Improved nonlinear sensorless control method for permanent magnet synchronous motor

Abstract

The application belongs to the technical field of motor control, and particularly relates to an improved nonlinear sensorless control method for a permanent magnet synchronous motor. The method comprises the following steps: S1: constructing an observer state equation for inner linear frequency domain design based on a closed-loop transfer function and a target transfer function; S2: injecting high-order nonlinear terms into the observer state equation to construct an improved nonlinear back-EMF observer; S3: embedding the group delay of the improved nonlinear back-EMF observer into a phase-locked loop of a phase-locked loop to obtain an improved phase-locked loop; and S4: using a dynamic factor to adaptively scale the nonlinear gain of the improved nonlinear back-EMF observer and the bandwidth of the improved phase-locked loop to realize sensorless control of the permanent magnet synchronous motor. The nonlinear gain of the back-EMF observer and the bandwidth of the phase-locked loop are adaptively scaled, so that collaborative dynamic acceleration is realized.

Description

Technical Field

[0001] This invention belongs to the field of motor control technology, and particularly relates to an improved nonlinear sensorless control method for permanent magnet synchronous motors. Background Technology

[0002] With their excellent power density and superior operating efficiency, permanent magnet synchronous motors (PMSMs) occupy an important position in many fields such as electric transportation and industrial servo drives. Conventional PMSM drive systems rely on mechanical position sensors to acquire the rotor's angular frequency and position signals. However, in practical engineering applications, these sensors not only increase hardware costs and assembly complexity but are also prone to failure under harsh operating conditions, becoming a key bottleneck limiting the reliability of the entire motor control system. Traditional nonlinear sensorless control methods have three inherent limitations: First, the lack of precise linear frequency domain design leads to amplitude attenuation and phase lag during back EMF signal extraction, directly causing steady-state errors in the rotor position observed by the phase-locked loop (PLL). Second, they lack targeted integer harmonic suppression capabilities, making it difficult to filter out strong harmonic disturbances caused by complex operating conditions such as dead-zone effects and inverter non-ideal characteristics. Third, there is a lack of parameter coordination design between the back EMF observer and the PLL. These three defects combine to restrict the overall control performance of traditional nonlinear sensorless control methods. Summary of the Invention

[0003] In view of this, the present invention aims to provide an improved nonlinear sensorless control method for permanent magnet synchronous motors (PMSMs) to address the problems of amplitude attenuation and phase lag, insufficient targeted integer harmonic suppression capability, and lack of parameter coordination design between the back-EMF observer and the phase-locked loop (PLL) in traditional nonlinear sensorless control methods. In the back-EMF observation stage, the present invention cleverly utilizes higher-order nonlinear terms to accelerate the dynamic convergence process of the outer back-EMF while strictly maintaining the high-precision characteristics of the inner linear frequency domain design. It not only achieves unity gain and zero phase lag at the fundamental operating point in steady state but also successfully achieves deep suppression of the -5th and +7th integer harmonics. In the PLL position observation stage, the present invention fundamentally reconstructs the PLL by embedding the group delay of the back-EMF observer into the position tracking loop. By adaptively scaling the nonlinear gain of the back-EMF observer and the bandwidth of the PLL, it achieves coordinated dynamic acceleration. The above mechanism effectively breaks through the performance limitations of traditional nonlinear control methods and provides a novel and efficient technical approach for the coordinated optimization of the dynamic and steady-state performance of sensorless control methods for PMSMs.

[0004] To achieve the above objectives, the technical solution created by this invention is implemented as follows: An improved nonlinear sensorless control method for permanent magnet synchronous motors includes the following steps: S1: Based on the complex coefficient voltage model of permanent magnet synchronous motor, a first-order current observer and a second-order internal model are constructed. Based on the first-order current observer and the second-order internal model, a closed-loop transfer function for back EMF observation is constructed. Based on the closed-loop transfer function and the target transfer function, the observer state equation for the inner linear frequency domain design is constructed. S2: Inject higher-order nonlinear terms into the observer's state equations to construct an improved nonlinear back EMF observer; S3: The group delay of the improved nonlinear back EMF observer is embedded into the phase-locked loop of the phase-locked loop to obtain the improved phase-locked loop; S4: By using dynamic factor adaptive scaling to improve the nonlinear gain of the nonlinear back EMF observer and improve the bandwidth of the phase-locked loop, sensorless control of the permanent magnet synchronous motor can be achieved.

[0005] Furthermore, in step S1, the expression for the complex coefficient voltage model of the permanent magnet synchronous motor is: ; in, For differential operators, The stator current complex vector is the one that is stationary. For stator inductance, The stator voltage complex vector is the stationary axis. For stator resistance, It is the complex vector of back electromotive force on the stationary axis.

[0006] Furthermore, in step S1, the expression for the first-order current observer is: ; in, For differential operators, For the estimated stator current state of the synchronous shaft, The actual stator voltage complex vector of the synchronous shaft. For stator resistance, For the estimated back EMF complex vector of the synchronous axis, For stator inductance, The imaginary unit, For the estimated rotor angular frequency, The feedback gain of the first-order current observer. The complex vector of stator current estimation error for the synchronous shaft.

[0007] Furthermore, in step S1, the expression for the second-order internal model element is: ; in, For the estimated back EMF complex vector of the synchronous axis, , and For the numerator polynomial coefficients of the second-order internal mode, and For the coefficients of the denominator polynomial of the second-order internal module, The complex vector of stator current estimation error for the synchronous shaft. For the Laplace operator of the synchronous axis.

[0008] Furthermore, in step S1, the expression for the closed-loop transfer function of the back potential observation is: ; in, The Laplace domain representation of the actual back electromotive force complex vector of the synchronous axis. , and For the numerator polynomial coefficients of the second-order internal mode, and For the coefficients of the denominator polynomial of the second-order internal module, For the Laplace operator of the synchronous axis, For stator inductance, These are the stator electrical characteristic parameters.

[0009] Furthermore, the expression for the observer state equation that completes the inner-layer linear frequency domain design is as follows: ; in, The feedback gain of the first-order current observer. For stator resistance, For stator inductance, and For the coefficients of the denominator polynomial of the second-order internal module, The horizontal distance from the dominant pole to the imaginary axis. The horizontal distance from the conjugate poles to the imaginary axis. The perpendicular distance from the dominant pole to the conjugate pole. For total gain, For the real coefficients of the polynomial parameters, , and For the numerator polynomial coefficients of the second-order internal mode, This is the estimated rotor angular frequency.

[0010] Furthermore, in step S2, the expression for the improved nonlinear back potential observer is: ; in, For differential operators, The actual stator voltage complex vector of the synchronous shaft. For the estimated stator current state of the synchronous shaft, and For internal state variables, The estimated back EMF complex vector for the synchronous axis. For the estimated rotor electrical angle, The imaginary unit, The stator voltage complex vector is the stationary axis. The complex vector of stator current estimation error on the stationary axis. For stator resistance, For stator inductance, For the estimated rotor angular frequency, The feedback gain of the first-order current observer. The complex vector of stator current estimation error for the synchronous shaft. These are the gains corresponding to the higher-order nonlinear terms in each state equation. It is a higher-order nonlinear term. and For the coefficients of the denominator polynomial of the second-order internal module, The estimated back electromotive force is the complex vector of the stationary axis.

[0011] Furthermore, in step S3, the phase-locked loop is improved as follows: ; ; in, The derivative of the estimated rotor angle, For the estimated rotor angular frequency, These represent the feedback gains for each state of the improved phase-locked loop. The derivative of the estimated rotor angular frequency, For the estimated rotor angular acceleration, For the derivative of the estimated rotor angular acceleration, This is the position error signal. To improve the group delay of the nonlinear back potential observer, For the desired real pole frequency, For the desired conjugate pole frequency, is the damping ratio.

[0012] Furthermore, in step S4, the specific operation of improving the nonlinear gain of the nonlinear back potential observer using dynamic factor adaptive scaling is as follows: ; in, As a dynamic factor, It is a higher-order nonlinear term. and For the coefficients of the denominator polynomial of the second-order internal module, For stator inductance, The complex vector of stator current estimation error for the synchronous shaft. For the real coefficients of the polynomial parameters, These are the gains of the higher-order nonlinear terms corresponding to each state equation.

[0013] Furthermore, in step S4, the specific operation of improving the bandwidth of the phase-locked loop using dynamic factor adaptive scaling is as follows: ; in, For the desired real pole frequency, For the desired conjugate pole frequency, The nominal natural frequency of the conjugate poles. The preset phase-locked loop bandwidth, This is the preset upper limit of the dynamic factor. As a dynamic factor, This is the proportionality coefficient for the real poles.

[0014] Compared with the prior art, the present invention can achieve the following beneficial effects: The improved nonlinear sensorless control method for permanent magnet synchronous motors described in this invention features an inner-layer linear frequency domain design strictly controlled by a single group delay parameter. This ensures unity gain and zero phase lag at the fundamental frequency operating point in steady state, as well as deep suppression of the -5th and +7th integer harmonics. In dynamic conditions, the higher-order nonlinear term gain of the improved nonlinear back-EMF observer at the front end and the position tracking bandwidth of the improved phase-locked loop at the back end are unified by a dynamic factor. The system performs global linkage. This collaborative dynamic acceleration mechanism enables the system to synchronously expand bandwidth to significantly improve dynamic tracking capabilities under transient operating conditions, and automatically back down to the nominal bandwidth in steady state to suppress harmonics, ultimately achieving global optimization of both dynamic and steady-state performance. Attached Figure Description

[0015] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments and descriptions of the invention are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings: Figure 1 A flowchart illustrating the improved nonlinear sensorless control method for permanent magnet synchronous motors described in the embodiments of the present invention; Figure 2 A schematic diagram of the structure of the improved nonlinear sensorless control process of the permanent magnet synchronous motor described in the embodiment of the present invention; Figure 3 To create two different equivalent Bode plots as described in the embodiments of the present invention, (a) is to improve the nonlinear back potential observer in different... Bode plot below, (b) for improving phase-locked loop in different Bode plot below; Figure 4 The steady-state experimental results of the two methods at a rated speed of 1400 r / min described in the embodiments of the present invention are as follows: (a) is the steady-state experimental result of the traditional nonlinear sensorless control method, and (b) is the steady-state experimental result of the improved nonlinear sensorless control method of the present invention. Figure 5 The following diagram shows the dynamic experimental results of the two methods under step acceleration dynamics described in the embodiments of the present invention: (a) shows the dynamic experimental results of the traditional nonlinear sensorless control method, and (b) shows the dynamic experimental results of the improved nonlinear sensorless control method of the present invention. Figure 6 The zero-pole distribution diagram of the real coefficient observation back EMF transfer function of the synchronous shaft described in the embodiment of the present invention. Detailed Implementation

[0016] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not constitute a limitation thereof.

[0017] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0018] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicating orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation on this invention. Furthermore, the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, features defined with "first," "second," etc., may explicitly or implicitly include one or more of that feature. In the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0019] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art will understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0020] The invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0021] like Figure 1 As shown, this invention provides an improved nonlinear sensorless control method for permanent magnet synchronous motors, specifically including the following steps: S1: Based on the complex coefficient voltage model of permanent magnet synchronous motor, a first-order current observer and a second-order internal model are constructed. Based on the first-order current observer and the second-order internal model, a closed-loop transfer function for back EMF observation is constructed. Based on the closed-loop transfer function and the target transfer function, the observer state equation for the inner linear frequency domain design is constructed. S2: Inject higher-order nonlinear terms into the observer's state equations to construct an improved nonlinear back EMF observer; S3: The group delay of the improved nonlinear back EMF observer is embedded into the phase-locked loop of the phase-locked loop to obtain the improved phase-locked loop; S4: By using dynamic factor adaptive scaling to improve the nonlinear gain of the nonlinear back EMF observer and improve the bandwidth of the phase-locked loop, sensorless control of the permanent magnet synchronous motor can be achieved.

[0022] It should be noted that, firstly, based on the complex coefficient voltage model of the permanent magnet synchronous motor, a first-order current observer and a second-order internal model are designed. By configuring the transfer function of the back EMF observer, the linear frequency domain design of the inner layer is realized. On this basis, higher-order nonlinear terms are introduced to form an improved nonlinear back EMF observer. Then, the group delay of the improved nonlinear back EMF observer is embedded into the phase-locked loop (PLL) bribery to reconstruct the improved PLL. Finally, by using a dynamic factor to adaptively scale the nonlinear gain of the improved nonlinear back EMF observer and the bandwidth of the improved PLL, sensorless control of the permanent magnet synchronous motor is achieved.

[0023] S1: First, establish the complex coefficient voltage model of the permanent magnet synchronous motor on the stationary axis: (1.1); in: For differential operators, The stator voltage complex vector is the stationary axis. The stator current complex vector is the one that is stationary. The complex vector of the back electromotive force along the stationary axis. For stator resistance, It is the stator inductance.

[0024] In order to achieve deep suppression of integer harmonics of -5th and +7th orders in a low-order structure, this invention designs the complex coefficient observation back EMF transfer function of the stationary axis as a filter structure with one dominant pole, two conjugate poles and two zeros, and uses this as the linear frequency domain design kernel for improving the nonlinear back EMF observer.

[0025] Laplace operator about the stationary axis Introducing operator transformation: ,in, It is the Laplace operator for the synchronous axis. The imaginary unit, Given the estimated rotor angular frequency, design the real-coefficient observed back EMF transfer function for the synchronous shaft: (1.2); In equation (1.2): for The real coefficient transfer function of the axis, i.e., the target transfer function; Total gain; Let be the polynomial parameters with real coefficients, and their algebraic relationship with the pole parameters is as follows: (1.3); In equation (1.3): where It is the horizontal distance from the dominant pole to the imaginary axis. It is the horizontal distance from the conjugate poles to the imaginary axis. This is the perpendicular distance from the dominant pole to the conjugate pole. To achieve accurate linear frequency domain design of the inner layer, the above poles are strictly mapped to a value inversely proportional to the single group delay parameter: (1.4); In equation (1.4): The target group delay parameter; The preset constant coefficients determine the low-pass filtering characteristics of the system. The zero-pole distribution described by equations (1.2), (1.3), and (1.4) is as follows: Figure 1 As shown. To avoid signal amplitude attenuation and to meet the unity gain requirement of sensorless control at the fundamental frequency operating point, The value should be obtained in real time based on the amplitude-frequency characteristics, so that equation (1.2) is in... The steady-state gain is always 1.

[0026] The kernel of the linear real coefficient transfer function in equation (1.2) While it can guarantee accurate linear frequency domain design under steady-state conditions, its dynamic response during transient processes is limited by a fixed bandwidth. To address this issue, this invention proposes to construct an improved nonlinear back EMF observer by introducing higher-order nonlinear terms.

[0027] First, this invention establishes a first-order current observer: (1.5); In equation (1.5): For the estimated stator current state of the synchronous shaft; The actual stator voltage complex vector of the synchronous shaft; For the estimated back EMF complex vector of the synchronous axis; The complex vector of stator current estimation error for the synchronous shaft; Let be the feedback gain of the current observer. To ensure it precisely matches the target transfer function in equation (1.2). The present invention further uses For input, establish a system containing internal state variables. and Second-order internal model stage: (1.6); In equation (1.6): For the numerator polynomial coefficients of the second-order internal mode; Let be the coefficients of the denominator polynomial of the second-order internal mode element. By combining the error dynamics of the first-order current observer in equation (1.5) with the second-order internal mode element in equation (1.6), the closed-loop transfer function from the actual back EMF to the estimated back EMF can be obtained: (1.7); In equation (1.7): The Laplace domain representation of the actual back electromotive force complex vector of the synchronous axis; Let (1.7) be the stator electrical characteristic parameters. Then, combine (1.7) with the aforementioned target transfer function. By performing identity comparison, the matching relationships of all parameters can be analytically derived, thereby completely realizing the linear frequency domain design of the inner layer: (1.8); S2: To overcome the limitations of fixed bandwidth under transient conditions, this invention introduces a higher-order nonlinear term. , It is about The Sigmoid function is used to estimate the error based on the stator current. The amplitude is dynamically adjusted to control the output weight. By injecting this higher-order nonlinear term into the state equation of the observer, which has already been designed in the linear frequency domain, a complete improved nonlinear back EMF observer is constructed: (1.9); In equation (1.9): For the estimated rotor electrical angle; and These are the coordinate rotation transformation factors for the positive and negative directions, respectively; The estimated back electromotive force complex vector is the stationary axis; The complex vector of stator current estimation error for the stationary axis; These represent the gains of the higher-order nonlinear terms corresponding to each state equation. Equation (1.9) shows that the improved nonlinear back-potential observer proposed in this invention accelerates the dynamic convergence process of the outer layer using higher-order nonlinear terms, while the stator current estimation error in steady state is reduced. Approaching zero, the higher-order nonlinear terms decay, and the system seamlessly reverts to the precise linear frequency domain design state, while simultaneously balancing transient convergence speed and steady-state observation accuracy.

[0028] S3: In traditional nonlinear sensorless control methods, transient velocity deviations exist in the back-end position tracking loop. This error couples with the group delay of the front-end back EMF observer. This coupling causes phase hysteresis, resulting from both the velocity deviation and the group delay, to unexpectedly enter the angle error, severely weakening the system's dynamic tracking capability. To fundamentally decouple these interactions, this invention explicitly embeds the improved group delay of the nonlinear back EMF observer into the phase-locked loop's phase-locked loop circuit. The reconstructed and improved phase-locked loop is as follows: (1.10); In equation (1.10): The derivative of the estimated rotor angle, For the estimated rotor angular frequency, The derivative of the estimated rotor angular frequency, For the estimated rotor angular acceleration, For the derivative of the estimated rotor angular acceleration, This is the position error signal. These represent the feedback gains for each state of the improved phase-locked loop. By matching the coefficients of the characteristic polynomial of the improved phase-locked loop with the standard parameterized pole equations, the phase-locked loop gain configuration rules including group delay compensation can be analytically derived. (1.11); In equation (1.11): The desired real pole frequency; The desired frequency of the conjugate poles; Let be the damping ratio. Substituting (1.11) into (1.10), the closed-loop error transfer function from the actual position to the position estimation error is: (1.12); In equation (1.12): Let the Laplace domain representation of the position estimation error be used. This is the Laplace domain representation of the actual rotor electrical angle; Let be the Laplace operator. From equation (1.12), it can be intuitively seen that the poles of the denominator of the reconstructed closed-loop error transfer function do not contain group delay. Therefore, the improved phase-locked loop successfully maintains its pole placement characteristic independent of group delay, effectively solving the coupling problem caused by velocity deviation. Furthermore, according to the final value theorem (1.12), regardless of whether the external input signal manifests as a step position change, a step speed change, or a ramp speed change, the steady-state position estimation error generated by the improved phase-locked loop will eventually converge strictly to zero. This characteristic fully verifies that even under complex dynamic conditions, the reconstructed position tracking loop of this invention can maintain extremely high position observation accuracy, providing a backend architectural guarantee for achieving overall collaborative dynamic acceleration.

[0029] S4: To determine the gain of the higher-order nonlinear terms in the improved nonlinear back-potential observer, this invention introduces a dynamic factor. Configure gain Constant, dynamic factor Compared with other auxiliary higher-order nonlinear terms, the gain It strictly follows the following autonomous scheduling law during runtime: (1.13); Equation (1.13) elegantly normalizes the originally complex multi-degree-of-freedom nonlinear gain tuning problem into a problem controlled by a single dynamic factor. The dominant scaling process. In the back-end position tracking loop, to completely eliminate the coupling risks caused by transient velocity deviations and achieve global collaborative dynamic acceleration, this invention incorporates the instantaneous dynamic factor of the front-end observer. The signal is passed to the improved phase-locked loop at the back end: (1.14); In equation (1.14): The nominal natural frequency of the conjugate poles; The preset phase-locked loop bandwidth; This is the preset upper limit of the dynamic factor; The real pole proportionality coefficient satisfies .

[0030] like Figure 2 As shown, It is the reference angular frequency. yes The axis reference current, PI represents the proportional-integral controller. The improved nonlinear sensorless control method provided by this invention uses a phase-locked loop to estimate the back EMF vector. The estimated angular frequency of the rotor is obtained from this. and estimated location It then feeds back the data to the rest of the system's control loops in real time.

[0031] like Figure 3 As shown, with As the system gradually converges, the higher-order nonlinear terms significantly broaden the transient bandwidth during periods of large transient errors, resulting in remarkable synergistic dynamic acceleration. In steady state, where the error approaches zero, the system reverts to a precise linear frequency domain design kernel, strictly maintaining the notch characteristics at specific frequencies and achieving deep suppression of the -5th and +7th integer harmonics. This frequency domain characteristic further validates the superiority of this invention in overcoming the bottleneck of dynamic-steady-state tradeoffs and achieving global performance optimization.

[0032] like Figure 4 As shown, from top to bottom, the waveforms are the estimated back EMF waveform, the back EMF harmonic spectrum, the rotor position estimation waveform, and the position estimation error waveform. It is evident that compared to traditional nonlinear sensorless control methods, this invention significantly improves the steady-state observation accuracy of the system. Thanks to the precise linear frequency domain design of the inner layer, this invention substantially reduces the DC bias of the back EMF, suppresses the -5th and +7th integer harmonics, and significantly reduces the total harmonic distortion (THD) of the estimated back EMF. The mean and standard deviation of the position estimation error are further compressed to 0.040 rad and 0.002 rad, respectively, representing reductions of 92.5% and 75.0%. Experimental results fully demonstrate that this invention effectively overcomes the performance limitations of traditional methods at rated speeds. With its reconstructed improved nonlinear back EMF observer and improved phase-locked loop, it achieves stronger integer harmonic suppression capability and more accurate position observation accuracy, verifying the technical superiority of this invention under steady-state conditions.

[0033] like Figure 5 As shown in the experiment, the reference speed was changed stepwise at 200 r / min, 600 r / min and 1000 r / min at 2-second intervals, and finally reached the rated speed of 1400 r / min. Figure 5The figures, from top to bottom, show the corresponding speed tracking curves, speed estimation errors, steady-state position error statistics, and peak transient position error comparisons. It is evident that the method proposed in this invention significantly suppresses both peak speed estimation errors and peak transient position errors, demonstrating the beneficial effects of synergistic dynamic acceleration. Furthermore, upon reaching each steady-state speed range, the system seamlessly reverts to a precise linear frequency domain design kernel, resulting in extreme compression of the standard deviation of the position estimation error and maintaining the average position error at an extremely low level. These dynamic experimental results are highly consistent with the conclusions of the aforementioned steady-state experiments at rated speed, fully verifying the global optimization capability of this invention for dynamic steady-state performance across the entire speed range.

[0034] like Figure 6 As shown, the -5th and +7th integer harmonics of the stationary axis are converted into those of the synchronous axis through operator transformation. Second harmonics cause the distribution of zeros and poles to revolve around the fundamental frequency. Symmetrical distribution, where If the rotor angular frequency is zero, then the total phase contribution of the zero poles is 0, which satisfies the zero phase lag requirement for back EMF observation.

[0035] It should be understood that the various forms of processes shown above can be used to reorder, add, or delete steps. For example, the steps described in this invention disclosure can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution disclosed in this invention can be achieved, and this is not limited herein.

[0036] The specific embodiments described above do not constitute a limitation on the scope of protection of this invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. An improved nonlinear sensorless control method for permanent magnet synchronous motors, characterized in that: Specifically, the steps include the following: S1: Based on the complex coefficient voltage model of permanent magnet synchronous motor, a first-order current observer and a second-order internal model are constructed. Based on the first-order current observer and the second-order internal model, a closed-loop transfer function for back EMF observation is constructed. Based on the closed-loop transfer function and the target transfer function, the observer state equation for the inner linear frequency domain design is constructed. S2: Inject higher-order nonlinear terms into the observer's state equations to construct an improved nonlinear back EMF observer; S3: The group delay of the improved nonlinear back EMF observer is embedded into the phase-locked loop of the phase-locked loop to obtain the improved phase-locked loop; S4: By using dynamic factor adaptive scaling to improve the nonlinear gain of the nonlinear back EMF observer and improve the bandwidth of the phase-locked loop, sensorless control of the permanent magnet synchronous motor can be achieved.

2. The improved nonlinear sensorless control method for permanent magnet synchronous motors according to claim 1, characterized in that: In step S1, the expression for the complex coefficient voltage model of the permanent magnet synchronous motor is: ； in, For differential operators, The stator current complex vector is the one that is stationary. For stator inductance, The stator voltage complex vector is the stationary axis. For stator resistance, It is the complex vector of back electromotive force on the stationary axis.

3. The improved nonlinear sensorless control method for permanent magnet synchronous motors according to claim 1, characterized in that: In step S1, the expression for the first-order current observer is: ； in, For differential operators, For the estimated stator current state of the synchronous shaft, The actual stator voltage complex vector of the synchronous shaft. For stator resistance, The estimated back EMF complex vector for the synchronous axis. For stator inductance, The imaginary unit, For the estimated rotor angular frequency, The feedback gain of the first-order current observer. The complex vector of stator current estimation error for the synchronous shaft.

4. The improved nonlinear sensorless control method for permanent magnet synchronous motors according to claim 1, characterized in that: In step S1, the expression for the second-order internal model element is: ； in, The estimated back EMF complex vector for the synchronous axis. , and For the numerator polynomial coefficients of the second-order internal mode, and For the coefficients of the denominator polynomial of the second-order internal module, The complex vector of stator current estimation error for the synchronous shaft. For the Laplace operator of the synchronous axis.

5. The improved nonlinear sensorless control method for permanent magnet synchronous motors according to claim 1, characterized in that: In step S1, the expression for the closed-loop transfer function of the back potential observation is: ； in, The estimated back EMF complex vector for the synchronous axis. The Laplace domain representation of the actual back electromotive force complex vector of the synchronous axis. , and For the numerator polynomial coefficients of the second-order internal mode, and For the coefficients of the denominator polynomial of the second-order internal module, For the Laplace operator of the synchronous axis, For stator inductance, These are the stator electrical characteristic parameters.

6. The improved nonlinear sensorless control method for permanent magnet synchronous motors according to claim 1, characterized in that: The expression for the observer state equation after completing the inner linear frequency domain design is as follows: ； in, The feedback gain of the first-order current observer. For stator resistance, For stator inductance, and For the coefficients of the denominator polynomial of the second-order internal module, The horizontal distance from the dominant pole to the imaginary axis. The horizontal distance from the conjugate poles to the imaginary axis. The perpendicular distance from the dominant pole to the conjugate pole. For total gain, For the real coefficients of the polynomial parameters, , and For the numerator polynomial coefficients of the second-order internal mode, This is the estimated rotor angular frequency.

7. The improved nonlinear sensorless control method for permanent magnet synchronous motors according to claim 1, characterized in that: In step S2, the expression for the improved nonlinear back potential observer is: ； in, For differential operators, The actual stator voltage complex vector of the synchronous shaft. For the estimated stator current state of the synchronous shaft, and For internal state variables, The estimated back EMF complex vector for the synchronous axis. For the estimated rotor electrical angle, The imaginary unit, The stator voltage complex vector is the stationary axis. The complex vector of stator current estimation error on the stationary axis. For stator resistance, For stator inductance, For the estimated rotor angular frequency, The feedback gain of the first-order current observer. The complex vector of stator current estimation error for the synchronous shaft. These are the gains corresponding to the higher-order nonlinear terms in each state equation. It is a higher-order nonlinear term. and For the coefficients of the denominator polynomial of the second-order internal module, The estimated back electromotive force is the complex vector of the stationary axis.

8. The improved nonlinear sensorless control method for permanent magnet synchronous motors according to claim 1, characterized in that: In step S3, the phase-locked loop is improved as follows: ； ； in, The derivative of the estimated rotor angle, For the estimated rotor angular frequency, These represent the feedback gains for each state of the improved phase-locked loop. The derivative of the estimated rotor angular frequency, For the estimated rotor angular acceleration, For the derivative of the estimated rotor angular acceleration, This is the position error signal. To improve the group delay of the nonlinear back potential observer, For the desired real pole frequency, For the desired conjugate pole frequency, is the damping ratio.

9. The improved nonlinear sensorless control method for permanent magnet synchronous motors according to claim 1, characterized in that: In step S4, the specific operation of improving the nonlinear gain of the nonlinear back potential observer using dynamic factor adaptive scaling is as follows: ； in, As a dynamic factor, It is a higher-order nonlinear term. and For the coefficients of the denominator polynomial of the second-order internal module, For stator inductance, The complex vector of stator current estimation error for the synchronous shaft. For the real coefficients of the polynomial parameters, These are the gains of the higher-order nonlinear terms corresponding to each state equation.

10. The improved nonlinear sensorless control method for permanent magnet synchronous motors according to claim 1, characterized in that: In step S4, the specific operation of improving the bandwidth of the phase-locked loop using dynamic factor adaptive scaling is as follows: ； in, For the desired real pole frequency, For the desired conjugate pole frequency, The nominal natural frequency of the conjugate poles. The preset phase-locked loop bandwidth, This is the preset upper limit of the dynamic factor. As a dynamic factor, This is the proportionality coefficient for the real poles.

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