishing motor voltage equation and current state equation, construct the sliding mode observer using fast terminal hyper spiral control law, the control law includes proportional term, integral term and the linear term related to sliding surface.Then design polynomial saturation function, it is continuous smooth cubic polynomial in boundary layer, it is sign function outside boundary layer.Polynomial saturation function is substituted into observer control law, replaces sign switching function, estimates back electromotive force using observer, integral term in control law directly outputs back electromotive force estimation value, without low-pass filter.Finally, through heterodyne method according to back electromotive force, rotor position and speed are calculated, sensorless closed-loop control is realized.The present application effectively suppresses chattering, avoids phase delay, improves estimation accuracy, and is suitable for new energy vehicles and industrial robot driving system.

Description

Technical Field

[0001] This invention relates to the field of permanent magnet synchronous motor control technology, and in particular to a sensorless control method and system for a PMSM using a polynomial saturated function sliding mode observer. Background Technology

[0002] In the vector control system of permanent magnet synchronous motors, the rotor speed and position need to be detected in real time to achieve closed-loop speed control. Traditional solutions typically use mechanical position sensors, but installing position sensors has disadvantages such as high cost, low reliability, and inconvenient installation and maintenance, limiting the application of the motor in harsh environments. Therefore, sensorless control technology has become a research hotspot in the field of permanent magnet synchronous motor control.

[0003] Among numerous sensorless control methods, the sliding mode observer method obtains rotor position and speed information by estimating back electromotive force or flux linkage. It exhibits excellent dynamic performance and strong robustness, low computational complexity, and insensitivity to changes in motor parameters and external disturbances, thus enjoying widespread application in engineering practice. However, traditional sliding mode observers often use sign functions to construct error feedback for state variables. Due to the discontinuity of sign functions, high-frequency chattering inevitably occurs. To eliminate chattering, a low-pass filter is usually introduced to filter the estimated back electromotive force, but this leads to phase lag and introduces estimation errors. To compensate for phase lag, a position compensation circuit based on speed and filter bandwidth needs to be designed, which complicates the system structure. To fundamentally solve the chattering problem, existing research mainly focuses on improving the sliding mode observer structure and the switching function, but problems such as slow convergence speed, insufficient smoothness of the switching function, and difficulty in parameter tuning still exist. Summary of the Invention

[0004] In view of this, the purpose of this invention is to propose a sensorless control method and system for PMSM using a polynomial saturated function sliding mode observer, in order to solve the problems of chattering caused by the use of sign functions in the traditional sliding mode observer of existing sensorless control of permanent magnet synchronous motors, phase delay caused by the introduction of low-pass filters to eliminate chattering, and limited convergence speed of existing improved sliding mode observers.

[0005] To achieve the above objectives, this invention provides a sensorless control method for a PMSM (Permanent Magnet Synchronous Motor) using a polynomial saturated function sliding mode observer, comprising the following steps:

[0006] Step S1: Establish the current state equation of the permanent magnet synchronous motor and construct a fast terminal super-helical sliding mode observer. The control law of the observer includes a proportional term, an integral term, and a fast term, wherein the fast term contains a fast term gain δ.

[0007] Step S2: Design a polynomial saturation function to replace the sign switching function in the fast terminal super-spiral sliding mode observer. The polynomial saturation function is a continuous smooth polynomial function with respect to the current error inside the sliding surface boundary layer and a sign function outside the boundary layer.

[0008] Step S3: Substitute the polynomial saturation function into the control law of the fast terminal super-spiral sliding mode observer, and use the observer to estimate the back electromotive force. The integral term in the control law is directly output as the back electromotive force estimate after integral filtering.

[0009] Step S4: Calculate the rotor position and speed directly based on the estimated back electromotive force to achieve sensorless closed-loop control.

[0010] Preferably, in step S1, the control law of the fast terminal superspiral sliding mode observer... satisfy:

[0011] ;

[0012] in For sliding surface, , For sliding mode gain, For the fast term gain, For symbolic functions, The first-order time derivative of the auxiliary state variable is used, and the control law is applied to the α-axis and β-axis respectively.

[0013] Preferably, the current error state equation of the fast terminal superspiral sliding mode observer constructed in step S1 is:

[0014] ;

[0015] in, , For current observation error, For the system matrix, This is the estimated value for the d-axis inductance. , This is the actual back electromotive force. , The sliding surface is the component of the control law applied to the α and β axes. .

[0016] Preferably, in step S2, the polynomial saturation function Defined as:

[0017] ;

[0018] in, For boundary layer thickness, Constructed using Hermite interpolation polynomials, the expression is:

[0019]

[0020] Where K is the saturation function gain.

[0021] Preferably, the saturation function gain K is taken as... The expression for the polynomial saturation function within the boundary layer is:

[0022] .

[0023] Preferably, in step S3, after substituting the polynomial saturation function, the control law of the sliding mode observer is:

[0024] ;

[0025] in , These are stator current observations. , This is the stator voltage.

[0026] Preferably, in step S3, when the observer's state variable reaches the sliding mode surface and the current observation error is zero, the estimated value of the back electromotive force is:

[0027] ;

[0028] The estimated position error is obtained using the heterodyne method shown in the following formula:

[0029] ;

[0030] in, , This is an estimate of the back electromotive force. To estimate the rotor position, Where k is the actual rotor position, and k is the back electromotive force coefficient. To address the position estimation error, closed-loop control is used to... The rotor position is obtained when the value approaches zero.

[0031] Preferably, the convergence time of the sliding mode motion of the polynomial saturated function satisfies:

[0032]

[0033]

[0034]

[0035]

[0036] in, For sliding mode variables, For boundary layer thickness, The constant related to the sliding mode gain is obtained by integrating the above differential equation, which gives the finite convergence time from any point in the boundary layer to the origin.

[0037] The present invention also provides a sensorless control system for a permanent magnet synchronous motor employing the above method, comprising:

[0038] The data acquisition unit is used to acquire the stator voltage and current signals of the permanent magnet synchronous motor.

[0039] The sliding mode observer unit has the polynomial saturation function built in and is configured to perform back electromotive force estimation in step S3 of the above method based on the voltage and current signals.

[0040] The position and velocity calculation unit is configured to execute step S4 in the above method, calculate the real-time position and velocity of the rotor based on the estimated back electromotive force, and output the result to the closed-loop control module of the motor.

[0041] The present invention also provides a permanent magnet synchronous motor drive system, comprising:

[0042] Permanent magnet synchronous motor;

[0043] Inverter, used to drive the permanent magnet synchronous motor;

[0044] And the aforementioned sensorless control system for permanent magnet synchronous motor, wherein the control system is connected to the inverter.

[0045] The beneficial effects of this invention are:

[0046] 1. This invention designs a saturation function based on Hermite interpolation polynomials. This saturation function is a continuous and smooth cubic polynomial within the boundary layer and a sign function outside the boundary layer. By adjusting the boundary layer thickness and the saturation function gain, a continuous transition from linear saturation to a sign function can be obtained. The construction process uses multi-node Hermite interpolation, with nodes set to 0, 0, Φ, Φ. The constraints are the function value and derivative value, ensuring a smooth connection of the saturation function at the boundary layer endpoints. Compared with traditional sign functions and linear saturation functions, the polynomial saturation function constructed in this invention has higher smoothness and adjustable parameters, fundamentally suppressing sliding mode chattering. Furthermore, it eliminates the need for low-pass filters, thus avoiding the phase delay problem caused by low-pass filters and simplifying the system structure.

[0047] 2. This invention applies the aforementioned polynomial saturation function to the fast terminal superspiral sliding mode observer, replacing the original sign switching function. The fast terminal superspiral control law contains linear terms related to the sliding surface, resulting in faster convergence compared to traditional superspiral algorithms. Furthermore, since the integral term in the control law directly outputs the back EMF estimate, this integral term performs integral filtering on the polynomial saturation function, making the back EMF signal smooth and free of high-frequency components. This eliminates the need for subsequent filtering and allows direct use for rotor position calculation, further improving the real-time performance and accuracy of position estimation.

[0048] 3. This invention uses the heterodyne method as a phase detector to extract the rotor position error signal from the estimated back electromotive force, and constructs a phase-locked loop (PLL) closed-loop adjustment to bring the phase error close to zero, thereby obtaining accurate rotor position and speed. Theoretical analysis shows that under the action of a polynomial saturation function, the convergence time of sliding mode motion from any point within the boundary layer to the origin is a finite value, and the convergence speed can be adjusted by the boundary layer thickness and gain parameters. Compared with traditional sliding mode observers and existing improved super-helical sliding mode observers, this invention has smaller speed observation errors and position estimation errors in both low-speed and steady-state operation, making it particularly suitable for permanent magnet synchronous motor drive systems for new energy vehicles and industrial robots that require high control accuracy and stability. Attached Figure Description

[0049] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only for this invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0050] Figure 1 This is a flowchart of the PMSM sensorless control method for the polynomial saturated function sliding mode observer of the present invention;

[0051] Figure 2 This is a block diagram of the PMSM sensorless control of the polynomial saturated function sliding mode observer of the present invention;

[0052] Figure 3 This is a comparison of the switching function curves under different K values, assuming the boundary layer thickness is set to one.

[0053] Figure 4 This is a comparison chart of motor speed observation errors under the vector control model of permanent magnet synchronous motor in this invention, specifically the traditional sliding mode observer, the fast terminal superspiral sliding mode observer, and the polynomial saturated function fast terminal superspiral sliding mode observer. Detailed Implementation

[0054] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.

[0055] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0056] Example 1:

[0057] like Figure 1 As shown, this embodiment provides a sensorless control method for a polynomial saturated function sliding mode observer (PMSM), including the following steps, and its control block diagram is shown below. Figure 2 As shown.

[0058] Step S1: Establish the voltage equation and current state equation of the stationary two-phase coordinate system of the permanent magnet synchronous motor. Based on the current state equation of the motor, design a back EMF sliding mode observer based on a fast terminal super spiral, and obtain the rotor speed and position through a phase-locked loop.

[0059] The voltage equations for the stationary two-phase coordinate system of the permanent magnet synchronous motor are as follows:

[0060] ;

[0061] in, , The stator voltage component is in a stationary two-phase coordinate system. , The stator current component is in a stationary two-phase coordinate system. , For inductance , The estimated value; For resistors The estimated value.

[0062] The expression for the back electromotive force is: ;

[0063] in It is a permanent magnet flux chain. This is the rotor position angle.

[0064] Using stator current as the state variable, , Assuming the input control quantity, the state equation with current as the state variable is obtained as follows:

[0065] ;

[0066] Among them, the system matrix ;

[0067] The constructed sliding mode observer model is as follows:

[0068] ;

[0069] in, , These are stator current observations; , For the control law of the fast terminal superspiral sliding mode observer.

[0070] The control law of the sliding mode observer adopts the form of a fast terminal superhelix, and its expression is:

[0071] ;

[0072] In the formula, k1 and k2 are sliding mode gains. The gain of the fast term can be adjusted to increase the convergence speed, and z is an auxiliary state variable.

[0073] The current error state equation is:

[0074] ;

[0075] in, , This represents the error in current observation.

[0076] When the system enters the sliding mode Then the control law for the fast terminal superspiral sliding mode observer is:

[0077] ;

[0078] Substituting the above control law into the observer model, we obtain the complete sliding mode observer expression as follows:

[0079] .

[0080] Step S2: Design a polynomial saturation function to replace the sign switching function in the sliding mode observer. The designed polynomial saturation function... ;

[0081] in For boundary layer thickness, Constructed using Hermite interpolation polynomials, with nodes set to 0, 0, Φ, Φ. The standard form of the Hermite interpolation polynomial is:

[0082] ;

[0083] Where K is the saturation function gain.

[0084] The standard form of the Hermite interpolation polynomial is:

[0085] ;

[0086] In the formula: represent The average difference of the order, Representative node .

[0087] node If a function has both function value constraints and derivative value constraints, it is considered a multiple node. For a saturated function, the node configuration is as follows:

[0088] node , Set to 0 (representing the constraint at the origin), node , Set as (Representing the constraints at the boundary layer), i.e. .

[0089] The constraint values ​​corresponding to the nodes are: , , , .

[0090] For non-repeating nodes, the first-order mean difference is defined as:

[0091] ;

[0092] For repeated nodes (i.e.) According to the definition of a limit:

[0093] ;

[0094] The zeroth-order mean difference is:

[0095] , ;

[0096] First-order mean difference calculation:

[0097] ;

[0098] ;

[0099] ;

[0100] Substituting the first-order mean difference into the above, we can obtain the second-order mean difference as follows:

[0101] ;

[0102] ;

[0103] Substituting the second-order mean difference into the above, we can obtain the third-order mean difference as follows:

[0104] ;

[0105] Substituting into the interpolation polynomial, we get:

[0106] ;

[0107] When the saturation function gain K reaches the critical gain When the above expression simplifies to

[0108] ;

[0109] At this point, the polynomial saturation function is

[0110] , .

[0111] Step S3: Substitute the polynomial saturation function into the control law of the sliding mode observer, and use the observer to estimate the back electromotive force.

[0112] The sliding mode observer model after substituting the polynomial saturation function is:

[0113] ;

[0114] When the observer state variable reaches the sliding surface, the system is stable, the current error is zero, and the output of the integral term in the control law is the estimated value of the back electromotive force, expressed as:

[0115] ;

[0116] Step S4: Calculate the rotor position and speed based on the estimated back electromotive force to achieve sensorless closed-loop control.

[0117] The position error signal is extracted from the estimated back electromotive force using the heterodyne method as a phase detector.

[0118]

[0119] in Represents the back electromotive force coefficient. Represents the estimated position of the rotor. It is the estimated position error of the rotor. Closed-loop regulation via phase-locked loop enables By approaching zero, a precise estimated rotor position can be obtained. .

[0120] In the above method, the convergence time of the sliding mode motion of the polynomial saturated function satisfies the equation:

[0121] ;

[0122] To simplify the calculation, let ,but , The above formula simplifies to

[0123] ;

[0124] Calculation from boundary layer edge To any point within the layer Transform into arrive time :

[0125] ;

[0126] The detailed calculation process of the above formula is as follows:

[0127] ;

[0128] in .

[0129] The results indicate that the convergence time from any point within the boundary layer to the origin is finite, and the convergence speed can be adjusted by parameters and the boundary layer thickness.

[0130] This invention also provides a sensorless control system for a permanent magnet synchronous motor using the above-described method, comprising a data acquisition unit, a sliding mode observer unit, and a position and velocity calculation unit. The data acquisition unit acquires the stator voltage and current signals of the permanent magnet synchronous motor; the sliding mode observer unit has a built-in polynomial saturation function and performs back electromotive force estimation based on the acquired voltage and current signals; the position and velocity calculation unit calculates the real-time position and velocity of the rotor based on the estimated back electromotive force and outputs it to the motor's closed-loop control module.

[0131] The present invention also provides a permanent magnet synchronous motor drive system, including a permanent magnet synchronous motor, an inverter for driving the permanent magnet synchronous motor, and a sensorless control system for the permanent magnet synchronous motor, wherein the control system is connected to the inverter.

[0132] Example 2:

[0133] In a specific embodiment of the present invention, the parameters of the permanent magnet synchronous motor are taken as typical values, the boundary layer thickness Φ is taken as a value between 0.5 and 1, the saturation function gain K is selected according to the critical gain K=3 / Φ, and the fast terminal superhelical gain k1, k2 and fast term gain δ are tuned according to the dynamic performance requirements of the system. Figure 3 The switching function curves for different K values ​​are given when the boundary layer thickness Φ=1. It can be seen that the larger the K value, the larger the slope of the function in the boundary layer, and the faster it approaches the sign function. When K=3, the function curve transitions smoothly and has excellent chattering suppression performance. Figure 4 A comparison of rotational speed observation errors under the same operating conditions is presented for the traditional sliding mode observer, the fast terminal superspiral sliding mode observer, and the polynomial saturated function fast terminal superspiral sliding mode observer of the present invention. The results show that the method of the present invention has the smallest observation error and the fastest convergence speed.

[0134] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed in this application can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0135] In the embodiments provided in this application, it should be understood that the disclosed devices / terminal equipment and methods can be implemented in other ways. For example, the device / terminal equipment embodiments described above are merely illustrative. For instance, the division of modules or units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the displayed or discussed mutual coupling or direct coupling or communication connection may be through some interfaces; the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms.

[0136] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0137] If the integrated module / unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the content included in the computer-readable medium can be appropriately added or removed according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable media do not include electrical carrier signals and telecommunication signals.

[0138] The implementation of all or part of the processes in the methods of the above embodiments can also be accomplished by a computer program product. When the computer program product is run on a terminal device, the terminal device can implement the steps in the various method embodiments described above.

[0139] The embodiments described above are only used to illustrate the technical solutions of this application, and are not intended to limit it. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A sensorless control method for a polynomial saturated function sliding mode observer (PMSM), characterized in that, Includes the following steps: Step S1: Establish the current state equation of the permanent magnet synchronous motor and construct a fast terminal super-helical sliding mode observer. The control law of the observer includes a proportional term, an integral term, and a fast term, wherein the fast term contains a fast term gain δ. Step S2: Design a polynomial saturation function to replace the sign switching function in the fast terminal super-spiral sliding mode observer. The polynomial saturation function is a continuous smooth polynomial function with respect to the current error inside the sliding surface boundary layer and a sign function outside the boundary layer. Step S3: Substitute the polynomial saturation function into the control law of the fast terminal super-spiral sliding mode observer, and use the observer to estimate the back electromotive force. The integral term in the control law is directly output as the back electromotive force estimate after integral filtering. Step S4: Calculate the rotor position and speed directly based on the estimated back electromotive force to achieve sensorless closed-loop control.

2. The PMSM sensorless control method for a polynomial saturated function sliding mode observer according to claim 1, characterized in that, In step S1, the control law of the fast terminal superspiral sliding mode observer satisfy: ； in For sliding surface, , For sliding mode gain, For the fast term gain, For symbolic functions, The first-order time derivative of the auxiliary state variable is used, and the control law is applied to the α-axis and β-axis respectively.

3. The PMSM sensorless control method for a polynomial saturated function sliding mode observer according to claim 2, characterized in that, The current error state equation of the fast terminal superhelical sliding mode observer constructed in step S1 is: ； in, , For current observation error, For the system matrix, This is the estimated value for the d-axis inductance. , This is the actual back electromotive force. , The sliding surface is the component of the control law applied to the α and β axes. .

4. The PMSM sensorless control method for a polynomial saturated function sliding mode observer according to claim 1, characterized in that, In step S2, the polynomial saturation function Defined as: ； in, For boundary layer thickness, Constructed using Hermite interpolation polynomials, the expression is: Where K is the saturation function gain.

5. The PMSM sensorless control method for a polynomial saturated function sliding mode observer according to claim 4, characterized in that, The gain K of the saturation function is taken as follows The expression for the polynomial saturation function within the boundary layer is: 。 6. The PMSM sensorless control method for a polynomial saturated function sliding mode observer according to claim 1, characterized in that, In step S3, after substituting the polynomial saturation function, the control law of the sliding mode observer is: ； in , These are stator current observations. , This is the stator voltage.

7. The PMSM sensorless control method for a polynomial saturated function sliding mode observer according to claim 1, characterized in that, In step S3, when the observer's state variable reaches the sliding mode surface and the current observation error is zero, the estimated value of the back electromotive force is: ； The estimated position error is obtained using the heterodyne method shown in the following formula: ； in, , This is an estimate of the back electromotive force. To estimate the rotor position, Where is the actual rotor position, and k is the back electromotive force coefficient. To address the position estimation error, closed-loop control is used to... The rotor position is obtained when the value approaches zero.

8. The PMSM sensorless control method for a polynomial saturated function sliding mode observer according to claim 1, characterized in that, The convergence time of the sliding mode motion of the polynomial saturated function satisfies: in, For sliding mode variables, For boundary layer thickness, The constant related to the sliding mode gain is obtained by integrating the above differential equation, which gives the finite convergence time from any point in the boundary layer to the origin.

9. A sensorless control system for a permanent magnet synchronous motor employing the method described in any one of claims 1 to 8, characterized in that, include: The data acquisition unit is used to acquire the stator voltage and current signals of the permanent magnet synchronous motor. The sliding mode observer unit, which has the polynomial saturation function built in, is configured to perform the back electromotive force estimation of step S3 of claim 1 based on the voltage and current signals. The position and velocity calculation unit is configured to perform step S4 of claim 1, calculate the real-time position and velocity of the rotor based on the estimated back electromotive force, and output the result to the closed-loop control module of the motor.

10. A permanent magnet synchronous motor drive system, characterized in that, include: Permanent magnet synchronous motor; Inverter, used to drive the permanent magnet synchronous motor; And the sensorless control system for the permanent magnet synchronous motor as described in claim 9, wherein the control system is connected to the inverter.

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