A self-correction method for gain and bias of double current sensor of switched reluctance motor

Abstract

The application discloses a double-current sensor gain and bias self-correction method for a switched reluctance motor, and relates to the technical field of current detection. The method comprises the following steps: establishing a current measurement mapping matrix of double-sensor output according to the direction and equivalent number of turns of three-phase winding current through two current sensors, and constructing an affine measurement model containing sensor gain and bias; constructing a left null space event residual in the interval of individual conduction of each phase to eliminate the current of the currently conducting phase, obtain the bias estimation value of the double sensor, and compensate the original sensor output by using the bias estimation value; injecting a voltage pulse into the winding of the individually conducting phase in the low-speed stage, estimating the gain coefficient of the double sensor, and performing gain compensation; dividing each cycle into six subintervals according to the switching combination of the power switch tube of each phase, determining the zero-current phase in each interval, combining the zero space relationship between the double-sensor measurement relationship after bias and gain compensation and the current measurement mapping matrix, and realizing three-phase current reconstruction under normal operation and fault-tolerant operation conditions. The method does not need to increase an additional current sensor, can compensate the measurement signal when the sensor has bias and gain error, reduces the three-phase current reconstruction error caused by the change of the sensor parameter, and has good engineering application value.

Description

Technical Field

[0001] This invention relates to the field of current detection technology, specifically a method for gain and bias self-calibration of dual current sensors in a switched reluctance motor. Background Technology Switched reluctance motors (SRMs) are characterized by their simple structure, high reliability, wide speed range, and strong fault tolerance, and are widely used in aerospace, new energy vehicles, and industrial drives. Phase current is a crucial feedback quantity for the closed-loop current control and torque regulation of SRMs, and the accuracy of current detection directly affects the motor's operating performance. To reduce the number of sensors and lower hardware costs, existing technologies typically use two current sensors to collect bus or bridge arm currents and reconstruct the three-phase current by combining the conduction relationships of each phase winding within the current cycle. However, most existing current reconstruction methods assume that sensor parameters remain constant and do not consider sensor gain and bias. When there are bias or gain errors in the sensors, the measurement errors directly affect the three-phase current reconstruction results. After a power switching device failure, the fault-tolerant operating topology changes the original phase current loop, making it difficult to directly reuse the reconstruction relationship from the normal operating mode. Adding additional current sensors would increase system cost, size, and complexity. Therefore, a three-phase current reconstruction method is needed that can correct the bias and gain of dual sensors using existing system information without adding current sensors, and is applicable to both normal and fault-tolerant operating modes. Summary of the Invention The purpose of this invention is to address the problem that existing dual-sensor current reconstruction methods for switched reluctance motors are easily affected by sensor bias and gain, and are difficult to adapt to different measurement relationships under normal operation and fault-tolerant operation modes. This invention proposes a self-calibration method for the gain and bias of dual current sensors in switched reluctance motors. The technical solution proposed in this invention is as follows: A method for gain and bias self-calibration of dual current sensors in a switched reluctance motor is proposed. This method establishes a current measurement mapping matrix for the dual sensor outputs based on the direction of the three-phase winding current passing through the two current sensors and the equivalent number of turns. An affine measurement model incorporating sensor gain and bias is constructed. Left null-space event residuals are constructed within the individual conduction intervals of each phase to eliminate the current of the currently conducting phase, obtaining a bias estimate for the dual sensors. This bias estimate is then used to compensate for the original sensor outputs. During the low-speed phase, voltage pulses are injected into the individually conducting phase windings to estimate the gain coefficients of the dual sensors and perform gain compensation. Each cycle is divided into six sub-intervals based on the switching combinations of the power switches in each phase. The zero-current phase within each interval is determined. Combining the dual-sensor measurement relationship after bias and gain compensation with the null-space relationship of the current measurement mapping matrix, three-phase current reconstruction under normal and fault-tolerant operating conditions is achieved. The present invention discloses a method for gain and bias self-calibration of dual current sensors in a switched reluctance motor, comprising the following steps: Step 1: Establish a dual-sensor affine current measurement model including gain and bias; Step 2: Construct the left null space event residual in the individual conduction interval of each phase, estimate the dual sensor bias, and use the bias estimate to compensate the dual sensor output; Step 3: Inject voltage pulses into the individual conducting phase winding during the low-speed phase, estimate the dual-sensor gain coefficient, and perform gain compensation; Step 4: Divide each cycle into six sub-intervals according to the switching combination of each phase power switch transistor, determine the zero current phase in each interval, and combine the dual sensor measurement relationship after completing bias and gain compensation with the zero-space relationship of the current measurement mapping matrix to realize the three-phase current reconstruction in normal and fault-tolerant modes. The three-phase current vector x is: In the formula, i a i b and i c These are the winding currents of phase A, phase B, and phase C of the switched reluctance motor, respectively. The output vector z of the dual sensors is: In the formula, i L1 and i L2 These are the actual outputs of sensor 1 and sensor 2, respectively. Based on the direction of the three-phase winding current through the two current sensors and the equivalent number of turns, a current measurement mapping matrix M for the dual-sensor output is established: In the formula, m js Let m be the measurement coefficient of the s-th phase current in the j-th sensor; s Let s be the column vector corresponding to the s-th column in the measurement matrix, where s∈{a, b, c}. Considering the gain and bias of the current sensor, the dual-sensor affine measurement model is expressed as: In the formula, Let β1 and β2 be the bias vectors of the two sensors, respectively, and let k be the gain coefficient of the two sensors. Within the single-phase conduction interval, assuming that only the current of the s-th phase is non-zero, the dual-sensor affine measurement model can be expressed as: In the formula, is It represents the non-zero s-th phase current within the single-phase conduction interval. Choose a non-zero vector g s To satisfy: In the formula, g s For m s The left null space vector. Construct the event residual r corresponding to the single-phase conduction interval of phase s. s : Arrange the residuals corresponding to the N effective single-phase conduction events sequentially to construct the event residual vector r: In the formula, N is the number of effective single-phase conduction events used for bias estimation. The regression vector g corresponding to each event t T Arranged by rows, forming the regression matrix Γ: Establish a linear regression model with bias parameters: The bias parameters are estimated using weighted least squares: In the formula, is the estimated value of the bias parameters of the two sensors; W is the weight matrix. By selecting the left null space vector H of the regression matrix, we can obtain: Constructing residual η: An event-triggered bias estimation update mechanism is constructed based on the consistency residual threshold criterion, when |η|≤η th When the current event data satisfies the consistency condition of the bias model, the sensor bias estimate is updated, where η is... th The preset judgment threshold; The bias-compensated dual-sensor affine measurement vector is: In the formula, z cThis is the bias-compensated dual-sensor affine measurement vector. The bias-compensated dual-sensor affine measurement vector can be expressed as: The equivalent measured current of phase s is: In the formula, The equivalent phase current including sensor gain can be obtained. . The voltage equation for the s-th phase winding is: In the formula, u s R is the phase voltage of the s-th phase winding; s ψ is the resistance of the s-th phase winding; s Let θ be the magnetic flux linkage of the s-th phase; s ω represents the rotor position of phase s; ω represents the rotor angular velocity; d represents the differential operator; In the formula, L s =∂ψ s / ∂i s e is the incremental inductance of phase s; s =∂ψ s / ∂θ s Let be the opposite electromotive force of the sth digit. Will Substituting, we get: Integrating over the pulse injection interval [t0, t1], we obtain: Sensor gain estimate It can be represented as: get: To reduce the measurement error of a single pulse, N pulses satisfying the validity condition are applied consecutively. The gain estimate can then be expressed as: The measurement vector y after bias and gain compensation is: In the formula, y1 and y2 are the outputs of sensor 1 and sensor 2 after bias and gain compensation, respectively. The current measurement mapping matrix M has full row rank, i.e. Choose a non-zero vector n such that it satisfies: In the formula, n is a basis vector in the right null space of the current measurement mapping matrix M. Moore–Penrose pseudoinverse M of current measurement mapping matrix M + for: A particular solution to the dual-sensor measurement equation after bias and gain compensation is: In the formula, x cgq This is the minimum Euclidean norm solution of the dual-sensor measurement equation after bias and gain compensation. The general solution for three-phase current can be expressed as: In the formula, q is the coordinate of the three-phase current in the right zero direction of the current measurement mapping matrix. Based on the switching combinations of the power switches in each phase, each cycle is divided into six sub-intervals, and the current of the j-th phase in each interval is determined to be zero, i.e. ;δ j If the j-th unit vector is, then Substituting into the general solution of the three-phase current, we get: get: In the formula, δ j T n≠0; Substituting q, we obtain the expression for the reconstructed current: Beneficial Effects: Due to the adoption of the above technical solution, this invention is applicable to a dual current sensor gain and bias self-calibration method for switched reluctance motors, effectively solving the problems of existing three-phase current reconstruction methods not considering sensor gain and bias, and difficulty in simultaneously taking into account different current loops under normal operation and fault-tolerant operation modes. A current measurement mapping matrix for the dual sensor output is established based on the direction of the three-phase winding current through the two current sensors and the equivalent number of turns, constructing an affine measurement model including sensor gain and bias; a left null space event residual is constructed in the individual conduction interval of each phase to eliminate the current of the currently conducting phase, obtaining the bias estimate of the dual sensors, and using the bias estimate to compensate the original sensor output; voltage pulses are injected into the individually conducting phase winding during the low-speed stage to estimate the gain coefficient of the dual sensors, and gain compensation is performed on the dual sensor output; each cycle is divided into six sub-intervals according to the switching combination of the power switches of each phase, determining the zero-current phase in each interval, and combining the dual sensor measurement relationship with the null space relationship of the measurement matrix to achieve three-phase current reconstruction under normal operation and fault-tolerant operation conditions. This method does not require the addition of an extra current sensor and can compensate for the measurement signal when there are bias and gain errors in the sensor, thereby reducing the three-phase current reconstruction error caused by changes in sensor parameters. Attached Figure Description Figure 1 This is a flowchart of a method for self-calibrating the gain and bias of a dual current sensor in a switched reluctance motor according to the present invention. Figure 2 This is a diagram of the phase current detection scheme proposed in an embodiment of the present invention. Figure 3 This is a diagram illustrating the specific manner in which the phase currents of each phase pass through the current sensor in an embodiment of the present invention. Figure 4 This embodiment of the invention divides each period into different sub-interval diagrams. Detailed Implementation The following description, in conjunction with the accompanying drawings, provides a further illustration of an embodiment of the three-phase 12 / 8 switched reluctance motor to which this invention applies: A flowchart of a method for self-calibrating the gain and bias of a dual current sensor for a switched reluctance motor is shown below. Figure 1 Three-phase current vector x : In the formula, i a i b and i c These are the winding currents of phase A, phase B, and phase C of the switched reluctance motor, respectively. The output vector z of the dual sensors is: In the formula, i L1 and i L2 These are the actual outputs of sensor 1 and sensor 2, respectively. Based on the direction of the three-phase winding current through the two current sensors and the equivalent number of turns, a current measurement mapping matrix M for the dual-sensor output is established: In the formula, m js Let m be the measurement coefficient of the s-th phase current in the j-th sensor; s The measurement matrix is ​​the column vector corresponding to the s-th column, where s∈{a, b, c}; This embodiment proposes a new phase current detection scheme by optimizing the installation position of the current sensor. The installation position of the current sensor is as follows: Figure 2 As shown in the formula, LEM1 and LEM2 are two sensors. The specific way in which the current of each phase of the switched reluctance motor passes through the two current sensors is as follows: Figure 3 As shown, i a , i b and i c The reference current is passed through the current sensor LEM1 twice, once, and once, respectively, in the positive, negative, and negative directions. i b and i c The reference current is passed through the current sensor LEM2 once in the positive direction and once in the opposite direction, respectively. The current measurement mapping matrix output by the dual sensors can be specifically represented as: Considering the gain and bias of the current sensor, the dual-sensor affine measurement model is expressed as: In the formula, Let β1 and β2 be the bias vectors of the two sensors, respectively, and let k be the gain coefficient of the two sensors. Within the single-phase conduction interval, assuming that only the current of the s-th phase is non-zero, the dual-sensor affine measurement model can be expressed as: In the formula, i s Let be the non-zero s-th phase current within the single-phase conduction interval; specifically, m a =[2,0] T , m b =[-1,1]T , m c =[-1,-1] T . Choose a non-zero vector g s To satisfy: In the formula, g s For m s The left null space vector; specifically, g a =[0,1] T , g b =[1,1] T , g c =[1,-1] T . Construct the event residual r corresponding to the single-phase conduction interval of phase s. s : Arrange the residuals corresponding to the N effective single-phase conduction events sequentially to construct the event residual vector r: In the formula, N is the number of effective single-phase conduction events used for bias estimation. The regression vector g corresponding to each event t T Arranged by rows, forming the regression matrix Γ: Establish a linear regression model with bias parameters: The bias parameters are estimated using weighted least squares: In the formula, is the estimated value of the dual-sensor bias parameters; W is the weight matrix; By selecting the left null space vector H of the regression matrix, we can obtain: Constructing residual η: An event-triggered bias estimation update mechanism is constructed based on the consistency residual threshold criterion, when |η|≤ηth When the current event data satisfies the consistency condition of the bias model, the sensor bias estimate is updated, where η is... th This is the preset judgment threshold. The bias-compensated dual-sensor affine measurement vector is: In the formula, z c This is the bias-compensated dual-sensor affine measurement vector. The bias-compensated dual-sensor affine measurement vector can be expressed as: The equivalent measured current of phase s is: In the formula, The equivalent phase current including sensor gain can be obtained. . The voltage equation for the s-th phase winding is: In the formula, u s R is the phase voltage of the s-th phase winding; s ψ is the resistance of the s-th phase winding; s Let θ be the magnetic flux linkage of the s-th phase; s ω represents the rotor position of phase s; ω represents the rotor angular velocity; d represents the differential operator; In the formula, L s =∂ψ s / ∂i s e is the incremental inductance of phase s; s =∂ψ s / ∂θ s Let be the opposite electromotive force of the sth digit. Will Substituting, we get: Integrating over the pulse injection interval [t0, t1], we obtain: Sensor gain estimate It can be represented as: get: To reduce the measurement error of a single pulse, N pulses satisfying the validity condition are applied consecutively. The gain estimate can then be expressed as: The measurement vector y after bias and gain compensation is: In the formula, y1 and y2 are the outputs of sensor 1 and sensor 2 after bias and gain compensation, respectively. The current measurement mapping matrix M has full row rank, i.e. Choose a non-zero vector n such that it satisfies: In the formula, n is a basis vector in the right null space of the current measurement mapping matrix M; specifically, in this embodiment, n is selected as... n =[1,1,1] T . Moore–Penrose pseudoinverse M of current measurement mapping matrix M + for: A particular solution to the dual-sensor measurement equation after bias and gain compensation is: In the formula, x cgq This is the minimum Euclidean norm solution to the dual-sensor measurement equations after bias and gain compensation; specifically, . The general solution for three-phase current can be expressed as: In the formula, q represents the coordinates of the three-phase current in the right zero direction of the current measurement mapping matrix; specifically, . Each cycle is divided into six sub-intervals based on the switching combination of the power switches in each phase. Figure 4 Divide the period into sub-intervals, where, θ on To open the angle, θ off For the shut-off angle, θ ov To determine the overlap angle, the first interval within each interval is used to determine the first overlap angle. jThe phase current is zero, that is... δ j If the j-th unit vector is, then Specifically, δ a =[1,0,0] T , δ b =[0,1,0] T , δ c =[0,0,1] T . Substituting into the general solution of the three-phase current, we get: get: In the formula, δ j T n≠0; Substituting q, we obtain the expression for the reconstructed current: Specifically, when i c =0, that is Then the currents of the other two phases can be expressed as follows: , The same applies to the other intervals. The above description is merely a claim of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, shall fall within the scope of protection of the technical solution of the present invention.

Claims

1. A method for self-calibrating the gain and bias of dual current sensors in a switched reluctance motor, characterized in that, Based on the direction of the three-phase winding current through the two current sensors and the equivalent number of turns, a current measurement mapping matrix for the dual-sensor output is established, and an affine measurement model including sensor gain and bias is constructed. In the individual conduction interval of each phase, a left null space event residual is constructed to eliminate the current of the current conduction phase, and the bias estimate of the dual sensors is obtained. The bias estimate is then used to compensate the original sensor output. During the low-speed phase, voltage pulses are injected into the winding of the individual conducting phase to estimate the gain coefficient of the dual sensors and perform gain compensation. Based on the switching combination of the power switches of each phase, each cycle is divided into six sub-intervals, and the zero-current phase in each interval is determined. By combining the dual sensor measurement relationship after bias and gain compensation with the zero-space relationship of the current measurement mapping matrix, the three-phase current reconstruction under normal operation and fault-tolerant operation conditions is realized. The method for gain and bias self-calibration of dual current sensors in a switched reluctance motor includes the following steps: Step 1: Establish a dual-sensor affine current measurement model including gain and bias; Step 2: Construct the left null space event residual in the individual conduction interval of each phase, estimate the dual sensor bias, and use the bias estimate to compensate the dual sensor output; Step 3: Inject voltage pulses into the individual conducting phase winding during the low-speed phase, estimate the dual-sensor gain coefficient, and perform gain compensation; Step 4: Divide each cycle into six sub-intervals according to the switching combination of each phase power switch transistor, determine the zero current phase in each interval, and combine the dual sensor measurement relationship after bias and gain compensation with the zero-space relationship of the current measurement mapping matrix to realize the three-phase current reconstruction in normal and fault-tolerant modes. The specific steps in step 1 are as follows: The three-phase current vector x is: In the formula, i a i b and i c These are the winding currents of phase A, phase B, and phase C of the switched reluctance motor, respectively. The output vector z of the dual sensors is: In the formula, i L1 and i L2 These are the actual outputs of sensor 1 and sensor 2, respectively. Based on the direction of the three-phase winding current through the two current sensors and the equivalent number of turns, a current measurement mapping matrix M for the dual-sensor output is established: In the formula, m js Let m be the measurement coefficient of the s-th phase current in the j-th sensor; s The measurement matrix is ​​the column vector corresponding to the s-th column, where s∈{a, b, c}; Considering the gain and bias of the current sensor, the dual-sensor affine measurement model is expressed as: In the formula, Let β1 and β2 be the bias vectors of the two sensors, respectively, and let k be the gain coefficient of the two sensors. The specific steps in step 2 are as follows: Within the single-phase conduction interval, assuming that only the current of the s-th phase is non-zero, the dual-sensor affine measurement model can be expressed as: In the formula, i s The non-zero s-th phase current within the single-phase conduction interval; Choose a non-zero vector g s To satisfy: In the formula, g s For m s The left null space vector; Construct the event residual r corresponding to the single-phase conduction interval of phase s. s : Arrange the residuals corresponding to the N effective single-phase conduction events sequentially to construct the event residual vector r: In the formula, N is the number of effective single-phase conduction events used for bias estimation; The regression vector g corresponding to each event t T Arranged by row, forming the regression matrix Γ: Establish a linear regression model with bias parameters: The bias parameters are estimated using weighted least squares: In the formula, is the estimated value of the dual-sensor bias parameters; W is the weight matrix; By selecting the left null space vector H of the regression matrix, we can obtain: Constructing residual η: An event-triggered bias estimation update mechanism is constructed based on the consistency residual threshold criterion, when |η|≤η th When the current event data satisfies the consistency condition of the bias model, the sensor bias estimate is updated, where η is... th The preset judgment threshold; The specific steps in step 3 are as follows: The bias-compensated dual-sensor affine measurement vector is: In the formula, z c This is the bias-compensated dual-sensor affine measurement vector; The bias-compensated dual-sensor affine measurement vector can be expressed as: The equivalent measured current of phase s is: In the formula, The equivalent phase current including sensor gain can be obtained. ; The voltage equation for the s-th phase winding is: In the formula, u s R is the phase voltage of the s-th phase winding; s ψ is the resistance of the s-th phase winding; s Let θ be the magnetic flux linkage of phase s; s ω represents the rotor position of phase s; ω represents the rotor angular velocity; d represents the differential operator; In the formula, L s =∂ψ s / ∂i s e is the incremental inductance of phase s; s =∂ψ s / ∂θ s The s-th opposite electromotive force; Will Substituting, we get: Integrating over the pulse injection interval [t0, t1], we obtain: Sensor gain estimate It can be represented as: get: To reduce the measurement error of a single pulse, N pulses satisfying the validity condition are applied consecutively. The gain estimate can then be expressed as: The measurement vector y after bias and gain compensation is: In the formula, y1 and y2 are the outputs of sensor 1 and sensor 2 after bias and gain compensation, respectively; The specific steps in step 4 are as follows: The current measurement mapping matrix M has full row rank, i.e. Choose a non-zero vector n such that it satisfies: In the formula, n is a basis vector in the right null space of the current measurement mapping matrix M; Moore–Penrose pseudoinverse M of current measurement mapping matrix M + for: A particular solution to the dual-sensor measurement equation after bias and gain compensation is: In the formula, x cgq This is the minimum Euclidean norm solution to the dual-sensor measurement equation after bias and gain compensation; The general solution for three-phase current can be expressed as: In the formula, q is the coordinate of the three-phase current in the right zero direction of the current measurement mapping matrix; Based on the switching combinations of the power switches in each phase, each cycle is divided into six sub-intervals, and the current of the j-th phase in each interval is determined to be zero, i.e. ;δ j If the j-th unit vector is, then Substituting into the general solution of the three-phase current, we get: get: In the formula, δ j T n≠0; Substituting q, we obtain the expression for the reconstructed current:

Images