Permanent magnet synchronous motor position and speed estimation method of phase-locked loop based on complementary sliding mode observer and augmented sliding mode

Abstract

The invention discloses a permanent magnet synchronous motor position and speed estimation method of a phase-locked loop based on a complementary sliding mode observer and an augmented sliding mode, and the method comprises the following steps: 1, sampling the three-phase current of a permanent magnet synchronous motor, and obtaining the current under a two-phase static coordinate system through coordinate transformation; 2, an estimated current value is calculated according to the estimated current value mathematical model of the permanent magnet synchronous motor, a current error is obtained through calculation, and the current error serves as input of a follow-up observer; 3, calculating a feedback law according to the complementary sliding mode observer mathematical model, and calculating to obtain a back electromotive force; and step 4, performing integral calculation on the position error signal by utilizing the designed improved phase-locked loop based on augmented sliding mode control based on the back electromotive force to obtain the rotating speed of the motor and the position of the rotor. The dynamic performance of the sensorless control system of the permanent magnet synchronous motor can be effectively improved.

Description

Technical Field

[0001] The present invention relates to the technical field of permanent magnet synchronous motor control, and in particular to a permanent magnet synchronous motor position and speed estimation method based on a complementary sliding mode observer and an augmented sliding mode phase-locked loop. Background Art

[0002] Permanent magnet synchronous motor (PMSM) is widely used in modern electric vehicles, aerospace drive systems and other industrial fields due to its simple structure, high power density and wide speed range. Vector control is the most commonly used control strategy for PMSM, and its key technology relies on the feedback of rotor position and speed. The traditional method of obtaining rotor position and speed is to install mechanical position sensors, but these sensors are expensive, inconvenient to install, and unreliable under harsh working conditions, which easily increase system costs and reduce reliability. Therefore, in order to achieve high-performance control of PMSM, the research on position sensorless control technology has become a hot topic. According to different estimation principles, PMSM position sensorless control can be divided into two categories: methods based on motor back electromotive force or flux linkage and methods based on motor salient pole effect. The method based on motor salient pole characteristics is mainly high-frequency signal injection method, which uses the difference of motor AC and DC axis inductance to realize the rotor position estimation when the motor runs at zero low speed. The method based on motor back electromotive force or flux linkage is mainly used for rotor position estimation when the motor runs at medium and high speed. The sliding mode observer method is widely used in the medium and high speed field of PMSM due to its fast response and strong robustness. However, there is a problem of high-frequency jitter in the system due to the large sliding mode control gain and the use of switching functions.

[0003] In traditional SMO, the switching function is often used as the error feedback of the state variable, but due to the discontinuity of the switching function, it will cause system jitter. To improve this problem, a piecewise square root switching function in the prior art uses the characteristics of the function being continuous within the boundary layer and saturated outside the boundary layer to improve the switching function, effectively suppressing the jitter problem. The prior art uses a custom piecewise linear function to replace the sign function, but by introducing two-stage filtering and phase compensation, the system becomes more complicated. In addition, according to the boundary layer law, a linear saturation function is used to replace the sign function, and a saturation function fuzzy system with a nonlinear slope is further introduced to eliminate jitter, but the system has uncertainty problems.

[0004] In addition to introducing a continuous switching function to improve the switching function, measures such as adjusting the appropriate sliding mode gain, optimizing the sliding mode approach rate, and designing a new filter can also effectively suppress system jitter. The prior art provides a variable gain super-helical sliding mode observer, whose sliding mode gain value changes in real time with the speed, so as to improve the sliding mode jitter problem and improve the observer's observation accuracy of the speed and rotor position. The prior art provides an improved super-helical observer algorithm, which improves the system dynamic performance by designing an adaptive parameter strategy to improve the jitter problem. In addition, a new synchronous reference system filter is designed to filter out the higher harmonics of the estimated back electromotive force signal, further improving the speed and rotor position observation accuracy. The state observer of the prior art observes the feedback signal to avoid the phase error problem caused by the low-pass filter. This method achieves a wider speed regulation range.

[0005] After the back electromotive force or rotor flux is estimated by the observer, it is usually necessary to estimate the rotor position and speed of the motor through a phase-locked loop (PLL). However, the traditional phase-locked loop position tracking dynamic error and steady-state error cannot be taken into account at the same time. In the prior art, an improved phase-locked loop structure is used in the phase-locked loop to replace the fixed PI coefficient with an adaptive proportional integral (PI) parameter, thereby improving the dynamic performance of the phase-locked loop. In the prior art, a fractional-order phase-locked loop (FOPLL) replaces the original integer-order PI with a fractional-order PI, and the tracking error in the dynamic process can be effectively reduced by selecting a suitable fractional-order coefficient. However, only the PI design in the phase-locked loop is optimized, but the prior art does not change the essence of the traditional phase-locked loop second-order system, so it is impossible to completely eliminate the position tracking error of the phase-locked loop in the dynamic process.

[0006] The improved sliding mode observer strategy proposed in the prior art alleviates the chattering problem to a certain extent and improves the observation accuracy, but it still has some limitations, such as complex parameter settings and phase error problems introduced by low-pass filters. Summary of the invention

[0007] The purpose of the present invention is to provide a method for estimating the position and speed of a permanent magnet synchronous motor based on a complementary sliding mode observer and an augmented sliding mode phase-locked loop, so as to further improve the observation accuracy and robustness of the observer.

[0008] The technical solution adopted by the present invention is:

[0009] A method for estimating position and speed of a permanent magnet synchronous motor based on a phase-locked loop of a complementary sliding mode observer and an augmented sliding mode comprises the following steps:

[0010] Step 1, sampling the three-phase current of the permanent magnet synchronous motor, and obtaining the current in a two-phase stationary coordinate system through coordinate transformation;

[0011] Step 2, calculating the estimated current value according to the mathematical model of the estimated current value of the permanent magnet synchronous motor, and calculating the current error, and taking the current error as the input of the subsequent observer;

[0012] Specifically, the complementary sliding theory can effectively reduce the steady-state error and improve the convergence of the system by adding a complementary sliding surface that is orthogonal to the traditional generalized sliding surface in space.

[0013] Step 3, calculating the feedback law according to the complementary sliding mode observer mathematical model, and calculating the back electromotive force;

[0014] Step 4, based on the back electromotive force calculated in step 3, the position error signal is integrated and calculated by using the improved phase-locked loop based on augmented sliding mode control to obtain the motor speed and rotor position;

[0015] Furthermore, step 2 specifically includes the following steps:

[0016] Step 2-1, the current estimation equation of the permanent magnet synchronous motor is written as:

[0017]

[0018] In the formula, i α 、i β are the actual current values ​​on the α-axis and β-axis respectively; are the estimated current values ​​on the α-axis and β-axis respectively, are the estimated back electromotive force values ​​on the α-axis and β-axis respectively; u α 、u β are the voltage values ​​on the α-axis and β-axis respectively; L s , R s are the stator inductance and stator resistance of the motor respectively;

[0019] Step 2-2, get the observation error:

[0020]

[0021] Furthermore, the specific steps of step 3 are as follows:

[0022] Step 3-1, construct the saturation function sat(·) of the generalized sliding surface and the complementary sliding surface of the generalized sliding surface to represent the saturation function. The specific expression of sat(·) is:

[0023]

[0024] Among them, Sg represents the generalized sliding surface, S c represents the complementary sliding surface of the generalized sliding surface, φ is the boundary layer;

[0025] Step 3-2, calculate and obtain the back electromotive force of the equivalent control part and the back EMF of the switching control part The corresponding expressions are as follows:

[0026]

[0027] Among them, B i is the back electromotive force coefficient, i a is the actual current value of the α-axis, is the estimated current value of the α-axis, φ is the boundary layer, k is the constant in the sliding surface, and e is the error; ρ is the switching gain, that is, the upper bound of the external total disturbance H;

[0028] Step 3-3, the control law of the complementary sliding mode observer of the estimated back electromotive force of the α-axis in the stationary coordinate system is obtained as follows:

[0029]

[0030] In the formula, Represents the back electromotive force of the equivalent control part, for the system control under ideal conditions; Represents the back electromotive force of the switching control part, which is used to overcome external disturbances of the system.

[0031] Furthermore, the generalized sliding surface S in step 3-1 g , that is, S g The expression of (t) is as follows:

[0032]

[0033] Where k is a constant in the sliding surface, n is the order of the system, e(τ)dτ represents the error integral term, and τ is the integral variable.

[0034] Further, in step 3-1, the complementary synovial surface S c , that is, S c The expression of (t) is as follows:

[0035]

[0036] Where k is a constant in the sliding surface, n is the order of the system, e(τ)dτ represents the error integral term, and τ is the integral variable.

[0037] Furthermore, step 4 specifically includes the following steps:

[0038] Step 4-1, normalize the back electromotive force obtained by the observer to obtain the position error signal ΔE:

[0039]

[0040] in, are the estimated back electromotive force values ​​on the α-axis and β-axis respectively; θ e is the actual rotor position, To estimate the rotor position; is the permanent magnet flux, ω e is the electrical angular velocity;

[0041] Step 4-2, taking the position error signal as the input of the improved phase-locked loop based on augmented sliding mode control, wherein the expression of the improved phase-locked loop based on augmented sliding mode control is:

[0042]

[0043] in, To estimate the electrical angular velocity, To estimate the derivative of the electrical angular velocity, To estimate the acceleration, To estimate the derivative of acceleration, To estimate the rotor position, is the derivative to estimate the rotor position;

[0044] λ1, λ2, λ3 represent the coefficients of the corresponding nonlinear functions f1, f2, f3 respectively; the specific expressions of f1, f2, f3 are as follows:

[0045]

[0046] Among them, m j =j(m1-1)+1,n j =j(n1-1)+1, j is the subscript in the nonlinear functions f1, f2, f3, j=1, 2, 3, m1=1-ε, n1=1+ε, and the parameter ε is a sufficiently small positive constant;

[0047] Step 4-3, the estimated rotor position and speed are obtained by improving the phase-locked loop to estimate the rotor position and the derivative integral of the speed.

[0048] Compared with the existing technology, the advantages of the improved phase-locked loop based on augmented sliding mode are: when the estimation error in the system is large, the nonlinear error term It can speed up the convergence of the estimation error. When the estimation error is small, the nonlinear term The convergence speed of the error is faster than that of the traditional linear term. Secondly, the improved phase-locked loop based on the augmented sliding mode has a certain filtering effect when observing the speed and rotor position, which can effectively improve the observation accuracy. Therefore, the improved phase-locked loop based on the augmented sliding mode can provide more accurate observation results and stronger anti-interference ability, and better dynamic performance.

[0049] The present invention adopts the above technical solution, and introduces the complementary sliding mode control concept into the design of the observer to address the problem of decreased rotor position and speed observation accuracy caused by jitter in the traditional sliding mode observer, and proposes a sensorless control method based on the complementary sliding mode observer. At the same time, in order to address the problem of insufficient accuracy of the traditional phase-locked loop in estimating the rotor position and speed during the dynamic response of the system, the augmented sliding mode phase-locked loop is used to improve the estimation accuracy and dynamic performance of the rotor during the dynamic response of the system. Under different operating conditions, the present invention can effectively improve the dynamic performance of the sensorless control system of the permanent magnet synchronous motor. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments;

[0051] Figure 1 A schematic diagram of the structure of a system used in a method for estimating the position and speed of a permanent magnet synchronous motor based on a complementary sliding mode observer and an augmented sliding mode phase-locked loop according to the present invention;

[0052] Figure 2 It is a schematic diagram of the principle structure of the improved phase-locked loop based on augmented sliding mode of the present invention;

[0053] Figure 3 This is the principle block diagram of the experimental platform; DETAILED DESCRIPTION

[0054] In order to make the purpose, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application.

[0055] The following embodiments will further illustrate the present invention in conjunction with the accompanying drawings.

[0056] Embodiment 1: Figure 1 The schematic diagram of the designed permanent magnet synchronous motor position and speed estimation method is shown in Figure 2. Figures 1 to 3 As shown in FIG. 1 , the position and speed estimation method of the permanent magnet synchronous motor designed by the present invention can be divided into a complementary sliding mode observer part and a phase-locked loop part based on an augmented sliding mode. The designed position and speed estimation method of the permanent magnet synchronous motor completes the following steps in each control cycle:

[0057] Step 1, sampling the three-phase current of the permanent magnet synchronous motor, and obtaining the current in a two-phase stationary coordinate system through coordinate transformation;

[0058] Step 2, calculating the estimated current value according to the mathematical model of the estimated current value of the permanent magnet synchronous motor, and calculating the current error, and taking the current error as the input of the subsequent observer; specifically comprising the following steps:

[0059] Step 2-1, the current estimation equation of the permanent magnet synchronous motor is written as:

[0060]

[0061] In the formula, To estimate the current value, is the estimated value of back electromotive force;

[0062] Step 2-2, get the observation error:

[0063]

[0064] Step 3, calculating the feedback law according to the complementary sliding mode observer mathematical model, and calculating the back electromotive force;

[0065] Specifically, the complementary sliding theory can effectively reduce the steady-state error and improve the convergence of the system by adding a complementary sliding surface that is orthogonal to the traditional generalized sliding surface in space.

[0066] Complementary sliding mode control law: To ensure the stability of the system, a corresponding control law needs to be designed. A complementary sliding mode control law is designed by the equivalent control method. Taking the estimated back electromotive force of the α axis in the stationary coordinate system as an example, the specific steps of step 3 are as follows:

[0067] Step 3-1, construct the saturation function sat(·) of the generalized sliding surface and the complementary sliding surface of the generalized sliding surface to represent the saturation function. The specific expression of sat(·) is:

[0068]

[0069] Among them, S g represents the generalized sliding surface, S c represents the complementary sliding surface of the generalized sliding surface, φ is the boundary layer;

[0070] Step 3-2, calculate and obtain the back electromotive force of the equivalent control part and the back EMF of the switching control part The corresponding expressions are as follows:

[0071]

[0072] Among them, B i is the back electromotive force coefficient, ia is the actual current value of the α-axis, is the estimated current value of the α-axis, φ is the boundary layer, k is the constant in the sliding surface, and e is the error; Represents the equivalent control part, which is for the system control under ideal conditions; represents the switching control part, which is used to overcome the external disturbance of the system; ρ is the switching gain, and ρ>D, that is, the value is greater than the upper bound of the external total disturbance uncertainty term H(t);

[0073] Step 3-3, the control law of the complementary sliding mode observer of the estimated back electromotive force of the α-axis in the stationary coordinate system is obtained as follows:

[0074]

[0075] In the formula, Represents the back electromotive force of the equivalent control part, for the system control under ideal conditions; Represents the back electromotive force of the switching control part, which is used to overcome external disturbances of the system.

[0076] Furthermore, the generalized sliding surface S in step 3-1 g , that is, S g The expression of (t) is as follows:

[0077]

[0078] Where k is a constant in the sliding surface, n is the order of the system, e(τ)dτ represents the error integral term, and τ is the integral variable.

[0079] Further, in step 3-1, the complementary synovial surface S c , that is, S c The expression of (t) is as follows:

[0080]

[0081] Where k is a constant in the sliding surface, n is the order of the system, e(τ)dτ represents the error integral term, and τ is the integral variable.

[0082] Step 4, based on the back electromotive force calculated in step 3, the motor speed and rotor position are calculated by integrating the position error signal using the improved phase-locked loop based on augmented sliding mode control; further, step 4 specifically includes the following steps:

[0083] Step 4-1, normalize the back electromotive force obtained by the observer to obtain the position error signal ΔE:

[0084]

[0085] in, are the estimated back electromotive force values ​​on the α-axis and β-axis respectively; θ e is the actual rotor position, To estimate the rotor position; is the permanent magnet flux, ω e is the electrical angular velocity;

[0086] Improved phase-locked loop based on augmented sliding mode: The back electromotive force contains the speed and rotor position information. After the back electromotive force is obtained by the improved complementary sliding mode observer designed by the present invention, a phase-locked loop is usually used to estimate the speed and rotor position of the motor to obtain the error information ΔE of the traditional orthogonal phase-locked loop.

[0087] When the rotor position estimation error When it is believed that After the back electromotive force is normalized, the speed and rotor position information are estimated through the PI regulator in the phase-locked loop. The present invention is a phase-locked loop based on augmented sliding mode to improve the dynamic performance of the observer. In the movement process of the motor rotor,

[0088]

[0089] Where: θ e is the rotor position, ω e is the rotation speed, a e is the acceleration of the rotation speed; d is the jerk.

[0090] Step 4-2, taking the position error signal as the input of the improved phase-locked loop based on augmented sliding mode control, and using the high-order sliding mode theory to design the improved phase-locked loop based on augmented sliding mode control to estimate the augmented state of the motor speed, the expression of the phase-locked loop is:

[0091]

[0092] in, To estimate the electrical angular velocity, To estimate the derivative of the electrical angular velocity, To estimate the acceleration, To estimate the derivative of acceleration, To estimate the rotor position, is the derivative to estimate the rotor position;

[0093] λ1, λ2, λ3 represent the coefficients of the corresponding nonlinear functions f1, f2, f3 respectively; the specific expressions of f1, f2, f3 are as follows:

[0094]

[0095] Among them, m j =j(m1-1)+1,n j=j(n1-1)+1, j is the subscript in the nonlinear functions f1, f2, f3, j=1, 2, 3, m1=1-ε, n1=1+ε, and the parameter ε is a sufficiently small positive constant; the schematic diagram of the phase-locked loop is shown in Figure 2 shown.

[0096] Step 4-3, the estimated rotor position and speed are obtained by improving the phase-locked loop to estimate the rotor position and the derivative integral of the speed.

[0097] Compared with the existing technology, the advantages of the improved phase-locked loop based on augmented sliding mode are: when the estimation error in the system is large, the nonlinear error term It can speed up the convergence of the estimation error. When the estimation error is small, the nonlinear term The convergence speed of the error is faster than that of the traditional linear term. Secondly, the improved phase-locked loop based on the augmented sliding mode has a certain filtering effect when observing the speed and rotor position, which can effectively improve the observation accuracy. Therefore, the improved phase-locked loop based on the augmented sliding mode can provide more accurate observation results and stronger anti-interference ability, and better dynamic performance.

[0098] The present invention adopts the above technical solution, and introduces the complementary sliding mode control concept into the design of the observer to address the problem of decreased rotor position and speed observation accuracy caused by jitter in the traditional sliding mode observer, and proposes a sensorless control method based on the complementary sliding mode observer. At the same time, in order to address the problem of insufficient accuracy of the traditional phase-locked loop in estimating the rotor position and speed during the dynamic response of the system, the augmented sliding mode phase-locked loop is used to improve the estimation accuracy and dynamic performance of the rotor during the dynamic response of the system. Under different operating conditions, the present invention can effectively improve the dynamic performance of the sensorless control system of the permanent magnet synchronous motor.

[0099] Obviously, the described embodiments are part of the embodiments of the present application, rather than all of the embodiments. In the absence of conflict, the embodiments in the present application and the features in the embodiments can be combined with each other. The components of the embodiments of the present application generally described and shown in the drawings here can be arranged and designed in various different configurations. Therefore, the detailed description of the embodiments of the present application is not intended to limit the scope of the application claimed for protection, but merely represents the selected embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians of the art without making creative work are within the scope of protection of the present application.

Claims

1. A method for estimating position and speed of a permanent magnet synchronous motor based on a complementary sliding mode observer and an augmented sliding mode phase-locked loop, characterized in that: It includes the following steps ； Step 1, sampling the three-phase current of the permanent magnet synchronous motor, and obtaining the current in a two-phase stationary coordinate system through coordinate transformation; Step 2, calculating the estimated current value according to the mathematical model of the estimated current value of the permanent magnet synchronous motor, and calculating the current error, and taking the current error as the input of the subsequent observer; Step 3, calculating the feedback law according to the complementary sliding mode observer mathematical model, and calculating the back electromotive force; Step 4: The back electromotive force is integrated with the position error signal using an improved phase-locked loop based on augmented sliding mode control to calculate the motor speed and rotor position.

2. According to step 2-1 of the method for estimating position and speed of a permanent magnet synchronous motor based on a complementary sliding mode observer and an augmented sliding mode phase-locked loop according to claim 1, the current estimation equation of the permanent magnet synchronous motor is written as: In the formula, i α 、i β are the actual current values ​​on the α-axis and β-axis respectively; are the estimated current values ​​on the α-axis and β-axis respectively, are the estimated back electromotive force values ​​on the α-axis and β-axis respectively; u α 、u β are the voltage values ​​on the α-axis and β-axis respectively; L s , R s are the stator inductance and stator resistance of the motor respectively; Step 2-2, get the observation error: in, e represents the observation error.

3. The method for estimating position and speed of a permanent magnet synchronous motor based on a complementary sliding mode observer and an augmented sliding mode phase-locked loop according to claim 1, characterized in that: The specific steps of step 3 are as follows: Step 3-1, construct the saturation function sat(·) of the generalized sliding surface and the complementary sliding surface of the generalized sliding surface, which represents the saturation function; the specific expression of sat(·) is: Among them, S g represents the generalized sliding surface, S c represents the complementary sliding surface of the generalized sliding surface, φ is the boundary layer; Step 3-2, calculate and obtain the back electromotive force of the equivalent control part and the back EMF of the switching control part The corresponding expressions are as follows: Among them, B i is the back electromotive force coefficient, i a is the actual current value of the α-axis, is the estimated current value of the α-axis, φ is the boundary layer, k is the constant in the generalized sliding surface, and e is the observation error; ρ is the switching gain, that is, the upper bound of the external total disturbance H; i corresponds to different working conditions; L s , R s are the stator inductance and stator resistance of the motor respectively; Step 3-3, the control law of the complementary sliding mode observer of the estimated back electromotive force of the α-axis in the stationary coordinate system is obtained as follows: In the formula, represents the estimated value of back electromotive force on the α-axis; Represents the back electromotive force of the equivalent control part, for the system control under ideal conditions; Represents the back electromotive force of the switching control part, which is used to overcome external disturbances of the system.

4. The method for estimating position and speed of a permanent magnet synchronous motor based on a complementary sliding mode observer and an augmented sliding mode phase-locked loop according to claim 3, characterized in that: The generalized sliding surface S in step 3-1 g , that is, S g The expression of (t) is as follows: Where k is a constant in the sliding surface, n is the order of the system, e(τ)dτ represents the error integral term, and τ is the integral variable.

5. A method for estimating position and speed of a permanent magnet synchronous motor based on a complementary sliding mode observer and an augmented sliding mode phase-locked loop according to claim 3 or 4, characterized in that: Step 3-1 Complementary synovial surface S c , that is, S c The expression of (t) is as follows: Where k is a constant in the sliding surface, n is the order of the system, e(τ)dτ represents the error integral term, and τ is the integral variable.

6. The method for estimating position and speed of a permanent magnet synchronous motor based on a complementary sliding mode observer and an augmented sliding mode phase-locked loop according to claim 1, characterized in that: Step 4 specifically includes the following steps: Step 4-1, normalize the back electromotive force obtained by the observer to obtain the position error signal ΔE: in, are the estimated back electromotive force values ​​on the α-axis and β-axis respectively; θ e is the actual rotor position, To estimate the rotor position; is the permanent magnet flux, ω e is the electrical angular velocity; Step 4-2, taking the position error signal as the input of the improved phase-locked loop based on augmented sliding mode control, wherein the expression of the improved phase-locked loop based on augmented sliding mode control is: where β To estimate the electrical angular velocity, To estimate the derivative of the electrical angular velocity, To estimate the acceleration, To estimate the derivative of acceleration, To estimate the rotor position, is the derivative to estimate the rotor position; λ1, λ2, λ3 represent the coefficients of the corresponding nonlinear functions f1, f2, f3 respectively; the specific expressions of f1, f2, f3 are as follows: Among them, m j =j(m1-1)+1,n j =j(n1-1)+1, j is the subscript in the nonlinear functions f1, f2, f3, j=1, 2, 3, m1=1-ε, n1=1+ε, and the parameter ε is a sufficiently small positive constant; Step 4-3, the estimated rotor position and speed are obtained by improving the phase-locked loop to estimate the rotor position and the derivative integral of the speed.

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