A method for compensating phase delay error of a brushless direct current motor
By employing an Adaline filter with a recursive least squares algorithm and a PI regulator in a brushless DC motor, phase delay error is compensated in real time, thus solving the problem of decreased control performance of brushless DC motors under high-speed conditions and improving motor efficiency.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- DALIAN MARITIME UNIVERSITY
- Filing Date
- 2023-02-01
- Publication Date
- 2026-07-07
AI Technical Summary
The control performance of brushless DC motors degrades under high-speed conditions due to phase delay errors, while traditional Adaline filters suffer from slow convergence speed and low steady-state accuracy.
An Adaline filter based on a recursive least squares algorithm is used in conjunction with a PI controller to collect three-phase current data of the motor in real time. The fundamental current is extracted by an adaptive linear neuron filter, and coordinate transformation and phase compensation are performed. The parameters of the PI controller are dynamically adjusted to obtain the optimal compensation angle.
It improves the convergence speed and steady-state accuracy of the weighting factor, reduces the peak-to-peak current, reduces motor heating, and improves the operating efficiency of the brushless DC motor.
Smart Images
Figure CN116667731B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of brushless DC motor control technology, and in particular to a method for compensating for phase delay error in brushless DC motors. Background Technology
[0002] Brushless DC motors typically employ a six-step commutation control method, widely used in aerospace and other industrial fields due to their simple control, low cost, and high power density. Six-step commutation control usually requires six discrete commutation points, with the inverter commutating every 60 degrees. However, commutation errors are common, leading to reduced efficiency. Non-ideal commutation points are mainly caused by two types of errors: rotor position detection error and phase delay error. For brushless DC motor drivers, the ideal current waveform should be rectangular. However, this is not the case in reality. A freewheeling period always exists when the driver switches from one sector to another. For traditional low-speed brushless DC motors, this is usually negligible because the freewheeling period is very short. However, at high speeds, the longer freewheeling time causes the phase current to lag behind the back electromotive force (EMF), and the phase deviation between the current and the back EMF also degrades control performance. To address this issue, most researchers employ phase advance control. Since phase deviation is difficult to measure directly, the d-axis current is used as a substitute value. Since the phase current of a brushless DC motor contains a large number of harmonics, and the d-axis current after coordinate transformation also contains harmonics with amplitudes exceeding integer multiples of 6 of the DC value, an Adaline filter is used to extract the fundamental frequency of the phase current, thereby obtaining a stable d-axis current. However, traditional Adaline filters suffer from slow convergence speed of the weight factors and low steady-state accuracy. To address this, an Adaline filter using a recursive least squares (RLS) algorithm to update the weight factors is proposed to solve the problems existing in the prior art. Summary of the Invention
[0003] To address the problems existing in the prior art, this invention discloses a method for compensating for phase delay error in a brushless DC motor, specifically including the following steps:
[0004] Real-time acquisition of three-phase current data of brushless DC motor;
[0005] An adaptive linear neuron filter based on recursive least squares is constructed in a DSP to extract the fundamental wave of the three-phase current.
[0006] The fundamental wave of the three-phase current is transformed into the synchronous coordinate system to obtain the d-axis current.
[0007] The difference between the d-axis current and 0 is output to the PI controller, and the output of the PI controller is the phase compensation angle.
[0008] After several cycles of adaptive compensation, the PI regulator will stabilize, and the final output compensation angle will be the optimal phase compensation angle under this operating condition.
[0009] Furthermore, a three-phase current sampling circuit for the lower bridge arm is designed on the driver board to acquire three-phase current data in real time. The acquired current data is transmitted to the ADC module of the DSP to be converted into digital quantity, then converted into fundamental frequency by the Adaline filter, converted into d-axis current by coordinate transformation, and then generated by the PI regulator to generate phase compensation angle.
[0010] The mathematical model of the adaptive linear neuron filter is expressed as follows:
[0011]
[0012] Where x i It is the reference input vector, ω i Here, y is the weight factor of the corresponding vector, k is the selected output, and k is 2. The two reference input vectors should be related to the velocity, represented as...
[0013]
[0014] Where ω e The electric angular velocity of the motor is defined by the corresponding weighting factors ω1 and ω2, and the sampling time is set to T. s The nth sampling point of the reference input vector x(n) and the weight factor ω(n) is represented as:
[0015]
[0016] According to equation (1), the selected output is calculated from the input vector and the weighting factor.
[0017] y=x1ω1+x2ω2 (4)
[0018] Write the selected output of the nth sampling point in vector format as follows:
[0019] y(n)=x(n) T ω(n) (5)
[0020] The weighting factor ω(n) is adaptively changed so that the output y(n) has the same fundamental frequency as the original input d(n) at the nth sampling point, where d is the phase current. The error between d(n) and y(n) at the nth sampling point is defined as...
[0021] e(n)=d(n)-y(n) (6)
[0022] The goal of using the RLS algorithm for adaptive learning of weight factors is to minimize a predefined error criterion, making the output closer to the learning object. The RLS algorithm follows these criteria:
[0023]
[0024] Where λ is the forgetting factor, the weight factor that minimizes the criterion function J(n) is found using the gradient descent method, and the update rule of the weight factor is as follows.
[0025] ω(n)=ω(n-1)+e(n)k(n) (8)
[0026] Where, the gain matrix k(n) is
[0027]
[0028] The inverse matrix P(n) of the autocorrelation matrix is
[0029]
[0030] For the RLS algorithm, the initial values of ω(n) and P(n) are chosen as follows:
[0031]
[0032] Where I is the identity matrix and σ is a positive constant. For the RLS algorithm, the selection of σ and λ affects the performance of the Adaline filter, and the initial value of P(n) helps the filter converge.
[0033] Furthermore, the phase current fundamental wave obtained through the adaptive linear neuron filter is transformed to the synchronous coordinate system after coordinate transformation to obtain i. d ;
[0034] The transformation function from the three-phase stationary coordinate system to the synchronous coordinate system is expressed as follows:
[0035]
[0036] in,
[0037] θ=ω e t (13)
[0038] After coordinate transformation, i d As a criterion for determining phase delay error: after coordinate transformation, the phase delay error ε lag Transformed into a current vector in a synchronous reference frame and back electromotive force vector The deviation between them is due to the phase delay error ε lag The d-axis current vector is no longer zero, and the magnitude of the d-axis current can be expressed as...
[0039]
[0040] in, It is a space vector of current. Size.
[0041] When the d-axis current is 0, ε lag A value of 0 indicates that the phase delay error has been compensated.
[0042] Furthermore, the d-axis current i d The difference between the current value and 0 is output as a phase compensation angle by a PI regulator. This compensation angle is superimposed on the traditional commutation angle to determine the actual commutation angle.
[0043] Furthermore, obtaining the optimal compensation angle under operating conditions is a dynamic process that requires adjusting the parameters of the PI controller to obtain the optimal dynamic performance. When the motor operating conditions change, the PI controller can adaptively output the optimal compensation angle under the operating conditions after several cycles of adjustment, forming a closed loop in the system.
[0044] By employing the above-mentioned technical solutions, this invention provides a method for compensating for phase delay error in a brushless DC motor. This method utilizes an improved Adaline filter to accelerate the convergence speed of the weighting factor and improve steady-state accuracy. Using the d-axis current to reflect the phase delay error and employing PI regulator closed-loop control to compensate for it, this method clearly demonstrates that it can reduce the peak-to-peak current, decrease motor heating, and improve motor efficiency. Therefore, this invention has the advantage of improving the operating efficiency of brushless DC motors. Attached Figure Description
[0045] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0046] Figure 1 This is a general block diagram of the brushless DC motor phase delay error compensation method in an embodiment of the present invention;
[0047] Figure 2 This is a diagram of the Adaline filter structure in an embodiment of the present invention;
[0048] Figures 3(a) and (b) are schematic diagrams comparing the weight factor update process of the Adaline filter based on the recursive least squares algorithm (RLS) and the Adaline filter based on the traditional least mean square algorithm (LMS) in the embodiments of the present invention. Figure 3(a) is LMS, and Figure 3(b) is RLS;
[0049] Figure 4i before and after compensation in the example of this invention d Schematic diagram of phase compensation angle change;
[0050] Figure 5 This is a schematic diagram showing the change in peak-to-peak current before and after compensation under full load at 3000 rpm in an example of the present invention. Detailed Implementation
[0051] To make the technical solutions and advantages of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention:
[0052] like Figure 1 The method for compensating phase delay error of a brushless DC motor, as shown, includes the following steps: real-time acquisition of three-phase current data of the brushless DC motor using hardware; constructing an Adaline filter based on recursive least squares (RLS) in a DSP to extract the fundamental wave of the three-phase current; transforming the extracted fundamental wave of the three-phase current to the synchronous coordinate system to obtain the d-axis current; outputting the difference between the d-axis current and 0 to a PI controller, the output of which is the phase compensation angle; and through several cycles of adaptive compensation, the PI controller will tend to stabilize, and the final output compensation angle is the optimal phase compensation angle under this operating condition.
[0053] In one implementation case, the driver board is designed with a three-phase current sampling circuit of the lower bridge arm to acquire three-phase current data in real time. The acquired current data is sent to the ADC module of the DSP to be converted into digital quantity, then passed through an Adaline filter to be converted into fundamental frequency, then converted into d-axis current through coordinate transformation, and then generated by a PI regulator to generate phase compensation angle.
[0054] In one implementation case, the traditional Adaline filter uses the Least Mean Square (LMS) algorithm to update the weight factors, which suffers from slow convergence speed and low steady-state accuracy. Therefore, it is necessary to redesign the Adaline filter using the Recursive Least Squares (RLS) algorithm. The specific design process is as follows:
[0055] Figure 2 This is a diagram of the Adaline filter structure.
[0056] The mathematical model of an Adaline filter can be expressed as follows:
[0057]
[0058] Where x i It is the reference input vector, ω iThese are the weighting factors for the corresponding vectors, where d and y are the original input and the selected output, respectively. In this case, they are the phase current and the fundamental frequency of the phase current, respectively. k is set to 2, and the two reference input vectors should be velocity-dependent, expressed as...
[0059]
[0060] Where ω e This is the electric angular velocity of the motor. Then, the corresponding weighting factors can be defined as ω1 and ω2. This filter is used for discrete systems where the sampling time is set to T. s The nth sampling point of the reference input vector x(n) and the weight factor ω(n) can be represented as:
[0061]
[0062] According to equation (1), the selected output is calculated from the input vector and the weighting factor.
[0063] y=x1ω1+x2ω2 (4)
[0064] Then, the selected output of the nth sampling point can be written in vector format as
[0065] y(n)=x(n) T ω(n) (5)
[0066] The weighting factor ω(n) is adaptively changed so that the output y(n) has the same fundamental frequency as the original input d(n) at the nth sampling point. The error between d(n) and y(n) at the nth sampling point is defined as...
[0067] e(n)=d(n)-y(n) (6)
[0068] Then, the RLS algorithm is used for adaptive learning of the weight factors. The goal of adaptive learning is to minimize a predefined error criterion, making the output closer to the learned object. The RLS algorithm follows these criteria:
[0069]
[0070] Where λ is the forgetting factor, representing the degree of forgetting, which means that older data has a smaller impact on J(n). Applying gradient descent, we can find the weight factors that minimize the criterion function J(n), and then obtain the following update rule for the weight factors.
[0071]
[0072] Where, the gain matrix k(n) is
[0073]
[0074] The inverse matrix P(n) of the autocorrelation matrix is
[0075]
[0076] For the RLS algorithm, the initial values of ω(n) and P(n) are chosen as follows:
[0077]
[0078] Where I is the identity matrix and σ is a positive constant. For the RLS algorithm, the choice of σ and λ affects the performance of the Adaline filter. The initial value of P(n) helps the filter converge.
[0079] Figures 3(a)-(b) are schematic diagrams comparing the weight factor update process of the Adaline filter based on the recursive least squares (RLS) algorithm and the Adaline filter based on the traditional least mean squares (LMS) algorithm. The top one is LMS, and the bottom one is RLS.
[0080] In one implementation example, the fundamental phase current obtained through the Adaline filter is transformed to the synchronous coordinate system after coordinate transformation to obtain i. d ;
[0081] The transformation function from the three-phase stationary coordinate system to the synchronous coordinate system can be expressed as:
[0082]
[0083] in,
[0084] θ=ω e t (13)
[0085] The above process uses the coordinate transformed i d As a criterion for determining phase delay error:
[0086] After coordinate transformation, the phase delay error ε lag Transformed into a current vector in a synchronous reference frame and back electromotive force vector The deviation between them. Due to the phase delay error ε lag The d-axis current vector is no longer zero, and the magnitude of the d-axis current can be expressed as...
[0087]
[0088] in, It is a space vector of current. Size.
[0089] When the d-axis current is 0, ε lagA value of 0 indicates that the phase delay error has been compensated.
[0090] In one implementation case, the d-axis current i d The difference between the current value and 0 is output as a phase compensation angle by a PI regulator. This compensation angle is superimposed on the traditional commutation angle to determine the actual commutation angle.
[0091] In one implementation case, obtaining the optimal compensation angle under a certain operating condition is a dynamic process that requires adjusting the parameters of the PI controller to obtain the optimal dynamic performance. When the motor operating condition changes, the PI controller can adaptively output the optimal compensation angle under that operating condition after several cycles of adjustment, forming a system closed loop. Figure 4 The values of i before and after compensation are displayed. d And phase compensation angle change.
[0092] Compared with existing technologies, the advantages of this invention are that it accelerates the convergence speed of the weighting factor and improves steady-state accuracy by using an improved Adaline filter. It uses the d-axis current to reflect the phase delay error and employs a PI regulator closed-loop control to compensate for the phase delay error. Figure 5 A graph showing the change in peak-to-peak current before and after compensation at full load (3000 rpm) is presented. This graph clearly demonstrates that this method can reduce the peak-to-peak current, decrease motor heating, and improve motor efficiency. Therefore, this invention has the advantage of improving the operating efficiency of brushless DC motors.
[0093] The above description is only a preferred embodiment 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, should be covered within the scope of protection of the present invention.
Claims
1. A method for compensating phase delay error in a brushless DC motor, characterized in that... include: Real-time acquisition of three-phase current data of brushless DC motor; An adaptive linear neuron filter based on recursive least squares is constructed in a DSP to extract the fundamental wave of the three-phase current. The fundamental wave of the three-phase current is transformed into the synchronous coordinate system to obtain the d-axis current. The difference between the d-axis current and 0 is output to the PI controller, and the output of the PI controller is the phase compensation angle. After several cycles of adaptive compensation, the PI regulator will tend to stabilize, and the final output compensation angle is the optimal phase compensation angle under this operating condition. The mathematical model of the adaptive linear neuron filter is expressed as follows: (1) in x i It is the reference input vector. ω i These are the weight factors of the corresponding vector. y It is the selected output. k Choosing 2, the two reference input vectors should be related to velocity, represented as... (2) in ω e It is the electric angular velocity of the motor, and the corresponding weighting factor is defined as follows: ω 1 and ω 2. The sampling time is set to T s Reference input vector x ( n and weighting factors ω ( n ) n Each sampling point is represented as (3) According to equation (1), the selected output is calculated from the input vector and the weighting factor. (4) The first n The selected output of each sampling point is written in vector format. (5) Weighting factors ω ( n Adaptive change, making the output y ( n ) and the n The original input of each sampling point d ( n The fundamental frequency is the same here. d It is the phase current, the first n At each sampling point d ( n )and y ( n The error between ) is defined as (6) The goal of using the RLS algorithm for adaptive learning of weight factors is to minimize a predefined error criterion, making the output closer to the learning object. The RLS algorithm follows these criteria: (7) in, λ Let the forgetting factor be the criterion function to be minimized using gradient descent. J ( n The weighting factors are obtained, and the update rules for the weighting factors are as follows: (8) Wherein, the gain matrix k ( n )for (9) The inverse of the autocorrelation matrix P ( n )for (10) For the RLS algorithm, ω ( n )and P ( n The initial values for ) are chosen as follows: (11) in I It is the identity matrix. σ It is a positive constant. For the RLS algorithm, σ and λ The choice of [aspect name] affects the performance of the Adaline filter. P ( n The initial value of ) helps the filter converge.
2. The method for compensating phase delay error of a brushless DC motor according to claim 1, characterized in that: The driver board is designed with a three-phase current sampling circuit for the lower bridge arm to acquire three-phase current data in real time. The acquired current data is transmitted to the ADC module of the DSP to be converted into digital quantity, then converted into fundamental frequency by the Adaline filter, converted into d-axis current by coordinate transformation, and then generated by the PI regulator to generate phase compensation angle.
3. The method for compensating phase delay error of a brushless DC motor according to claim 1, characterized in that: The phase current fundamental wave obtained through the adaptive linear neuron filter is transformed to the synchronous coordinate system after coordinate transformation. i d ; The transformation function from the three-phase stationary coordinate system to the synchronous coordinate system is expressed as follows: (12) in, (13)。 4. The method for compensating phase delay error of a brushless DC motor according to claim 1, characterized in that: After coordinate transformation i d As a criterion for determining phase delay error: after coordinate transformation, the phase delay error... ε lag Transformed into a current vector in a synchronous reference frame and back electromotive force vector The deviation between them is due to phase delay error. ε lag The d-axis current vector is no longer zero, and the magnitude of the d-axis current can be expressed as... (14) in, It is a space vector of current. Size; When the d-axis current is 0, ε lag A value of 0 indicates that the phase delay error has been compensated.
5. The method for compensating phase delay error of a brushless DC motor according to claim 1, characterized in that: d-axis current i d The difference between the current value and 0 is output as a phase compensation angle by a PI regulator. This compensation angle is superimposed on the traditional commutation angle to determine the actual commutation angle.
6. The method for compensating phase delay error of a brushless DC motor according to claim 1, characterized in that: Obtaining the optimal compensation angle under operating conditions is a dynamic process that requires adjusting the parameters of the PI controller to achieve optimal dynamic performance. When the motor operating conditions change, the PI controller can adaptively output the optimal compensation angle under the operating conditions after several cycles of adjustment, forming a closed loop in the system.