CKF-based switched reluctance motor sensorless control method

Abstract

The invention discloses a CKF-based switched reluctance motor sensorless control method. The method comprises the following steps: determining flux linkage characteristics and torque characteristics of a switched reluctance motor; setting a state vector, an observation vector and a control vector of the switched reluctance motor, and constructing a model space state equation and a measurement equation of the switched reluctance motor; carrying out discretization processing on the space state equation and the measurement equation; estimating the speed and the rotor position of the motor based on a cubature Kalman filter (CKF) algorithm; initializing a state vector and a state error covariance matrix, and then performing time updating and measurement updating; and finally obtaining estimated values of the speed and the rotor position. According to the method, excessive parameter adjustment is not needed, the calculation real-time performance is guaranteed, the position identification precision is improved, the system robustness is improved, and the defect that a traditional method is affected by the rotating speed range of the switched reluctance motor is effectively overcome.

Description

Technical Field

[0001] The invention belongs to the field of switched reluctance motor control, and in particular relates to a switched reluctance motor rotor position identification method based on a cubic Kalman filter (CKF) algorithm. Background Art

[0002] As one of the important components of the drive system, the motor's performance in different environments and working conditions and its processing and manufacturing costs are all important factors to consider. As strategic rare earth resources are increasingly scarce, their prices have also increased significantly. The switched reluctance motor drive system does not contain permanent magnets, has simple structure, low cost, high reliability, good fault tolerance and other advantages, and has broad application prospects. However, the continuous and stable operation of the switched reluctance motor requires real-time rotor position information. In special applications such as high temperature and high speed, humid dust environment and precision drive, mechanical sensors will not only occupy installation space, but also dust wear will greatly increase the failure rate of the position sensor, and the motor system will not be able to work stably. Therefore, it is necessary to study the position sensorless control scheme to improve the fault tolerance of the switched reluctance motor.

[0003] The position sensorless technology uses different methods depending on the speed range of the application. The traditional position sensorless control methods for switched reluctance motors include: inductance method, flux method, observer method, intelligent algorithm, etc. However, most algorithms can only work at specific speeds and characteristic loads, and the algorithms are complex and have high control frequency requirements. Summary of the invention

[0004] In view of the technical problems existing in the existing switch reluctance motor position sensorless control algorithm, the present invention proposes a switch reluctance motor position sensorless control method based on CKF, which solves the problem that the traditional position sensorless control method depends on the motor speed and has low estimation accuracy, so as to improve the dynamic performance of the switch reluctance motor speed control system and enhance the robustness of the system.

[0005] In order to achieve the above tasks, the present invention adopts the following technical solutions:

[0006] A position sensorless control method for a switched reluctance motor based on CKF, comprising:

[0007] Determine the flux linkage and torque characteristics of the switched reluctance motor;

[0008] Setting the motor state quantity and control quantity, constructing a switched reluctance motor model based on the flux linkage characteristics and torque characteristics, and setting the state vector, observation vector and control vector;

[0009] The switched reluctance motor model is discretized, and the angular velocity and speed of the motor are estimated based on a volumetric Kalman filter algorithm, wherein the volumetric Kalman filter algorithm includes:

[0010] The initial estimate of the state vector and the initial estimate of the error state covariance are initialized, and the time update of the volumetric Kalman filter algorithm is realized by calculating the volume points, propagating the nonlinear transformation of the volume points using the state equation, calculating the state quantity prediction value and the error covariance prediction value; the measurement update of the volumetric Kalman filter algorithm is realized by calculating the volume points, propagating the nonlinear transformation of the volume points using the observation equation, calculating the measurement estimate value, calculating the measurement error covariance and cross-covariance, calculating the Kalman gain, the state estimate value and the state error covariance matrix; finally, the estimated values ​​of the angular velocity and the velocity are determined using the state estimate value.

[0011] Further, the determining of the flux linkage characteristics and torque characteristics of the switched reluctance motor includes:

[0012] (I) The Fourier series expression of the magnetic flux characteristics is:

[0013] ψ(i,θ)=θ 1×5 ×λ 5×1 (1)

[0014] Where:

[0015]

[0016] where λ 5×1 are five unknown coefficients related to the phase current i; λ0(i), λ1(i), λ2(i), λ3(i), λ4(i) are flux linkage coefficients, which are related to the current; Θ 1×5 is the rotor position angle θ basis function matrix, and the superscript T represents the matrix transpose operation;

[0017] (II) The flux linkage of the motor at five special positions, 0°, 7.5°, 11.5°, 5° and 22.5°, can be expressed as:

[0018] ψ 5×1 =A 5×5 ×λ 5×1 (2)

[0019] in:

[0020]

[0021] In the above formula, A 5×5 represents the Fourier angle fitting coefficient matrix, ψ 0° ψ 7.5° ψ 11.25° ψ 15° ψ22.5 They are the flux linkage of the motor at 0°, 7.5°, 11.5°, 5° and 22.5° respectively;

[0022] (III) When the angle is fixed, the relationship between flux linkage and current can be expressed by a sixth-order polynomial fitting without a constant term:

[0023] ψ 5×1 =B 5×6 ×I 6×1 (3)

[0024] Among them, I 6×1 =[i 6 ,i 5 ,i 4 ,i 3 ,i 2 ,i] T is the current matrix, and the superscript numbers represent the phase current power or current order; B 5×6 is the fitting coefficient;

[0025] (IV) According to the equality of formula (2) and formula (3), we can get:

[0026] λ 5×1 =A 5×5 -1 ×B 5×6 ×I 6×1 (4)

[0027] (V) Using formulas (1) and (4), the torque formula of SRM can be further obtained:

[0028]

[0029] Where W c is the magnetic energy of the motor;

[0030] (VI) The single-phase current calculation formula can be obtained from the voltage balance equation of SRM:

[0031]

[0032] In the formula, t is the time parameter, u ph is the phase voltage, i ph is the phase current, R s is the stator phase resistance, ω is the angular velocity, ψ ph is the phase flux, is the partial derivative of the phase flux with respect to the phase current, The phase flux is the electrical angle θ of the phase ph The partial derivative of .

[0033] Furthermore, the setting of the motor state quantity and the control quantity, and the construction of a switched reluctance motor model based on the flux linkage characteristics and the torque characteristics, include:

[0034] The switched reluctance motor model is established based on the flux ψ(i,θ) and torque T(i,θ), and the three-phase current i a ,i b ,i c , speed ω, rotor position angle θ are five parameters as the state of the motor, and the three-phase voltage U a ,U b ,U c As control quantity:

[0035]

[0036] In formula (7), t is the time parameter, R a ,R b ,R c is the three-phase winding resistance, ψ a ,ψ b ,ψ c is the magnetic resistance of the flux linkage ψ(i,θ) on the three-phase winding, θ a ,θ b ,θ c is the three-phase angle, f r is the damping coefficient, J is the moment of inertia, T e is the torque T(i,θ), T L is the load torque, represents the time derivative, They respectively represent the partial derivatives of the three-phase flux A, B, and C with respect to the three-phase electrical angle.

[0037] Furthermore, the setting of the state vector, observation vector and control vector includes:

[0038] The selected state vector is: x = [i a i b i c ωθ] T , the observation vector is: y = [i a i b i c ] T =h(x,u), the control vector is: u = [u a u b u c ] T ,in:

[0039]

[0040] Furthermore, the switched reluctance motor model is discretized, including:

[0041]

[0042] Where x k With x k-1 are the state vectors of the system at time k and k-1 respectively, u k with u k-1 are the system k and k-1 moments respectively, y k —Observation vector of the system at time k, f()—state equation of the time-varying system, h()—observation equation of the time-varying system; process noise W k and observation noise V k are Gaussian white noises with mean 0 and variances Q and R respectively, and both Q and R are symmetric matrices.

[0043] Further, the initialization of the initial estimated value of the state vector and the initial estimated value of the error state covariance includes:

[0044]

[0045] In the formula, is the initial estimate of the state vector, x0 is the true value of the state vector, P0 is the initial estimate error state covariance, and E is the mathematical expectation operation.

[0046] Furthermore, the time update of the volumetric Kalman filter algorithm is realized by calculating the volume points, propagating the nonlinear transformation of the volume points by using the state equation, and calculating the predicted value of the state quantity and the predicted value of the error covariance, including:

[0047] (I) Calculation of volume points

[0048] Assume that we are now at time k and the estimated state at time k-1 is known and the k-1 state error covariance matrix P k-1k-1 , for the state error covariance matrix P k-1k-1 Perform Cholesky decomposition:

[0049]

[0050] In the formula, S k-1|k-1 P is k-1 time k-1|k-1 The Cholesky decomposition matrix of

[0051] According to the decomposed state error covariance matrix, the volume point is obtained according to the third-order spherical radial volume criterion:

[0052]

[0053] In the formula, is the i-th volume point at time k-1, is the i-th standard normal volume point, [1] i represents a vector whose i-th element is 1, i = 1, 2, 3…m, m = 2n, n is the dimension of the state vector;

[0054] (II) The volume point obtained above is propagated through the state equation f() through nonlinear transformation of the volume point:

[0055]

[0056] In the formula, is the predicted value of the i-th volume point at time k obtained by nonlinear transformation f(·);

[0057] (III) Calculate the predicted value of state quantity and the predicted value of error covariance:

[0058]

[0059] In the formula, is the predicted value of the i-th volume point at time k, P k|k-1 is the covariance matrix of the forecast error at time k, Q k-1 is the noise matrix at time k-1, and ∑(·) is the summation operation.

[0060] Further, the method of calculating volume points, propagating volume points nonlinear transformation using observation equations, calculating measurement estimates, calculating measurement error covariance and cross-covariance, calculating Kalman gains, state estimates, and state error covariance matrices to implement volumetric Kalman filter algorithm measurement update includes:

[0061] (I) Calculation of volume points

[0062] The state prediction error covariance matrix obtained by equation (14) is decomposed by Cholesky and the new volume point is calculated by the third-order spherical radial volume criterion:

[0063]

[0064] In the formula, S k|k-1 P is the kth moment k|k-1 The Cholesky decomposition matrix of

[0065] (II) According to the system described by equation (9), the volume point obtained above is propagated through the observation equation h() through nonlinear transformation of the volume point:

[0066]

[0067] In the formula, is the predicted value of the i-th volume point measurement at time k;

[0068] (III) Perform weighted summation on the propagated points to obtain the measurement estimate:

[0069]

[0070] In the formula, is the predicted value measured at time k;

[0071] (IV) Calculate the measurement error covariance and cross-covariance:

[0072]

[0073] In the formula, is the measurement error covariance matrix at time k, is the cross-covariance matrix of the measurement error at time k, and R is the measurement noise matrix;

[0074] (V) Calculate the Kalman gain K at the kth moment k , state estimate and the state error covariance matrix P k|k :

[0075]

[0076] Further, the determining the estimated values ​​of the angular velocity and the velocity by using the estimated state value comprises:

[0077]

[0078] in, The fourth element in the state vector is the estimated angular velocity, and the fifth element is the estimated angle.

[0079] Compared with the prior art, the present invention has the following technical features:

[0080] The present invention adopts a volumetric Kalman filter algorithm and selects the mean and variance of volume points as parameters based on the spherical radial volume criterion, so that the system has higher accuracy in three dimensions and above, and does not require too much parameter adjustment. While ensuring the real-time calculation, the position identification accuracy is improved, the system robustness is increased, and the algorithm is suitable for operation over the entire speed range, which effectively avoids the deficiency of traditional methods being affected by the motor speed range and broadens the application of the volumetric Kalman filter algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] Figure 1 This is a principle block diagram of a volumetric Kalman filter position estimation algorithm for a switched reluctance motor according to an embodiment of the present invention;

[0082] Figure 2A flow chart of position estimation of a switched reluctance motor with a volumetric Kalman filter algorithm according to an embodiment of the present invention;

[0083] Figure 3 It is an overall diagram and a partial enlarged comparison diagram of the estimated motor speed and the actual speed of the switch reluctance motor position sensorless speed control system based on the volumetric Kalman filter algorithm in an embodiment of the present invention;

[0084] Figure 4 It is an overall diagram and a partial enlarged comparison diagram of the estimated motor angle and the actual angle of the switch reluctance motor position sensorless speed control system based on the volumetric Kalman filter algorithm in an embodiment of the present invention; DETAILED DESCRIPTION

[0085] Aiming at the problems that the position-free control algorithm of the switched reluctance motor depends on the motor speed and has limited adaptability, and in order to broaden the application of the Kalman filter algorithm in the speed control system of the switched reluctance motor, the present invention proposes a position sensor-free control method for the switched reluctance motor based on CKF. Now, the present invention is further described in combination with a three-phase 12 / 8 switched reluctance motor as an embodiment and the accompanying drawings. The specific implementation method is as follows:

[0086] Step 1: determine the flux characteristics and torque characteristics of the switched reluctance motor.

[0087] The three-phase 12 / 8 switched reluctance motor is modeled, and the Fourier series model of the switched reluctance motor is established through the characteristic position to realize the online calculation of the motor characteristics.

[0088] In order to avoid storing a large number of motor characteristic parameters and occupying processor memory, this solution adopts a method to obtain the flux curve of an unknown position based on a known curve. By establishing a flux Fourier series model, the motor flux ψ(i,θ) and torque T(i,θ) are obtained online, as follows:

[0089] (I) The Fourier series expression of the magnetic flux characteristics is:

[0090] ψ(i,θ)=θ 1×5 ×λ 5×1 (1)

[0091] Where:

[0092]

[0093] where λ 5×1 are the five undetermined coefficients related to the phase current i, and the coefficient matrix can be obtained through the flux characteristics of the five special positions. λ0(i),λ1(i),λ2(i),λ3(i),λ4(i) are the coefficients of the flux at the five special positions, which are related to the current; Θ 1×5is the basis function matrix of the rotor position angle θ, and the superscript T represents the matrix transpose operation.

[0094] (II) The flux linkage of the motor at five special positions, 0°, 7.5°, 11.5°, 5° and 22.5°, can be expressed as:

[0095] ψ 5×1 =A 5×5 ×λ 5×1 (2)

[0096] in:

[0097]

[0098] In the above formula, A 5×5 represents the Fourier angle fitting coefficient matrix, ψ 0° ψ 7.5° ψ 11.25° ψ 15° ψ 22.5 These are the magnetic flux of the motor at 0°, 7.5°, 11.5°, 5° and 22.5° respectively.

[0099] (III) When the angle is fixed, the relationship between flux linkage and current can be expressed by a sixth-order polynomial fitting without a constant term:

[0100] ψ 5×1 =B 5×6 ×I 6×1 (3)

[0101] Among them, I 6×1 =[i 6 ,i 5 ,i 4 ,i 3 ,i 2 ,i] T is the current matrix, and the superscript numbers represent the phase current power or current order; B 5×6 is the fitting coefficient.

[0102] (IV) According to the equality of formula (2) and formula (3), we can get:

[0103] λ 5×1 =A 5×5 -1 ×B 5×6 ×I 6×1 (4)

[0104] (V) Using formulas (1) and (4), the torque formula of SRM can be further derived:

[0105]

[0106] Where Wc is the magnetic energy of the motor.

[0107] (VI) The single-phase current calculation formula can be derived from the voltage balance equation of SRM:

[0108]

[0109] In the formula, t is the time parameter, u ph is the phase voltage, i ph is the phase current, R s is the stator phase resistance, ω is the angular velocity, ψ ph is the phase flux, is the partial derivative of the phase flux with respect to the phase current, The phase flux is the electrical angle θ of the phase ph The partial derivative of is specifically expressed as:

[0110]

[0111] Step 2: Set the motor state quantity and control quantity, and build a switched reluctance motor model based on the flux linkage characteristics and torque characteristics.

[0112] According to the flux ψ(i,θ) and torque T(i,θ) obtained in step 1, a switched reluctance motor model is established, and the three-phase current i a ,i b ,i c , speed ω, rotor position angle θ are five parameters as the state of the motor, and the three-phase voltage U a ,U b ,U c As control quantity:

[0113]

[0114] In formula (7), t is the time parameter, R a ,R b ,R c is the three-phase winding resistance, ψ a ,ψ b ,ψ c is the magnetic resistance of the flux linkage ψ(i,θ) on the three-phase winding, θ a ,θ b ,θ c is the three-phase angle, f r is the damping coefficient, J is the moment of inertia, T e is the torque T(i,θ), T L is the load torque, represents the time derivative, They respectively represent the partial derivatives of the three-phase flux A, B, and C with respect to the three-phase electrical angle.

[0115]

[0116] According to the state equation of the switched reluctance motor, the state vector is selected as: x = [i a i b i c ωθ] T , the observation vector is: y = [i a i b i c ] T =h(x,u), the control vector is: u = [u a u b u c ] T .

[0117] Step 3: discretize the switched reluctance motor model.

[0118] The switched reluctance motor model is discretized using the Euler method and the system process noise and observation noise are considered to obtain:

[0119]

[0120] Where x k With x k-1 are the state vectors of the system at time k and k-1 respectively, u k with u k-1 are the system k and k-1 moments respectively, y k —The observation vector of the system at time k, f()—the state equation of the time-varying system, h()—the observation equation of the time-varying system. Since this embodiment is a three-phase 12 / 8 switched reluctance motor, its f() is formula (7) and h() is formula (8). Process noise W k and observation noise V k are Gaussian white noises with mean 0 and variances Q and R respectively, and both Q and R are symmetric matrices.

[0121] As can be seen from equation (8), both the state transfer equation and the observation equation are nonlinear, so the position observer can be constructed based on the cubature Kalman filter algorithm.

[0122] Step 4: Initialize the cubature Kalman filter algorithm:

[0123]

[0124] In the formula, is the initial estimate of the state vector, x0 is the true value of the state vector, P0 is the initial estimate error state covariance, and E is the mathematical expectation operation.

[0125] Step 5, cubature Kalman filter algorithm time update:

[0126] (I) Calculation of volume points

[0127] Assume that we are now at time k and the estimated state at time k-1 is known and the k-1 state error covariance matrix P k-1k-1 , for the state error covariance matrix P k-1k-1 Perform Cholesky decomposition:

[0128]

[0129] In the formula, S k-1|k-1 P is k-1 time k-1|k-1 The Cholesky decomposition matrix.

[0130] According to the decomposed state error covariance matrix, the volume point is obtained according to the third-order spherical radial volume criterion:

[0131]

[0132] In the formula, is the i-th volume point at time k-1, is the i-th standard normal volume point, [1] i Represents a vector whose i-th element is 1, i=1,2,3…m, m=2n, n is the dimension of the state vector, and in this embodiment, it is 5 state vectors in the motor state equation; a total of 2n volume points are obtained using the third-order spherical radial volume rule.

[0133] (II) According to the system described by equation (9), the volume point obtained above is propagated through the state equation f() by nonlinear transformation of the volume point:

[0134]

[0135] In the formula, is the predicted value of the ith volume point at time k obtained by nonlinear transformation f(·).

[0136] (III) Calculate the predicted value of state quantity and the predicted value of error covariance:

[0137]

[0138] In the formula, is the predicted value of the i-th volume point at time k, P k|k-1 is the covariance matrix of the forecast error at time k, Q k-1 is the noise matrix at time k-1, and ∑(·) is the summation operation.

[0139] Step 6: Volumetric Kalman Filter Algorithm Measurement Update

[0140] (I) Calculation of volume points

[0141] The state prediction error covariance matrix obtained by equation (14) is decomposed by Cholesky and the new volume point is calculated by the third-order spherical radial volume criterion:

[0142]

[0143] In the formula, S k|k-1 P is the kth moment k|k-1 The Cholesky decomposition matrix.

[0144] (II) According to the system described by equation (9), the volume point obtained above is propagated through the observation equation h() through nonlinear transformation of the volume point:

[0145]

[0146] In the formula, is the predicted value of the i-th volume point measurement at time k.

[0147] (III) Perform weighted summation on the propagated points to obtain the measurement estimate:

[0148]

[0149] In the formula, is the predicted value measured at time k.

[0150] (IV) Calculate the measurement error covariance and cross-covariance:

[0151]

[0152] In the formula, is the measurement error covariance matrix at time k, is the cross-covariance matrix of the measurement error at time k, and R is the measurement noise matrix.

[0153] (V) Calculate the Kalman gain K at the kth moment k , state estimate and the state error covariance matrix P k|k :

[0154]

[0155] Step 7, using the motor model established in steps 1 and 2, the estimated value of the motor state is obtained through the volumetric Kalman filter algorithm in steps 3, 4, 5 and 6. The present application extracts the angular velocity and angle information through formula (20):

[0156]

[0157] The fourth element in the state vector is the estimated angular velocity in rad / s, and the fifth element is the estimated angle in rad.

[0158] Compare the rotor position estimated by the cubature Kalman filter algorithm with the actual rotor position. The results are as follows: Figure 3 As shown, it can be seen that the cubature Kalman filter algorithm has good position estimation accuracy at both low and high speeds, and has good dynamic performance when the motor speed changes suddenly. Therefore, the method proposed by the present invention is effective.

[0159] The present invention adopts a volume Kalman filter algorithm, and selects the mean and variance of volume points as parameters based on the spherical radial volume criterion, so that the system has higher accuracy in three dimensions or above, and the state error covariance matrix will not be non-positive definite, thereby improving the stability of the system, improving the position identification accuracy while ensuring the real-time calculation, and increasing the robustness of the system. The algorithm is suitable for operation in the full speed range, and effectively avoids the deficiency of traditional methods being affected by the motor speed range.

[0160] The above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present application, and should all be included in the protection scope of the present application.

Claims

1. A position sensorless control method for a switched reluctance motor based on CKF, It is characterized in that include: Determine the flux linkage and torque characteristics of the switched reluctance motor; Setting the motor state quantity and control quantity, constructing a switched reluctance motor model based on the flux linkage characteristics and torque characteristics, and setting the state vector, observation vector and control vector; The switched reluctance motor model is discretized, and the angular velocity and speed of the motor are estimated based on a volumetric Kalman filter algorithm, wherein the volumetric Kalman filter algorithm includes: The initial estimate of the state vector and the initial estimate of the error state covariance are initialized, and the time update of the volumetric Kalman filter algorithm is realized by calculating the volume points, propagating the nonlinear transformation of the volume points using the state equation, calculating the state quantity prediction value and the error covariance prediction value; the measurement update of the volumetric Kalman filter algorithm is realized by calculating the volume points, propagating the nonlinear transformation of the volume points using the observation equation, calculating the measurement estimate value, calculating the measurement error covariance and cross-covariance, calculating the Kalman gain, the state estimate value and the state error covariance matrix; finally, the estimated values ​​of the angular velocity and the velocity are determined using the state estimate value.

2. The position sensorless control method of the switched reluctance motor based on CKF according to claim 1, It is characterized in that The determining of the flux linkage characteristics and torque characteristics of the switched reluctance motor includes: (I) The Fourier series expression of the magnetic flux characteristics is: ψ(i,θ)=θ 1×5 ×λ 5×1 (1) Where: where λ 5×1 are five unknown coefficients related to the phase current i; 0 (i),λ 1 (i),λ 2 (i),λ 3 (i),λ 4 (i) is the flux linkage coefficient, which is related to the current; Θ 1×5 is the rotor position angle θ basis function matrix, and the superscript T represents the matrix transpose operation; (II) The flux linkage of the motor at five special positions, 0°, 7.5°, 11.5°, 5° and 22.5°, can be expressed as: ψ 5×1 =A 5×5 ×λ 5×1 (2) in: In the above formula, A 5×5 represents the Fourier angle fitting coefficient matrix, ψ 0° ψ 7.5° ψ 11.25° ψ 15° ψ 22.5 They are the flux linkage of the motor at 0°, 7.5°, 11.5°, 5° and 22.5° respectively; (III) When the angle is fixed, the relationship between flux linkage and current can be expressed by a sixth-order polynomial fitting without a constant term: ψ 5×1 =B 5×6 ×I 6×1 (3) Among them, I 6×1 =[i 6 ,i 5 ,i 4 ,i 3 ,i 2 ,i] T is the current matrix, and the superscript numbers represent the phase current power or current order; B 5×6 is the fitting coefficient; (IV) According to the equality of formula (2) and formula (3), we can get: l 5×1 =A 5×5 -1 ×B 5×6 ×I 6×1 (4) (V) Using formulas (1) and (4), the torque formula of SRM can be further obtained: Where W c is the magnetic energy of the motor; (VI) The single-phase current calculation formula can be obtained from the voltage balance equation of SRM: In the formula, t is the time parameter, u ph is the phase voltage, i ph is the phase current, R s is the stator phase resistance, ω is the angular velocity, ψ ph is the phase flux, is the partial derivative of phase flux with respect to phase current, The phase flux is the electrical angle θ of the phase ph The partial derivative of .

3. The position sensorless control method of the switched reluctance motor based on CKF according to claim 1, It is characterized in that The setting of the motor state quantity and the control quantity, and the construction of the switched reluctance motor model based on the flux linkage characteristics and the torque characteristics, include: The switched reluctance motor model is established based on the flux ψ(i,θ) and torque T(i,θ), and the three-phase current i a ,i b ,i c , speed ω, rotor position angle θ are five parameters as the state of the motor, and the three-phase voltage U a ,U b ,U c As control quantity: In formula (7), t is the time parameter, R a ,R b ,R c is the three-phase winding resistance, ψ a ,ψ b ,ψ c is the magnetic resistance of the flux linkage ψ(i,θ) on the three-phase winding, θ a ,θ b ,θ c is the three-phase angle, f r is the damping coefficient, J is the moment of inertia, T e is the torque T(i,θ), T L is the load torque, represents the time derivative, They respectively represent the partial derivatives of the three-phase flux A, B, and C with respect to the three-phase electrical angle.

4. The position sensorless control method of the switched reluctance motor based on CKF according to claim 1, It is characterized in that The setting of the state vector, the observation vector and the control vector includes: The selected state vector is: x = [i a i b i c ωθ] T , the observation vector is: y = [i a i b i c ] T =h(x,u), the control vector is: u = [u a u b u c ] T ,in:

5. The position sensorless control method of the switched reluctance motor based on CKF according to claim 1, It is characterized in that Discretizing the switched reluctance motor model includes: Where x k With x k-1 are the state vectors of the system at time k and k-1 respectively, u k with u k-1 are the system k and k-1 moments respectively, y k —Observation vector of the system at time k, f()—state equation of the time-varying system, h()—observation equation of the time-varying system; process noise W k and observation noise V k are Gaussian white noises with mean 0 and variances Q and R respectively, and both Q and R are symmetric matrices.

6. The position sensorless control method of the switched reluctance motor based on CKF according to claim 1, It is characterized in that Initializing the initial estimated value of the state vector and the initial estimated value of the error state covariance includes: In the formula, is the initial estimate of the state vector, x 0 is the true value of the state vector, P 0 is the initial estimated error state covariance, and E is the mathematical expectation operation.

7. The position sensorless control method of the switched reluctance motor based on CKF according to claim 1, It is characterized in that The method of realizing the time update of the volumetric Kalman filter algorithm by calculating the volumetric points, using the state equation to propagate the nonlinear transformation of the volumetric points, and calculating the predicted value of the state quantity and the predicted value of the error covariance includes: (I) Calculation of volume points Assume that we are now at time k and the estimated state at time k-1 is known and the k-1 state error covariance matrix P k-1k-1 , for the state error covariance matrix P k-1k-1 Perform Cholesky decomposition: In the formula, S k-1|k-1 P is k-1 time k-1|k-1 The Cholesky decomposition matrix of According to the decomposed state error covariance matrix, the volume point is obtained according to the third-order spherical radial volume criterion: In the formula, is the i-th volume point at time k-1, is the i-th standard normal volume point, [1] i represents a vector whose i-th element is 1, i = 1, 2, 3…m, m = 2n, n is the dimension of the state vector; (II) The volume point obtained above is propagated through the state equation f() through nonlinear transformation of the volume point: In the formula, is the predicted value of the i-th volume point at time k obtained by nonlinear transformation f(·); (III) Calculate the predicted value of state quantity and the predicted value of error covariance: In the formula, is the predicted value of the i-th volume point at time k, P k|k-1 is the covariance matrix of the forecast error at time k, Q k-1 is the noise matrix at time k-1, and ∑(·) is the summation operation.

8. The position sensorless control method of a switched reluctance motor based on CKF according to claim 1, It is characterized in that The method includes calculating volume points, propagating volume points nonlinear transformation using observation equations, calculating measurement estimates, calculating measurement error covariance and cross-covariance, calculating Kalman gain, state estimates, and state error covariance matrix to implement volume Kalman filter algorithm measurement update, including: (I) Calculation of volume points The state prediction error covariance matrix obtained by equation (14) is decomposed by Cholesky and the new volume point is calculated by the third-order spherical radial volume criterion: In the formula, S k|k-1 P is the kth moment k|k-1 The Cholesky decomposition matrix of (II) According to the system described by equation (9), the volume point obtained above is propagated through the observation equation h() through nonlinear transformation of the volume point: In the formula, is the predicted value of the i-th volume point measurement at time k; (III) Perform weighted summation on the propagated points to obtain the measurement estimate: In the formula, is the predicted value measured at time k; (IV) Calculate the measurement error covariance and cross-covariance: In the formula, is the measurement error covariance matrix at time k, is the cross-covariance matrix of the measurement error at time k, and R is the measurement noise matrix; (V) Calculate the Kalman gain K at the kth moment k , state estimate and the state error covariance matrix P k|k : )。 9. The position sensorless control method of a switched reluctance motor based on CKF according to claim 1, It is characterized in that Determining the estimated values ​​of the angular velocity and the velocity by using the estimated state value includes: in, The fourth element in the state vector is the estimated angular velocity, and the fifth element is the estimated angle.

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