Position-free control method based on improved superspiral sliding mode

Abstract

The invention provides a position-free control method based on an improved superspiral sliding mode, and belongs to the technical field of motor control, and the method comprises the steps: building a current state equation of a permanent magnet synchronous motor under a two-phase static coordinate system; establishing an improved super-spiral sliding mode observer to obtain a current observation equation; wherein a sign function sign in the sliding mode control function is replaced by a hyperbolic tangent function tanh, and the value of the hyperbolic tangent function tanh is determined based on table look-up and linear interpolation; determining an error equation of the stator current; performing low-pass filtering on the sliding mode control rate to obtain a back electromotive force estimated value; inverse trigonometric function calculation is carried out, and compensation is carried out to obtain a compensated rotor rotation angle estimation value; and substituting into a nonlinear state equation to obtain an angular velocity estimation value. The method has the beneficial effects that a sign function sign is replaced by a continuous and smooth hyperbolic tangent function tanh, and a table look-up interpolation form is adopted, so that the operand is reduced while the buffeting problem of the system is further reduced, and the method can be applied to an embedded system with limited resources.

Description

Technical Field

[0001] The invention relates to the technical field of motor control, and in particular to a position-free control method based on an improved super-helical sliding mode. Background Art

[0002] Permanent magnet synchronous motors have high efficiency, high power density, and fast dynamic response capabilities. They can quickly respond to changing load and speed requirements. They are suitable for applications that require high-precision control and fast dynamic adjustment, and are widely used in various industries. Traditional permanent magnet synchronous motor control methods are all based on position sensor control methods, but the working environment of position sensors is very complex, and some working environments do not allow the installation of position sensors. The position sensorless control method is based on the vector control strategy, and estimates the back electromotive force by using the sliding mode variable structure theory, and then extracts the rotor signal and speed signal of the motor.

[0003] The traditional sliding mode observer has a simple model and mature technology, but it has the following problems: the traditional sliding mode observer usually uses a sign function as the switching function, which will cause high-frequency jitter; the convergence speed of the traditional sliding mode observer is average; when the sign function is changed to a function with smooth and continuous characteristics, the amount of calculation is large, which makes it difficult to apply in embedded systems. Summary of the invention

[0004] In order to solve the above technical problems, the present invention provides a position-free control method based on an improved super-helical sliding mode.

[0005] The technical problem solved by the present invention can be achieved by adopting the following technical solutions:

[0006] A position-free control method based on an improved super-helical sliding mode, comprising:

[0007] Step S1, establishing a voltage state equation of the permanent magnet synchronous motor in a two-phase stationary coordinate system, and converting the voltage state equation to obtain a current state equation;

[0008] Step S2, establishing an improved super-helical sliding mode observer to obtain a current observation equation; wherein the sign function sign in the sliding mode control function of the improved super-helical sliding mode observer is replaced by a hyperbolic tangent function tanh, and the value of the hyperbolic tangent function tanh is determined based on table lookup and linear interpolation;

[0009] Step S3, determining a stator current error equation according to the current state equation and the current observation equation;

[0010] Step S4, performing low-pass filtering on the sliding mode control rate in the current observation equation to obtain a back electromotive force estimation value;

[0011] Step S5, performing inverse trigonometric function calculation on the back electromotive force estimation value to obtain a rotor angle estimation value, and compensating the rotor angle estimation value to obtain a compensated rotor angle estimation value;

[0012] Step S6, substituting the compensated rotor angle estimation value into the nonlinear state equation to obtain the angular velocity estimation value.

[0013] Preferably, the current state equation is:

[0014]

[0015] In the formula,

[0016] Among them, i α 、i β are the current vectors in the α-β coordinate system; L d is the d-axis inductance; u α 、u β are the voltage vectors in the α-β coordinate system; α , β are the extended back electromotive force in the α-β coordinate system; R is the resistance of the stator winding; ω e is the rotor angular velocity; L q is the q-axis inductance.

[0017] Preferably, the calculation method of the extended back electromotive force λ is:

[0018]

[0019] Among them, ψ f is the permanent magnet flux; i d and i q is the current vector in the dq coordinate system; θ is the rotor position angle.

[0020] Preferably, the current observation equation is:

[0021]

[0022] In the formula,

[0023] in, are the observed values ​​of stator current in α-β coordinate system; L d is the d-axis inductance; u α 、u β are the voltage vectors in the α-β coordinate system; z α 、z β are the sliding mode control rates in the α-β coordinate system; R is the resistance of the stator winding; ω e is the rotor angular velocity; Lq is the q-axis inductance.

[0024] Preferably, the stator current error equation is:

[0025]

[0026] In the formula,

[0027] in, are the current observation errors in the α-β coordinate system; are the observed values ​​of stator current in α-β coordinate system respectively; i α 、i β are the current vectors in the α-β coordinate system; L d is the d-axis inductance; α , β are the extended back electromotive force in the α-β coordinate system; z α 、z β are the sliding mode control rates in the α-β coordinate system; R is the resistance of the stator winding; ω e is the rotor angular velocity; L q is the q-axis inductance.

[0028] Preferably, the sliding mode control rate z is calculated as follows:

[0029]

[0030] Where k is the sliding mode gain; i α 、i β are the current vectors in the α-β coordinate system respectively.

[0031] Preferably, the back electromotive force estimation value is calculated as follows:

[0032]

[0033] Among them, v α 、v β are the estimated values ​​of back electromotive force in the α-β coordinate system; s is the sliding mode variable; ω c is the cutoff frequency of the low-pass filter; z α 、z β are the sliding mode control rates in the α-β coordinate system respectively.

[0034] Preferably, the calculation method of the rotor angle estimation value is:

[0035]

[0036] Among them, v α 、v βThey are the estimated values ​​of back electromotive force in the α-β coordinate system; is the estimated value of the rotor angle.

[0037] Preferably, the method for calculating the estimated value of the compensated rotor angle is:

[0038]

[0039] in, is the estimated value of the rotor angle after compensation; is the estimated value of the rotor angle; ω e is the rotor angular velocity; ω c is the cutoff frequency of the low-pass filter.

[0040] Preferably, the angular velocity estimation value is calculated as follows:

[0041]

[0042] In the formula, u = -k p |x r tanh(x)-k i tanh(x)

[0043] Where x is the state variable, i.e. the estimated value of the rotor angle after compensation u is the input; y is the output, that is, the estimated value of angular velocity ω e ; t is time; a(t,x) and b(t,x) are continuous sliding mode variable structure functions; s(t,x) is the sliding surface function; k p is the scale parameter; k i is the integration parameter; r is a constant.

[0044] The advantages or beneficial effects of the technical solution of the present invention are:

[0045] The present invention not only achieves high-precision tracking performance, especially in speed and position control, by adopting improved super-helical sliding mode control, but also improves the accuracy of speed estimation; moreover, the super-helical sliding mode suppresses jitter through an integral term, which can effectively suppress the high-frequency jitter problem in traditional sliding mode control and enhance the robustness to external interference and parameter perturbations; at the same time, it exhibits rapid response capability in the face of sudden load changes and is superior to traditional sliding mode algorithms in terms of recovery time; in addition, by replacing the symbol function sign with a continuous and smooth hyperbolic tangent function tanh and adopting a table lookup interpolation form, the system jitter problem is further reduced while the amount of calculation is reduced, so that it can be applied in embedded systems with limited resources. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1It is a flow chart of a position-free control method based on an improved super-helical sliding mode (IST-SMO) in a preferred embodiment of the present invention;

[0047] Figure 2 A system block diagram of an improved super-spiral sliding mode (IST-SMO) motor control system in a preferred embodiment of the present invention;

[0048] Figure 3 A block diagram of an improved super spiral sliding mode (IST-SMO) in a preferred embodiment of the present invention;

[0049] Figure 4 It is a flow chart of the improved super-helical sliding mode control debugging in a preferred embodiment of the present invention;

[0050] Figure 5 This is a schematic diagram of chatter suppression using a sign function and a hyperbolic tangent function in a preferred embodiment of the present invention. DETAILED DESCRIPTION

[0051] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0052] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0053] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments, but they are not intended to limit the present invention.

[0054] In a preferred embodiment of the present invention, based on the above problems existing in the prior art, a position-free control method based on an improved super-twisting sliding mode observer (IST-SMO) is provided. Figure 1 As shown, including:

[0055] Step S1, establishing a voltage state equation of the permanent magnet synchronous motor in a two-phase stationary coordinate system, and converting the voltage state equation to obtain a current state equation;

[0056] Step S2, establishing an improved super-helical sliding mode observer to obtain a current observation equation; wherein the sign function sign in the sliding mode control function of the improved super-helical sliding mode observer is replaced by a hyperbolic tangent function tanh, and the value of the hyperbolic tangent function tanh is determined based on table lookup and linear interpolation;

[0057] Step S3, determining a stator current error equation according to the current state equation and the current observation equation;

[0058] Step S4, performing low-pass filtering on the sliding mode control rate in the current observation equation to obtain an estimated value of the back electromotive force;

[0059] Step S5, performing inverse trigonometric function calculation on the back electromotive force estimation value to obtain a rotor angle estimation value, and compensating the rotor angle estimation value to obtain a compensated rotor angle estimation value;

[0060] Step S6, substituting the compensated rotor angle estimation value into the nonlinear state equation to obtain the angular velocity estimation value.

[0061] Specifically, to address the problem that traditional sliding mode observers usually use sign functions as switching functions, which may cause high-frequency jitter, and that the convergence speed of traditional sliding mode observers is average, an embodiment of the present invention proposes a position-free control method based on an improved super-helical sliding mode.

[0062] Specifically, the super-helical sliding mode control can achieve high-precision tracking performance, especially in velocity and position control, and improve the accuracy of velocity estimation.

[0063] Super-helical sliding mode control has low jitter characteristics. The high-frequency jitter problem common in traditional sliding mode control is effectively suppressed in super-helical sliding mode control. This is because super-helical sliding mode control suppresses jitter through the integral term, thereby reducing the jitter of the system. At the same time, in order to further reduce the system jitter problem, the embodiment of the present invention replaces the sign function sign with a continuous and smooth hyperbolic tangent function tanh.

[0064] Superhelical sliding mode control is highly robust to external disturbances and parameter perturbations.

[0065] The super-helical sliding mode control exhibits fast response capability when facing sudden load changes and outperforms the traditional sliding mode algorithm in terms of recovery time.

[0066] Taking into account the problem that the amount of computation is large when the symbol function sign is changed into a function with smooth and continuous characteristics, and it is difficult to apply in embedded systems, the embodiment of the present invention greatly reduces the amount of computation by changing the hyperbolic tangent function tanh with a large amount of computation into a table lookup interpolation form, so that it can be used in embedded systems with limited resources.

[0067] See also Figure 2 and Figure 3 The position-free control method based on the improved super-helical sliding mode proposed in the embodiment of the present invention is specifically as follows:

[0068] The d-axis and q-axis inductances of the built-in permanent magnet synchronous motor are not equal, that is, L d ≠L q The voltage state equation of the interior permanent magnet synchronous motor in the α-β stationary coordinate system is:

[0069]

[0070] Among them, [u α u β ] T is the voltage vector in the α-β coordinate system; R is the resistance of the stator winding; p is the differential operator; L d is the d-axis inductance; L q is the q-axis inductance; ω e is the rotor angular velocity (electrical angle); [i α i β ] T is the current vector in the α-β coordinate system; ψ f is the permanent magnet flux; i d and i q is the current vector in the dq coordinate system; θ is the rotor position angle.

[0071] As a preferred embodiment, the calculation method of the extended back electromotive force λ (EEMF) is:

[0072]

[0073] Among them, ψ f is the permanent magnet flux; i d and i q is the current vector in the dq coordinate system; θ is the rotor position angle.

[0074] It can be seen that the parameter λ contains both the back electromotive force ω in the usual definition e ψ f [-sinθcosθ] T , and also includes the inductance changes caused by the saliency of the interior permanent magnet synchronous motor (IPMSM).

[0075] Therefore, the rotor position information can be obtained by observing the phase of the estimated EEMF.

[0076] Since it is not easy to solve the extended back electromotive force λ through the voltage state equation of the permanent magnet synchronous motor, a conversion strategy is adopted to convert it into a current state equation for processing.

[0077] As a preferred embodiment, the current state equation is:

[0078]

[0079] In the formula,

[0080] Among them, i α 、i β are the current vectors in the α-β coordinate system; L d is the d-axis inductance; u α 、u β are the voltage vectors in the α-β coordinate system; α , β are the extended back electromotive force in the α-β coordinate system; R is the resistance of the stator winding; ω e is the rotor angular velocity; L q is the q-axis inductance.

[0081] According to the sliding mode variable structure control theory and the above formula (3), in order to obtain the estimated value of the extended back electromotive force λ, a sliding mode observer is constructed.

[0082] As a preferred embodiment, the current observation equation is:

[0083]

[0084] in, are the observed values ​​of stator current in α-β coordinate system; L d is the d-axis inductance; u α 、u β are the voltage vectors in the α-β coordinate system, which serve as the control input of the observer; α 、z β are the sliding mode control rates in the α-β coordinate system; R is the resistance of the stator winding; ω e is the rotor angular velocity; L q is the q-axis inductance.

[0085] The stator current error equation can be obtained by subtracting the above formula (3) from formula (4).

[0086] As a preferred implementation, the stator current error equation is:

[0087]

[0088] In the formula,

[0089] in, are the current observation errors in the α-β coordinate system; are the observed values ​​of stator current in α-β coordinate system respectively; i α 、i β are the current vectors in the α-β coordinate system; L d is the d-axis inductance; α ,β are the extended back electromotive force in the α-β coordinate system; z α 、z β are the sliding mode control rates in the α-β coordinate system; R is the resistance of the stator winding; ω e is the rotor angular velocity; L q is the q-axis inductance.

[0090] As a preferred embodiment, the calculation method of the designed sliding mode control rate z is:

[0091]

[0092] Where k is the sliding mode gain; i α 、i β are the current vectors in the α-β coordinate system respectively.

[0093] When the observer's state variable reaches the sliding surface After that, the observer state will always remain on the sliding surface.

[0094] According to the equivalent control principle of sliding mode control, the control quantity at this time can be regarded as the equivalent control quantity, and we can get:

[0095]

[0096] Among them, E α 、E β They are respectively in the α-β coordinate system;

[0097] The super-helical sliding mode algorithm is a special algorithm in the second-order sliding mode control. It adopts the idea of ​​super-helical control and only needs to know the information of the sliding mode variable s, but does not need to know the value of the first-order derivative of the sliding mode variable s.

[0098] In super-helix control, different control methods are adopted according to the error value.

[0099] When the error is small, the controller uses traditional sliding mode control;

[0100] When the error is large, the controller improves the control accuracy by adjusting the super-helical motion mode.

[0101] Compared with traditional sliding mode control, the super-helical control algorithm uses integration to obtain the actual control quantity, does not contain high-frequency switching quantity, effectively suppresses system chattering, and has faster response speed and stronger robustness.

[0102] For a single-input nonlinear system, the following relationship exists:

[0103]

[0104] Among them, x is the state variable; u is the input; y is the output; t is the time; a(t,x) and b(t,x) are unknown continuous sliding mode variable structure functions; s(t,x) is the unknown sliding surface function.

[0105] Assume that the sliding mode variable s = yy*, then the super-helical sliding mode control algorithm is:

[0106]

[0107] Among them, u, v are state variables; y* is the reference signal; k p is the scale parameter; k i is the integral parameter; r is a constant; k p , k i and r are parameters to be designed.

[0108] From the above formula (9), it can be seen that the super-helical sliding mode control mainly consists of two components.

[0109] The first part is a nonlinear discontinuous function of the sliding mode variable. The nonlinear variable can be changed by changing the exponent r.

[0110] The second part is the integral value, which makes the second-order sliding mode control less affected by parameter changes than the first-order sliding mode control, and reduces the inherent jitter of the system, making the system more robust. Among them, r is generally taken as 0.5.

[0111] Since the traditional superhelix algorithm uses the sign function sign, due to the discontinuity of the sign function, it will cause a sudden change in the control input when the system switches, causing the system to vibrate.

[0112] In order to reduce the system chattering problem, consider replacing the sign function sign with a continuous and smooth hyperbolic tangent function tanh, whose expression is:

[0113]

[0114] In the formula: x is the state variable; c is a constant, and c takes an appropriate positive value.

[0115] like Figure 5 A schematic diagram of chatter suppression using a sign function and a hyperbolic tangent function is shown, which shows the chatter suppression effect when c=0.2, c=0.4, and c=0.6 using the sign function sign and the hyperbolic tangent function tanh

[0116] from Figure 5It can be seen that when c is smaller, the system control effect is better, but it will cause the chattering to increase, which can prove that the chattering is more obvious when the sign function sign is used; when c is larger, the chattering suppression effect will be significantly better. Therefore, taking a suitable c value and replacing the sign function sign with the hyperbolic tangent function tanh can make the switching of the sliding mode controller smoother, thereby reducing the chattering problem of the system.

[0117] At the same time, the hyperbolic tangent function tanh is a 4-exponential function and contains division, which will consume a lot of computing resources in resource-limited embedded systems. Therefore, considering using table lookup and linear interpolation to implement the hyperbolic tangent function tanh, a certain number of interpolation points can be used to calculate the value of the hyperbolic tangent function tanh very close to the formula, thereby greatly reducing the amount of calculation.

[0118] In order to extract a more stable and continuous estimated value of the extended back-EMF, a low-pass filter (LPF) is required to be performed on it to obtain an estimated back-EMF value.

[0119] As a preferred embodiment, the back electromotive force estimation value is calculated as follows:

[0120]

[0121]

[0122] Among them, v α 、v β are the estimated values ​​of back electromotive force in the α-β coordinate system; s is the sliding mode variable; ω c is the cutoff frequency of the low-pass filter; z α 、z β are the sliding mode control rates in the α-β coordinate system respectively.

[0123] The estimated value of the rotor angle can be obtained by calculating the back electromotive force component in the α-β coordinate system in the above formula (11) through inverse trigonometric function.

[0124] As a preferred embodiment, the calculation method of the estimated value of the rotor angle is:

[0125]

[0126] Among them, v α 、v β They are the estimated values ​​of back electromotive force in the α-β coordinate system; is the estimated value of the rotor angle.

[0127] Since the back electromotive force is obtained by filtering through a low-pass filter, a phase lag will be introduced. The phase delay caused by the low-pass filter is related to the cut-off frequency of the low-pass filter. The lower the cut-off frequency of the low-pass filter, the greater the phase lag of the corresponding frequency.

[0128] Therefore, based on the rotor position calculated by the above formula (8), an angle compensation (Δθ) needs to be added to compensate for the position angle estimation error caused by the delay effect of the low-pass filter.

[0129] After compensation, a relatively accurate rotor angle estimate is obtained

[0130] As a preferred embodiment, the calculation method of the estimated value of the compensated rotor angle is:

[0131]

[0132] in, is the estimated value of the rotor angle after compensation; is the estimated value of the rotor angle; ω e is the rotor angular velocity (electrical angle); ω c is the cutoff frequency of the low-pass filter.

[0133] The estimated rotor angular velocity is differentiated to obtain the estimated angular velocity ω e ,Right now

[0134] As a preferred implementation, the method for calculating the angular velocity estimation value is:

[0135]

[0136] In the formula, u = -k p |x r tanh(x)-k i tanh(x)

[0137] Where x is the state variable, i.e. the estimated value of the rotor angle after compensation u is the input; y is the output, that is, the estimated value of angular velocity ω e ; t is time; a(t,x) and b(t,x) are continuous sliding mode variable structure functions; s(t,x) is the sliding surface function; k p is the scale parameter; k i is the integration parameter; r is a constant.

[0138] In the above preferred embodiment, if Figure 4The schematic diagram of the process of debugging the improved super-helical sliding mode control is shown. The debugging process includes the following steps:

[0139] First, initialize the variables and parameters; then, sample the phase voltage and phase current, and perform Clark transform on the sampled values; then, improve the super-helical sliding mode operation; estimate the angular velocity; finally, determine whether the estimated value is accurate: if it is accurate, end the debugging process; if it is inaccurate, adjust the parameters and return to the step of improving the super-helical sliding mode operation or the step of estimating the angular velocity.

[0140] The use of the debugged improved super-helical sliding mode observer has the following advantages or beneficial effects:

[0141] (1) In terms of speed and position control, the accuracy of speed estimation is improved;

[0142] (2) The chattering phenomenon is greatly reduced, thereby obtaining better speed and position signals, which improves the performance of motor control;

[0143] (3) Strong robustness when motor parameters change or external disturbances occur;

[0144] (4) It exhibits rapid response capability when faced with sudden load changes and outperforms traditional sliding mode algorithms in terms of recovery time;

[0145] (5) The amount of computation and resource consumption are greatly reduced, making it applicable to common embedded systems and expanding its application scope.

[0146] The above are only preferred embodiments of the present invention, and are not intended to limit the implementation methods and protection scope of the present invention. Those skilled in the art should be aware that all solutions obtained by equivalent substitutions and obvious changes made using the contents of this specification and illustrations should be included in the protection scope of the present invention.

Claims

1. A position-free control method based on an improved super-helical sliding mode, characterized in that: include: Step S1, establishing a voltage state equation of the permanent magnet synchronous motor in a two-phase stationary coordinate system, and converting the voltage state equation to obtain a current state equation; Step S2, establishing an improved super-helical sliding mode observer to obtain a current observation equation; wherein the sign function sign in the sliding mode control function of the improved super-helical sliding mode observer is replaced by a hyperbolic tangent function tanh, and the value of the hyperbolic tangent function tanh is determined based on table lookup and linear interpolation; Step S3, determining a stator current error equation according to the current state equation and the current observation equation; Step S4, performing low-pass filtering on the sliding mode control rate in the current observation equation to obtain a back electromotive force estimation value; Step S5, performing inverse trigonometric function calculation on the back electromotive force estimation value to obtain a rotor angle estimation value, and compensating the rotor angle estimation value to obtain a compensated rotor angle estimation value; Step S6, substituting the compensated rotor angle estimation value into the nonlinear state equation to obtain the angular velocity estimation value.

2. The position-free control method based on the improved super-helical sliding mode according to claim 1 is characterized in that: The current state equation is: In the formula, Among them, i α 、i β are the current vectors in the α-β coordinate system; L d is the d-axis inductance; u α 、u β are the voltage vectors in the α-β coordinate system; α , β are the extended back electromotive force in the α-β coordinate system; R is the resistance of the stator winding; ω e is the rotor angular velocity; L q is the q-axis inductance.

3. The position-free control method based on the improved super-helical sliding mode according to claim 2 is characterized in that: The calculation method of the extended back electromotive force λ is: Among them, ψ f is the permanent magnet flux; i d and i q is the current vector in the dq coordinate system; θ is the rotor position angle.

4. The position-free control method based on the improved super-helical sliding mode according to claim 1 is characterized in that: The current observation equation is: In the formula, in, are the observed values ​​of stator current in α-β coordinate system; L d is the d-axis inductance; u α 、u β are the voltage vectors in the α-β coordinate system; z α 、z β are the sliding mode control rates in the α-β coordinate system; R is the resistance of the stator winding; ω e is the rotor angular velocity; L q is the q-axis inductance.

5. The position-free control method based on the improved super-helical sliding mode according to claim 1 is characterized in that: The stator current error equation is: In the formula, in, are the current observation errors in the α-β coordinate system; are the observed values ​​of stator current in α-β coordinate system respectively; i α 、i β are the current vectors in the α-β coordinate system; L d is the d-axis inductance; α , β are the extended back electromotive force in the α-β coordinate system; z α 、z β are the sliding mode control rates in the α-β coordinate system; R is the resistance of the stator winding; ω e is the rotor angular velocity; L q is the q-axis inductance.

6. The position-free control method based on the improved super-helical sliding mode according to claim 4 or 5, characterized in that: The calculation method of the sliding mode control rate z is: Where k is the sliding mode gain; i α 、i β are the current vectors in the α-β coordinate system respectively.

7. The position-free control method based on improved super-helical sliding mode according to claim 1 is characterized in that: The back EMF estimate is calculated as: Among them, v α 、v β are the estimated values ​​of back electromotive force in the α-β coordinate system; s is the sliding mode variable; ω c is the cut-off frequency of the low-pass filter; z α 、z β are the sliding mode control rates in the α-β coordinate system respectively.

8. The position-free control method based on improved super-helical sliding mode according to claim 1 is characterized in that: The calculation method of the rotor angle estimation value is: Among them, v α 、v β They are the estimated values ​​of back electromotive force in the α-β coordinate system; is the estimated value of the rotor angle.

9. The position-free control method based on improved super-helical sliding mode according to claim 1, characterized in that: The calculation method of the estimated value of the compensated rotor angle is: in, is the estimated value of the rotor angle after compensation; is the estimated value of the rotor angle; ω e is the rotor angular velocity; ω c is the cutoff frequency of the low-pass filter.

10. The position-free control method based on improved super-helical sliding mode according to claim 1, characterized in that: The angular velocity estimate is calculated as follows: where \(u = -k\) p |x r \(\tanh(x)-k\) i \(\tanh(x)\) Where x is the state variable, i.e. the estimated value of the rotor angle after compensation u is the input; y is the output, that is, the estimated value of angular velocity ω e ; t is time; a(t,x) and b(t,x) are continuous sliding mode variable structure functions; s(t,x) is the sliding surface function; k p is the scale parameter; k i is the integration parameter; r is a constant.

Images