Double-sliding-mode sensorless control method based on PMSMS

Abstract

The invention relates to the technical field of sliding mode control, in particular to a double-sliding-mode sensorless control method based on a PMSMS, and the method comprises the steps: setting a terminal sliding mode surface function, optimizing the rotating speed through a nonlinear control item, and introducing a variable gain coefficient; a Sigmoid function is introduced in combination with an approaching law in the design of a speed controller; the terminal sliding mode controller takes the given speed and the estimated rotating speed error of the motorized spindle as the input and takes the q-axis current as the output; carrying out stability analysis on the speed ring controller; the sliding-mode observer takes an actual current value and an observer current error as input, takes the speed and position information of an electric spindle rotor as output, improves buffeting of a sliding-mode control law in combination with a Sigmoid function, and is integrated with a phase locking ring for extracting the position and speed of the rotor; and carrying out stability judgment on the design of the sliding-mode observer. The problems of overshoot, buffeting, slow response and the like of a control system in practical application of a traditional sensorless control scheme are solved.

Description

Technical Field

[0001] The present invention relates to the technical field of sliding mode control, and in particular to a dual sliding mode sensorless control method based on PMSMS. Background Art

[0002] The high-speed electric spindle integrates the motor and the machine tool spindle, and is the core component of advanced CNC machine tools. The use of permanent magnetic materials can reduce the volume and weight of the spindle, thereby achieving an electric spindle with high power density, high reliability and high efficiency. In the control of the electric spindle, torque control is of great significance.

[0003] However, the traditional electric spindle control strategy has the following problems: dependence on sensors; insufficient control accuracy and stability; and insufficient sliding mode control and observers in the high-speed range.

[0004] At present, commonly used electric spindle control strategies, such as field-oriented control and direct torque control, rely on sensors to obtain rotor position and speed information; this not only increases the complexity and cost of the system, but may also be restricted by the operating environment and reduce the reliability of the system. Existing sensorless control strategies include high-frequency signal injection method, carrier frequency component method, direct calculation method, observer method and intelligent estimation method. Due to principle limitations, these methods are more effective in the zero-low speed range and the medium-high speed range, and are limited in the opposite direction. In addition, there are large overshoots and jitters in the control process, which further leads to the instability of the output torque of the electric spindle.

[0005] Sliding mode control is a commonly used nonlinear control technology. Although sliding mode control technology has strong robustness and anti-interference ability, it often encounters chattering problems due to switching time lag, space-time lag and control switching time lag caused by system inertia.

[0006] The dual sliding mode control proposed in the document “Research on Dual Sliding Mode Sensorless Vector Control of Permanent Magnet Synchronous Motor” introduces a hyperbolic tangent function to replace the switching function when designing the observer, and combines it with a sliding mode speed controller to enhance the robustness of the system and weaken the system jitter; however, the system still has severe overshoot during the startup phase.

[0007] The document "Research on PMSM Vector Control Based on Dual Sliding Mode Variable Structure MRAS" uses a sliding mode controller to replace the PI link and PI speed regulator in the observer, but the control system still has jitter. When tracking a high-speed spindle, the system will not converge due to high-frequency jitter.

[0008] In addition, although the existing technologies such as piecewise index function, fuzzy sliding mode observer, integral non-singular terminal sliding mode surface and variable gain super-twist sliding mode observer have improved the system performance to a certain extent, they have not been able to completely solve the problems of overshoot, jitter and insufficient anti-interference ability. Summary of the invention

[0009] In view of the shortcomings of the existing methods, the present invention solves the problems of overshoot, jitter and slow response of the control system in practical applications of traditional sensorless control schemes; and the difficulties of sliding mode control and observer design in dealing with singularity problems in the system, and the difficulty in controller design to balance control accuracy and system stability, resulting in unstable output torque.

[0010] The technical solution adopted by the present invention is: a dual sliding mode sensorless control method based on PMSMS comprises the following steps:

[0011] Step 1: Establish a terminal sliding mode controller model based on the PMSMS mathematical model, set the terminal sliding mode surface function, optimize the speed with nonlinear control items to improve the torque characteristics, and introduce a variable gain coefficient; combine the reaching law in the speed controller design, introduce the Sigmoid function to improve the discontinuity in the control; the terminal sliding mode controller uses the given speed of the electric spindle and the estimated speed error as input, and the q-axis current i q As output;

[0012] As a preferred embodiment of the present invention, the formula of the terminal sliding surface function is:

[0013]

[0014] Where x1 and x2 are tracking errors; parameter α>0; p and q are positive odd numbers; h(x1) is the variable gain; γ is an arbitrary real number; and sign is the switching function.

[0015] As a preferred implementation of the present invention, the switching function sign in the terminal sliding surface function is replaced by a sigmoid function.

[0016] As a preferred embodiment of the present invention, the formula of the sigmoid function is:

[0017]

[0018] Among them, b is the control parameter.

[0019] As a preferred embodiment of the present invention, the formula of the reaching law is:

[0020]

[0021] As a preferred embodiment of the present invention, the q-axis current i q The formula as output is:

[0022]

[0023] Where D = 1.5Pn Ψ f / J; J is the moment of inertia of the electric spindle rotor; Ψ f is the permanent magnet flux of the main shaft rotor; p n is the number of pole pairs of the electric spindle; ω m represents the mechanical angular velocity of the rotor; B is the viscous friction coefficient.

[0024] Step 2: Prove the finite time convergence of the terminal sliding surface function and perform stability analysis on the speed loop controller;

[0025] As a preferred implementation mode of the present invention, the Lyapunov function is used to perform stability analysis on the speed loop controller, and the reachability criterion is used to determine whether the speed controller reaches the sliding surface.

[0026] Step 3: Establish a sliding mode observer model based on the PMSMS mathematical model. The sliding mode observer takes the actual current value and the observer current error as input, and the motorized spindle rotor speed and position information as output. The sigmoid function is combined to improve the chattering of the sliding mode control law, and a phase-locked loop is integrated to extract the rotor position and speed.

[0027] As a preferred embodiment of the present invention, the formula of the Sigmoid function to improve the sliding mode control law is:

[0028]

[0029] Among them, δ, λ, μ are all non-zero constant coefficients; Indicates the error between the observed value and the actual current; V α ,V β It is the sliding mode control law.

[0030] Step 4: Determine the stability of the sliding mode observer design;

[0031] As a preferred implementation of the present invention, the Layapunov function is used to perform stability analysis on the sliding mode observer.

[0032] As a preferred embodiment of the present invention, the condition for the sliding mode observer to perform stability analysis is: δ≥max(|E α , E β |), E α , E β They represent the extended back electromotive force components in the α-β axes respectively.

[0033] Beneficial effects of the present invention:

[0034] 1. Effectively reduce jitter and torque pulsation: The application of NTSMC effectively reduces jitter and torque pulsation in the control system, reduces overshoot, and improves system response speed;

[0035] 2. Accurate rotor speed and position tracking: This strategy can accurately track rotor speed and position, becoming a viable alternative to mechanical sensors and broadening the potential application areas of electric spindles;

[0036] 3. Excellent anti-interference ability: This strategy shows excellent anti-interference ability under external load disturbance, ensuring the dynamic performance and stability of the system;

[0037] 4. The method of the present invention has obvious advantages in control accuracy, speed and parameter adjustment complexity, can reduce system costs, improve operating efficiency, and has significantly improved control performance compared to existing solutions. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 It is a structural block diagram of a dual sliding mode sensorless control method based on PMSMS;

[0039] Figure 2 This is a comparison chart of the characteristics of traditional linear sliding mode control and terminal sliding mode control;

[0040] Figure 3 It is the simulink simulation model of the present invention;

[0041] Figure 4 is the sigmoid(s) continuous function curve;

[0042] Figure 5 The torque response and time relationship of the surface mounted PMSMS under different speed control strategies;

[0043] Figure 6 The speed response and time relationship curves of PMSMS using different speed control strategies;

[0044] Figure 7 For the no-load start-up phase: local amplification of the speed response curves of different controllers;

[0045] Figure 8 For the load disturbance stage: local amplification of the speed response curve using different controllers;

[0046] Fig. 9 It is the speed tracking performance curve of PMSMS based on dual sliding mode sensorless control method;

[0047] Fig.10 is the relationship between the speed tracking error and time based on the dual sliding mode sensorless control method;

[0048] Fig.11 This is a comparison diagram between the actual position and the observed position of the PMSMS rotor;

[0049] Fig.12 This is a partial enlarged view of the PMSMS rotor position comparison curve. DETAILED DESCRIPTION

[0050] The present invention is further described below in conjunction with the accompanying drawings and embodiments. This figure is a simplified schematic diagram, which only illustrates the basic structure of the present invention in a schematic manner, and therefore it only shows the components related to the present invention.

[0051] like Figure 1 As shown, a dual sliding mode sensorless control method based on PMSMS includes the following steps:

[0052] The dual sliding mode joint vector control system based on the terminal sliding mode controller and the sliding mode observer adopts a dual closed-loop vector control scheme with a speed outer loop and a PI current inner loop; the observed speed error of the electric spindle is adjusted by the terminal sliding mode controller to obtain the quadrature axis current value i q *, output it to the current loop PI regulation to obtain the direct axis stator voltage u d * and quadrature axis stator voltage u q *,u d * and u q *After coordinate transformation, the rotation voltage u is obtained α * and voltage u β *, voltage u α * and voltage u β *After SVPWM conversion, the power switch acting on the main circuit inverter realizes the position sensorless vector drive control of the permanent magnet synchronous electric spindle.

[0053] Step 1: Establish a terminal sliding mode controller model based on the PMSMS mathematical model, redefine the terminal sliding mode surface function, optimize the speed with nonlinear control items to improve the torque characteristics, introduce variable gain coefficients to solve the singularity problem, and combine the reaching law in the speed controller design, introduce the Sigmoid function to improve the discontinuity in the control; the terminal sliding mode controller takes the given speed of the electric spindle and the estimated speed error as input, and the q-axis current i q as output.

[0054] The following assumptions are made for the permanent magnet synchronous electric spindle:

[0055] 1. The stator winding is star-connected, the three-phase winding is symmetrically distributed, and each phase differs by 120°;

[0056] 2. Ignore core saturation, eddy current and hysteresis losses;

[0057] 3. The magnetic field generated by the permanent magnet and the induced magnetic field generated by the three-phase winding are sinusoidally distributed;

[0058] 4. The stator winding current only generates sinusoidally distributed magnetic potential in the air gap without high-order harmonics.

[0059] First, the mathematical model of the surface-mounted permanent magnet synchronous electric spindle in the synchronous rotating coordinate system is established:

[0060]

[0061] Among them, the first and second are voltage equations, the third is the electromagnetic torque equation, and the fourth is the motion equation; and:

[0062]

[0063] Among them, u d ,u q Respectively represent the stator voltage in the dq axis; i d ,i q Respectively represent the stator current in the dq axis; L S Represents stator inductance; R s represents the stator resistance; ω m Indicates the rotor mechanical angular velocity; p n is the number of pole pairs of the electric spindle; ψ d , q are the stator winding cross-linkage flux in the dq coordinate system; f is the permanent magnet flux of the spindle rotor; J is the moment of inertia of the electric spindle rotor; T L is the load torque; T e is the electromagnetic torque; B is the viscous friction coefficient.

[0064] For surface mounted PMSMS, i d =0 control strategy, and L d =L q =L S , ignoring the viscous friction coefficient, the simplified surface-mounted PMSMS voltage equation and motion equation are obtained:

[0065]

[0066] To facilitate the design of the speed loop controller, rewrite it in the following form:

[0067]

[0068] Compared with the linear sliding surface, the terminal sliding surface can converge in a finite time. For a comparison of sliding properties, see Figure 2 ; However, the traditional terminal sliding mode has a singularity problem, so the terminal sliding mode surface function is redefined as follows:

[0069]

[0070] Where x1 and x2 are tracking errors, parameter α>0, p and q are positive odd numbers and p>q, h(x1) is the variable gain, and γ is an arbitrary real number.

[0071] Compared with the existing terminal sliding surface function, the redefined new terminal sliding surface function takes into account both fast convergence and avoidance of singularity problems.

[0072] The new terminal sliding surface function combines the advantages of linear sliding and nonlinear sliding. The function can be divided into two parts: the first two terms represent traditional linear sliding control, which can ensure rapid convergence when far away from the sliding surface; the latter term is a nonlinear element, which designs h(x) as a variable gain term, solves the traditional singularity problem, and accelerates convergence when approaching the equilibrium point; this combination of non-singular terminal sliding ensures rapid and stable convergence of the system at each stage.

[0073] Derivative the terminal sliding surface function, we get:

[0074]

[0075] In order to reduce chattering, the continuous function sigmoid(s) is used to replace the traditional switching function sign(s).

[0076] The continuous function formula is:

[0077]

[0078] Among them, b is the control parameter.

[0079] The function characteristics are as follows Figure 4 As shown, near x=0, it has the characteristics of smooth continuity and exponential change, and different values ​​of parameter b can affect the rate of change of the function graph.

[0080] Similarly, the new reaching law is designed in combination with the continuous function as follows:

[0081]

[0082] The reaching law is composed of a power reaching term and a constant speed reaching term, which enables the system to quickly approach the sliding surface when it is far away from the sliding surface, and slows down the approaching rate when it is close to the sliding surface, thereby suppressing chattering.

[0083] The state variables of the surface mounted PMSMS system are:

[0084]

[0085] In the formula, ω ref is the expected speed of the electric spindle; ω m is the actual mechanical speed of the rotor.

[0086] Definition u=i q , D = 1.5P n Ψ f / J;

[0087] Combining the equation of motion (1) and equation (9), we can obtain:

[0088]

[0089] Since the bandwidth and response speed of the current loop are much higher than those of the speed loop, we can get i q =i q * ; Combining the above, the q-axis reference current is:

[0090]

[0091] Among them, the approach coefficient

[0092] The sliding mode speed controller proposed in the literature "Research on PMSM Vector Control Based on Dual Sliding Mode Variable Structure MRAS" has the q-axis reference current as:

[0093]

[0094] Compared with the sliding mode speed controller of formula (12) in the literature, the new terminal sliding mode controller proposed in the present invention designs a new terminal sliding mode surface that can converge in a finite time on the basis of the traditional sliding mode controller, and optimizes the reaching law with a continuous function, thereby weakening the system chattering and improving the system response speed, thus avoiding the failure of the traditional sliding mode to converge the system error during high-speed tracking.

[0095] Step 2: Prove the finite time convergence of the terminal sliding mode surface function; and determine the stability of the above terminal sliding mode controller design;

[0096] The finite time convergence proof of the non-singular terminal sliding surface function in the present invention is as follows:

[0097] Let S = 0

[0098]

[0099] After differentiating equation (13), we get:

[0100]

[0101] Integrating both sides simultaneously, we get:

[0102]

[0103] The time from any initial state x≠0 to x=0 along the sliding surface is obtained:

[0104]

[0105] In summary, the terminal sliding surface function of the present invention satisfies the convergence condition within a finite time.

[0106] Next, the stability analysis of the speed loop controller is carried out:

[0107] Define the Lyapunov function:

[0108]

[0109] The derivation process for S is as follows:

[0110]

[0111] Taking the derivative of both sides of equation (17) and substituting it into the sliding mode reachability condition, we need:

[0112]

[0113] Since the time derivative of the Lyapunov function is negative definite, V gradually decreases, so the terminal sliding mode surface and its time derivative converge to the origin; that is, the reachability criterion is satisfied and the velocity controller can reach the sliding mode surface.

[0114] Step 3. Establish a sliding mode observer model based on the PMSMS mathematical model: The sliding mode observer takes the actual current value and the observer current error s as input, and the electric spindle rotor speed and position information as output. The Sigmoid function is combined to improve the jitter of the sliding mode control law, and a phase-locked loop (PLL) is integrated to extract the rotor position and speed, thereby improving the observation accuracy.

[0115] The voltage equation required for the sliding mode observer design is as follows:

[0116]

[0117] Among them, u α ,u β ,i α ,i β are all observer control inputs, u α ,u β Respectively represent the stator voltage in the α-β axis; i α ,i β They represent the stator current in the α-β axis respectively; E α , E β They represent the extended back electromotive force components in the α-β axis respectively;

[0118] Taking the state variable as the stator current, the sliding surface is designed as:

[0119]

[0120] Among them, I s represents the current vector, represents the observed value of stator current, Indicates the error between the observed value and the actual current.

[0121] The sliding mode observer equation is as follows:

[0122]

[0123] Among them, V α ,V β For the sliding mode control law, the control law is designed as:

[0124]

[0125] Among them, δ, λ, μ are all non-zero constant coefficients.

[0126] The current error equation is obtained by subtracting the voltage equation from the observer equation:

[0127]

[0128] When the system reaches the sliding surface, it will slide on the sliding surface. At this time, the sliding surface converges. According to the equivalent control principle, the formula is:

[0129]

[0130] in, is the observed value of back EMF without filtering.

[0131] Reference "Research on Dual Sliding Mode Sensorless Vector Control of Permanent Magnet Synchronous Motor[J]. Journal of Lanzhou University of Arts and Sciences (Natural Science Edition), 2022, 36(04): 47-52. DOI: 10.13804 / j.cnki.2095-6991.2022.04.017." When designing the observer, the hyperbolic tangent function is used instead of the traditional switching function. The designed control law is as follows:

[0132]

[0133] Compared with the above-mentioned sliding mode observer control law, the present invention adopts a smoother sigmoid function to optimize the traditional switching function; the Tanh function is relatively more linear in the entire definition domain, while the Sigmoid function is smoother and more stable in the (0-1) output region, which can avoid sharp changes in the control signal, thereby avoiding system instability caused by large fluctuations in the control signal; in the electric spindle control system, smooth control signal changes can reduce mechanical wear, increase the service life of the system, or avoid unnecessary stress on the actuator.

[0134] The back EMF is low-pass filtered, and the formula is:

[0135]

[0136] Among them, ω c is the cutoff frequency of the low-pass filter.

[0137] Considering the inverse tangent function to obtain the rotor position and speed information, the formula is:

[0138]

[0139] in, Represents the rotor angle observation value Represents the observed value of the rotor mechanical angular velocity.

[0140] In the inverse tangent operator, when When the rotor position has noise, it will cause rotor position estimation error and reduce the position observation accuracy. A phase-locked loop is further introduced to solve the above problem.

[0141] Back EMF α , E β The statement is as follows:

[0142]

[0143] According to the phase-locked loop input represented by formula (29), combined with trigonometric functions and differential product formulas, we get:

[0144]

[0145] From the above formula, we can see that when When , the sine function can be approximated as:

[0146]

[0147] Among them, θ e Indicates the actual rotor electrical angular velocity; Represents the observed value of electrical angular velocity.

[0148] ΔE is obtained by obtaining the angular velocity of the rotor and then integrating it to obtain the position of the rotor. The formula is as follows:

[0149]

[0150] Among them, Kp and Ki are non-zero constant coefficients.

[0151] Step 4: Determine the stability of the sliding mode observer design;

[0152] The Layapunov function is used to analyze the stability of the sliding mode observer. The process is as follows:

[0153]

[0154] After taking the derivative of V, we substitute the current error and the current error derivative into the equation:

[0155]

[0156] For the convenience of calculation demonstration, they are represented by AB respectively, where A satisfies:

[0157]

[0158] Since the first term of A is a constant negative value, it is necessary to satisfy Similarly, B also satisfies

[0159] As long as the above two inequalities hold true at the same time, the sliding mode motion can be stabilized, so the stability condition of the system is δ≥max(|E α , E β |).

[0160] The dual sliding mode sensorless control system based on surface-mounted PMSMS constructed in step three is simulated and verified.

[0161] like Figure 3 The design process is verified through the MATLAB / Simulink platform; the given parameters of the permanent magnet synchronous electric spindle are: rated speed N e =10,000r / min, rated power P W =15kW, stator inductance L S =2.8mH, stator resistance R S =0.15Ω, the moment of inertia is J = 0.015kg·m -2 , number of magnetic pole pairs P n =2, permanent magnet flux Ψ f =0.11wb.

[0162] In order to verify the performance of the proposed method in speed-torque control and rotor position tracking, the following experiments were designed and implemented: during the no-load startup phase, the speed was set to 6,000 r / min; at 1 s, the speed was increased to 10,000 r / min; then, at 2 s, a load of 10 N·m was suddenly applied to simulate the load disturbance in actual machining; under the same working conditions, comparative experiments were also carried out on traditional PI control, sliding mode control, and composite control strategies; the experimental results will be analyzed according to the order of the physical values ​​of torque, speed, and position.

[0163] The torque response curves based on three different control strategies are as follows: Figure 5 As shown in the figure, the PI controller has significant advantages in torque control due to its linear characteristics. The traditional sliding mode will have a large pulse amplitude even in the stable operation stage, and the error is close to 12N·m. The large error not only seriously affects the machining accuracy of the machine tool spindle, but may even cause tool damage. The proposed terminal sliding mode control can control the output error within the range of ±2.3N·m, thereby significantly reducing the torque pulsation of the electric spindle. In addition, from the local amplification Figure 5 It can be seen that when subjected to external load disturbances, the torque curve achieved by terminal sliding mode control shows significant robustness, which is better than other control methods; this robustness greatly reduces the adverse effects of external disturbances.

[0164] Judging from the torque curve, terminal sliding mode control can effectively alleviate oscillation and reduce torque changes, thus bringing considerable benefits to practical processing applications; these improvements not only improve processing efficiency and accuracy, but also reduce tool wear, thereby reducing overall processing costs.

[0165] Figure 6 It is the speed curve based on three different control strategies when the speed is set to 10,000r / min; Figure 7-8 According to Figure 6 The enlarged local image obtained; comparison Figure 7-8 It can be seen that compared with PI control and traditional sliding mode control, the terminal sliding mode control method shows better performance in speed regulation, and there is almost no overshoot phenomenon.

[0166] Fig. 9 and Fig.10 The speed tracking performance and speed error of PMSMS under the dual sliding mode sensorless control method are demonstrated respectively; it can be seen that the dual sliding mode sensorless control method can stably and quickly track the rotor speed in all stages, and at the same time weaken the jitter and reduce the error.

[0167] Figure 11-12The rotor position comparison curve of PMSMS is shown; it can be seen that the rotor position error based on the traditional PI sliding mode sensorless control method is large, while the estimated position based on the dual sliding mode sensorless control method is very close to the actual position curve, indicating that this method has excellent rotor position tracking capability.

[0168] Based on the above ideal embodiments of the present invention, the relevant staff can make various changes and modifications without departing from the technical concept of the present invention through the above description. The technical scope of the present invention is not limited to the contents of the specification, and its technical scope must be determined according to the scope of the claims.

Claims

1. A dual sliding mode sensorless control method based on PMSMS, characterized in that: The following steps are involved: Step 1: Construct a sliding mode controller model, set the terminal sliding mode surface function, optimize the speed with nonlinear control items, and introduce a variable gain coefficient; combine the reaching law in the speed controller and introduce the Sigmoid function; the terminal sliding mode controller takes the given speed of the electric spindle and the estimated speed error as input, and the q-axis current as output; Step 2: Prove the finite time convergence of the terminal sliding surface function and perform stability analysis on the speed loop controller; Step 3: Construct a sliding mode observer model. The sliding mode observer takes the actual current value and the observer current error as input, and the motorized spindle rotor speed and position information as output. The sigmoid function is combined to improve the chattering of the sliding mode control law, and a phase-locked loop is integrated to extract the rotor position and speed. Step 4: Determine the stability of the sliding mode observer.

2. The dual sliding mode sensorless control method based on PMSMS according to claim 1 is characterized in that: The formula of the terminal sliding surface function is: Where x1 and x2 are tracking errors; parameter α>0; p and q are positive odd numbers; h(x1) is the variable gain; γ is an arbitrary real number; and sign is the switching function.

3. The dual sliding mode sensorless control method based on PMSMS according to claim 2 is characterized in that: The switching function sign in the terminal sliding surface function is replaced by the sigmoid function.

4. The dual sliding mode sensorless control method based on PMSMS according to claim 3 is characterized in that: The formula for the sigmoid function is: Among them, b is the control parameter.

5. The dual sliding mode sensorless control method based on PMSMS according to claim 1, characterized in that: The formula of the reaching law is: in, 6. The dual sliding mode sensorless control method based on PMSMS according to claim 1, characterized in that: The formula for the q-axis current is: Where D = 1.5P n Ψ f / J; J is the moment of inertia of the electric spindle rotor; Ψ f is the permanent magnet flux of the main shaft rotor; p n is the number of pole pairs of the electric spindle; ω m represents the mechanical angular velocity of the rotor; B is the viscous friction coefficient.

7. The dual sliding mode sensorless control method based on PMSMS according to claim 1, characterized in that: The Lyapunov function is used to analyze the stability of the speed loop controller, and the reachability criterion is used to determine whether the speed controller reaches the sliding surface.

8. The dual sliding mode sensorless control method based on PMSMS according to claim 1, characterized in that: The formula of the Sigmoid function to improve the sliding mode control law is: Among them, δ, λ, μ are all non-zero constant coefficients; Indicates the error between the observed value and the actual current; V α ,V β It is the sliding mode control law.

9. The dual sliding mode sensorless control method based on PMSMS according to claim 1, characterized in that: The Layapunov function is used to analyze the stability of the sliding mode observer.

10. The dual sliding mode sensorless control method based on PMSMS according to claim 9, characterized in that: The condition for the sliding mode observer to perform stability analysis is: δ≥max(|E α , E β |), E α , E β They represent the extended back electromotive force components in the α-β axes respectively.

Images