Permanent magnet synchronous motor initial position identification method based on dual-distribution empire competition

Abstract

The invention discloses a permanent magnet synchronous motor initial position identification method based on dual-distribution empire competition, and belongs to the field of permanent magnet synchronous motor sensorless control. Constructing a motor rotor initial position angle function with the rotating speed equal to zero; converting the initial position angle function into an initial position angle cost function; calculating a gradient value, substituting the gradient value into a conjugate gradient method formula for calculation, and determining an identification interval; selecting a country with the minimum cost function as an empire, and dividing other countries to each empire to generate an initial empire group; selecting a minimum cost function as an empire, and taking other countries as colonies; selecting the country with the minimum cost function in the empire group as the empire, taking the rest as colonies, and removing the colonies with the highest cost function; iterating repeatedly, and when the number of the empire groups is reduced to half of the initial number, enabling the colonies to obey Cauchy distribution; and when only one country is left, taking the estimated angle value as a final initial angle identification result. The method is used for identifying the initial position of the permanent magnet synchronous motor.

Description

Technical Field

[0001] The invention belongs to the field of position sensorless control of permanent magnet synchronous motors, and in particular relates to an initial position identification method of a permanent magnet synchronous motor based on double-distributed imperial competition. Background Art

[0002] Permanent magnet synchronous motors have good dynamic performance, high starting torque and energy density, so they are widely used in the industrial field. However, the permanent magnet synchronous motor vector control system must use accurate information about the motor rotor position, and the use of position sensors will bring a series of problems, such as increased size, weight and cost, and reduced motor control reliability in extreme environments. In order to achieve good starting performance, it is necessary to accurately obtain the initial position of the permanent magnet synchronous motor. If the initial position is unknown, the motor may cause jitter, reversal or even failure to start when it starts. Therefore, it is of great significance to identify the rotor position of the permanent magnet synchronous motor under zero and low speed conditions.

[0003] At present, the speed of initial position identification is still a difficult problem to be solved. In order to avoid the problem of slow initial position identification caused by the existing initial position identification of obtaining the estimated position through the PI regulator, the cost function can be constructed according to the motor voltage equation, and the conjugate gradient method is used to perform a preliminary search for the angle, and then the angle is finely searched through the imperial competition method based on the double distribution variation, so as to quickly obtain the initial position within one calculation cycle. If there is a lack of a fast method for initial position estimation, it will limit the application of permanent magnet synchronous motor position-free control in fast start-up scenarios. Summary of the invention

[0004] The purpose of the present invention is to solve the problem of rapid initial position identification of a permanent magnet synchronous motor and to provide a method for initial position identification of a permanent magnet synchronous motor based on double distributed imperial competition.

[0005] The dual distribution refers to the use of Gaussian and Cauchy distributions respectively in different stages of imperial competition.

[0006] The method of the present invention uses the motor voltage equation to construct a cost function, and quickly searches the angle based on the double-distributed imperial competition method, effectively avoiding the problem of long time for calculating the initial position using a PI regulator, and has good application prospects in the use scenario of motor rapid start-up.

[0007] To achieve the above object, the technical solution adopted by the present invention is:

[0008] A method for identifying the initial position of a permanent magnet synchronous motor based on double-distributed imperial competition, the method comprising the following steps:

[0009] Step 1: Based on the voltage equation in the static state, construct a motor rotor initial position angle function based on the premise that the speed is equal to zero;

[0010] Step 2: Based on the function optimization theory, the convex function method based on the d-axis high-frequency voltage injection and the regularization term, the initial position angle function is converted into the initial position angle cost function;

[0011] Step 3: Select 0 as the initial value for optimization, calculate the gradient value of the initial position angle cost function obtained in step 2, substitute it into the conjugate gradient method formula, and determine the identification interval;

[0012] Step 4: In the identification interval, randomly generate 10N angle values ​​as initial countries, select N countries with the smallest cost function as empires, and the value of N is greater than 5; divide the remaining countries into various empires in proportion to the interval to generate an initial empire group; in each empire group, select the country with the smallest cost function as the empire again, and the remaining countries as colonies, so that the angle value of the colony changes randomly around its own initial angle according to the Gaussian distribution; after the change, select the country with the smallest cost function as the empire again in the empire group, and the rest as colonies, and remove the colony with the highest cost function from the empire group; iterate repeatedly, and when the number of empire groups is reduced to half of the initial number, make the colony obey the Cauchy distribution and change randomly around its own initial angle; when only one country is left, take its estimated angle value as the final initial angle identification result.

[0013] Furthermore, in step 1, based on the voltage equation in the static state, a motor rotor initial position angle function is constructed based on the premise that the speed is equal to zero; specifically:

[0014] The voltage equation of the permanent magnet synchronous motor in the α-β axis system is obtained based on the discretization of the Euler equation:

[0015]

[0016] Where: u α ,u β Represents the motor voltage in the stationary coordinate system; R s represents the stator resistance; i α ,i β Represents the motor current in the stationary coordinate system; L a ,L b represents the inductance matrix; ψ f represents the permanent magnet flux; θ e ,ω e Represent the motor electrical angle and electrical angular velocity respectively; T s represents the calculation cycle; k represents the number of time cycles; Δi α ,Δi βRepresents the change in the motor current under the stationary coordinate system at adjacent moments, and its expression is:

[0017]

[0018] Where: T pk is the coordinate transformation matrix;

[0019] The discrete form of the cost function constructed according to the voltage equation is:

[0020]

[0021] Where: Represent the estimated motor electrical angle and estimated electrical angular velocity respectively; represents the inductance matrix, Represents the coordinate transformation matrix, and its specific expressions are:

[0022]

[0023]

[0024] Where: L d , L q Represents the AC and DC axis inductance of the motor.

[0025] Furthermore, in step 2, the initial position angle function is converted into an initial position angle cost function based on the convex function method based on the function optimization theory, the d-axis high-frequency voltage injection and the regularization term; specifically:

[0026] The cost function with regularization is:

[0027]

[0028] Where: k1, k2 are constants;

[0029] The amplitude modulation function based on d-axis high-frequency voltage injection is:

[0030]

[0031] Where: ω1 represents the speed threshold.

[0032] Furthermore, in step 3, the process of determining the identification interval is:

[0033] When the difference between the estimated angle values ​​obtained from two consecutive iterations is less than the threshold, the last estimated angle value plus the threshold is used as the upper bound of the identification interval, and the last estimated angle value minus the threshold is used as the lower bound of the identification interval.

[0034] Furthermore, in step 3, 0 is selected as the initial value for optimization, the gradient value of the initial position angle cost function obtained in step 2 is calculated, and the formula of the conjugate gradient method is substituted to calculate and determine the identification interval; specifically:

[0035] In each calculation cycle, the constructed cost function is used as the objective function, the threshold is selected as ε, and the initial point Start, at this time the number of iterations k = 1, search along the negative gradient direction:

[0036]

[0037] Where: g1 represents the gradient direction at the first iteration, Represents the gradient value of the cost function, and p1 represents the optimization direction at the first iteration;

[0038] If ||g1||≤ε, stop, otherwise set:

[0039]

[0040] Where: is the estimated angle of the second iteration, λ1 is the coefficient, and by setting Calculated; is the estimated angle of the first iteration;

[0041] like Stop, otherwise Continue to calculate α k =||g k+1 || 2 / ||g k || 2 ,make:

[0042] p k+1 =-g k+1 +α k p k ,

[0043] Where: g k+1 represents the gradient direction at the k+1th iteration, α k represents the optimization direction coefficient, p k Indicates the optimization direction at the kth iteration;

[0044] Depend on Continue iterating until ||g k Stop searching when ||≤ε, and take As the initialization range of the imperial competition algorithm; k is the coefficient at the kth iteration.

[0045] Furthermore, step four is specifically as follows:

[0046] Randomly generate 10N countries as the initial countries within the range obtained in step 3, select the first N countries with the smallest cost function as empires, and the rest as colonies. Then divide the colonies according to the value of the empire cost function. The number of colonies of each empire is calculated according to the following formula:

[0047]

[0048] NR n =round{t n ×9N}

[0049] Where: R n is the cost function value of the nth empire; is the cost function value of the empire with the largest cost function among all empires; R' n is the normalized cost of the nth empire; t n is the normalized power size of the nth empire; NR n It is the number of colonies in the empire. Round means rounding.

[0050] Colonies move according to the following rules:

[0051] x~U(0,β×d)

[0052] θ~U(-γ,γ)

[0053] Where: x represents the moving distance; d represents the distance between the colony and the empire; β is the moving parameter, and a value greater than 1 allows the colony to be close to the empire; θ is the random deviation angle; U(0,β×d),U(-γ,γ) represents uniform distribution in the interval;

[0054] During the process of colony movement, if the cost function of a colony after the movement is less than that of the empire, the two identities will be exchanged, and other colonies will move towards the new empire;

[0055] After the colony is moved, the colony with the largest cost function in the largest empire is the object of imperial competition. The sum of the cost functions of different empires and their colonies is weighted as the empire weight value, and the colony is randomly competed with the empire weight value as the probability. After the weakest colony is occupied, mutation is performed through the Gaussian probability distribution function. If the number of empires is less than 5N at this time, mutation is performed through the Cauchy probability distribution function; if the number of empires is not one, the process of colony movement and imperial competition is repeated;

[0056] During the competition, if an empire loses all its colonies, the empire will perish. Finally, when only one empire remains, the algorithm ends and the angle value of the last empire is taken as the final initial position identification value.

[0057] The beneficial effects of the present invention compared to the prior art are: the present invention adopts a double-distributed imperial competition method to optimize the cost function constructed according to the voltage equation under the α-β axis system, and compared with the existing method, it can realize the rapid identification of the initial position of the permanent magnet synchronous motor, and provides a wide range of possibilities for the application of position-free control algorithms in fast start-up scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 It is a flow chart of the method for identifying the initial position of a permanent magnet synchronous motor based on double-distributed imperial competition of the present invention. DETAILED DESCRIPTION

[0059] Specific implementation method 1: Figure 1 As shown, this embodiment discloses a method for initial position identification of a permanent magnet synchronous motor based on double distributed imperial competition, and the method comprises the following steps:

[0060] Step 1: Based on the voltage equation in the static state, construct a motor rotor initial position angle function based on the premise that the speed is equal to zero; specifically:

[0061] The voltage equation of the permanent magnet synchronous motor in the α-β axis system is obtained based on the discretization of the Euler equation:

[0062]

[0063] Where: u α ,u β Represents the motor voltage in the stationary coordinate system; R s represents the stator resistance; i α ,i β Represents the motor current in the stationary coordinate system; L a ,L b represents the inductance matrix; ψ f represents the permanent magnet flux; θ e ,ω e Represent the motor electrical angle and electrical angular velocity respectively; T s represents the calculation cycle; k represents the number of time cycles; Δi α ,Δi β Represents the change in the motor current under the stationary coordinate system at adjacent moments, and its expression is:

[0064]

[0065] Where: T pk is the coordinate transformation matrix;

[0066] The discrete form of the cost function constructed according to the voltage equation is:

[0067]

[0068] Where: Represent the estimated motor electrical angle and estimated electrical angular velocity respectively;

[0069] represents the inductance matrix, Represents the coordinate transformation matrix, and its specific expressions are:

[0070]

[0071] Where: L d , L q Represents the AC and DC axis inductance of the motor.

[0072] Since the present invention can solve the initial position angle cost function designed in this step by using an optimization method to directly obtain the initial position value, the initial position identification can be completed within a calculation cycle of a digital signal processor, thereby solving the problem that the traditional initial position identification algorithm requires multiple cycles to obtain the initial position value using a PI regulator, and effectively shortening the starting time of the motor without a position sensor.

[0073] Step 2: Based on the function optimization theory, the convex function method based on the d-axis high-frequency voltage injection and the regularization term, the initial position angle function is converted into the initial position angle cost function; specifically:

[0074] The cost function with regularization is:

[0075]

[0076] Where: k1, k2 are constants;

[0077] The amplitude modulation function based on d-axis high-frequency voltage injection (injection signal) is:

[0078]

[0079] Where: ω1 represents the speed threshold.

[0080] Step 3: Select 0 as the initial value for optimization, calculate the gradient value of the initial position angle cost function obtained in step 2, substitute it into the conjugate gradient method formula, and determine the identification interval; specifically:

[0081] In each calculation cycle, the constructed cost function is used as the objective function, the threshold is selected as ε, and the initial point Start, at this time the number of iterations k = 1, search along the negative gradient direction:

[0082]

[0083] Where: g1 represents the gradient direction at the first iteration, Represents the gradient value of the cost function, and p1 represents the optimization direction at the first iteration;

[0084] If ||g1||≤ε, stop, otherwise set:

[0085]

[0086] Where: is the estimated angle of the second iteration, λ1 is the coefficient, and by setting Calculated; is the estimated angle of the first iteration;

[0087] like Stop, otherwise Continue to calculate α k =||g k+1 || 2 / ||g k || 2 ,make:

[0088] p k+1 =-g k+1 +α k p k ,

[0089] Where: g k+1 represents the gradient direction at the k+1th iteration, α k represents the optimization direction coefficient, p k Indicates the optimization direction at the kth iteration;

[0090] Depend on Continue iterating until ||g k Stop searching when ||≤ε, and take As the initialization range of the imperial competition algorithm; k is the coefficient at the kth iteration; the process of determining the identification interval is: when the difference between the estimated angle values ​​obtained in two consecutive iterations is less than the threshold, the last estimated angle value plus the threshold is used as the upper limit of the identification interval, and the last estimated angle value minus the threshold is used as the lower limit of the identification interval.

[0091] Step 4: In the identification interval, randomly generate 10N angle values ​​as the initial countries, select N countries with the smallest cost function as empires, and the value of N is greater than 5; divide the remaining countries into various empires in proportion to the interval to generate an initial empire group; in each empire group, select the country with the smallest cost function as the empire again, and the remaining countries as colonies, so that the angle value of the colony changes randomly around its initial angle according to the Gaussian distribution; after the change, select the country with the smallest cost function as the empire again in the empire group, and the rest as colonies, and remove the colony with the highest cost function from the empire group; iterate repeatedly, and when the number of empire groups is reduced to half of the initial number, make the colony obey the Cauchy distribution and change randomly around its initial angle; when only one country is left, take its estimated angle value as the final initial angle identification result; specifically:

[0092] Randomly generate 10N countries as the initial countries within the range obtained in step 3, select the first N countries with the smallest cost function as empires, and the rest as colonies. Then divide the colonies according to the value of the empire cost function. The number of colonies of each empire is calculated according to the following formula:

[0093]

[0094] NR n =round{t n ×9N}

[0095] Where: R n is the cost function value of the nth empire; is the cost function value of the empire with the largest cost function among all empires; R' n is the normalized cost of the nth empire; t n is the normalized power size of the nth empire; NR n It is the number of colonies in the empire. Round means rounding.

[0096] Colonies move according to the following rules:

[0097] x~U(0,β×d)

[0098] θ~U(-γ,γ)

[0099] Where: x represents the moving distance; d represents the distance between the colony and the empire; β is the moving parameter, and a value greater than 1 allows the colony to be close to the empire; θ is the random deviation angle; U(0,β×d),U(-γ,γ) represents uniform distribution in the interval;

[0100] During the process of colony movement, if the cost function of a colony after the movement is less than that of the empire, the two identities will be exchanged, and other colonies will move towards the new empire;

[0101] After the colony is moved, the colony with the largest cost function in the largest empire is the object of imperial competition. The sum of the cost functions of different empires and their colonies is weighted as the empire weight value, and the colony is randomly competed with the empire weight value as the probability. After the weakest colony is occupied, mutation is performed through the Gaussian probability distribution function. If the number of empires is less than 5N at this time, mutation is performed through the Cauchy probability distribution function; if the number of empires is not one, the process of colony movement and imperial competition is repeated;

[0102] During the competition, if an empire loses all its colonies, the empire will perish. Finally, when only one empire remains, the algorithm ends and the angle value of the last empire is taken as the final initial position identification value.

[0103] The above are only preferred specific implementation modes of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical solutions and inventive concepts of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A method for initial position identification of a permanent magnet synchronous motor based on double distributed imperial competition, characterized in that: The method comprises the following steps: Step 1: Based on the voltage equation in the static state, construct a motor rotor initial position angle function based on the premise that the speed is equal to zero; Step 2: Based on the function optimization theory, the convex function method based on the d-axis high-frequency voltage injection and the regularization term, the initial position angle function is converted into the initial position angle cost function; Step 3: Select 0 as the initial value for optimization, calculate the gradient value of the initial position angle cost function obtained in step 2, substitute it into the conjugate gradient method formula, and determine the identification interval; Step 4: In the identification interval, randomly generate 10N angle values ​​as initial countries, select N countries with the smallest cost function as empires, and the value of N is greater than 5; divide the remaining countries into various empires in proportion to the interval to generate an initial empire group; in each empire group, select the country with the smallest cost function as the empire again, and the remaining countries as colonies, so that the angle value of the colony changes randomly around its own initial angle according to the Gaussian distribution; after the change, select the country with the smallest cost function as the empire again in the empire group, and the rest as colonies, and remove the colony with the highest cost function from the empire group; iterate repeatedly, and when the number of empire groups is reduced to half of the initial number, make the colony obey the Cauchy distribution and change randomly around its own initial angle; when only one country is left, take its estimated angle value as the final initial angle identification result.

2. The method for initial position identification of a permanent magnet synchronous motor based on double-distributed imperial competition according to claim 1 is characterized in that: In step 1, based on the voltage equation in the static state, a motor rotor initial position angle function is constructed based on the premise that the speed is equal to zero; specifically: The voltage equation of the permanent magnet synchronous motor in the α-β axis system is obtained based on the discretization of the Euler equation: Where: u α ,u β Represents the motor voltage in the stationary coordinate system; R s represents the stator resistance; i α ,i β Represents the motor current in the stationary coordinate system; L a ,L b represents the inductance matrix; ψ f represents the permanent magnet flux; θ e ,ω e Represent the motor electrical angle and electrical angular velocity respectively; T s represents the calculation cycle; k represents the number of time cycles; Δi α ,Δi β Represents the change in the motor current under the stationary coordinate system at adjacent moments, and its expression is: Where: T pk is the coordinate transformation matrix; The discrete form of the cost function constructed according to the voltage equation is: Where: Represent the estimated motor electrical angle and estimated electrical angular velocity respectively; represents the inductance matrix, Represents the coordinate transformation matrix, and its specific expressions are: Where: L d , L q Represents the AC and DC axis inductance of the motor.

3. The method for initial position identification of a permanent magnet synchronous motor based on double distributed imperial competition according to claim 2 is characterized in that: In step 2, the initial position angle function is converted into an initial position angle cost function based on the function optimization theory, the convex function method based on the d-axis high-frequency voltage injection and the regularization term; specifically: The cost function with regularization is: Where: k1, k2 are constants; The amplitude modulation function based on d-axis high-frequency voltage injection is: Where: ω1 represents the speed threshold.

4. The method for initial position identification of a permanent magnet synchronous motor based on double distributed imperial competition according to claim 3 is characterized in that: In step 3, the process of determining the identification interval is: When the difference between the estimated angle values ​​obtained from two consecutive iterations is less than the threshold, the last estimated angle value plus the threshold is used as the upper bound of the identification interval, and the last estimated angle value minus the threshold is used as the lower bound of the identification interval.

5. The method for initial position identification of a permanent magnet synchronous motor based on double-distributed imperial competition according to claim 4 is characterized in that: In step 3, 0 is selected as the initial value for optimization, the gradient value of the initial position angle cost function obtained in step 2 is calculated, and the value is substituted into the conjugate gradient method formula to determine the identification interval; Specifically: In each calculation cycle, the constructed cost function is used as the objective function, the threshold is selected as ε, and the initial point Start, at this time the number of iterations k = 1, search along the negative gradient direction: Where: g1 represents the gradient direction at the first iteration, Represents the gradient value of the cost function, and p1 represents the optimization direction at the first iteration; If ||g1||≤ε, stop, otherwise set: Where: is the estimated angle of the second iteration, λ1 is the coefficient, and by setting Calculated; is the estimated angle of the first iteration; like Stop, otherwise Continue to calculate α k =||g k+1 || 2 / ||g k || 2 ,make: p k+1 1-g k+1 +α k p k , Where: g k+1 represents the gradient direction at the k+1th iteration, α k represents the optimization direction coefficient, p k Indicates the optimization direction at the kth iteration; Depend on Continue iterating until ||g k Stop searching when ||≤ε, and take As the initialization range of the imperial competition algorithm; k is the coefficient at the kth iteration.

6. The method for initial position identification of a permanent magnet synchronous motor based on double distributed imperial competition according to claim 5 is characterized in that: Step 4 is as follows: Randomly generate 10N countries as the initial countries within the range obtained in step 3, select the first N countries with the smallest cost function as empires, and the rest as colonies. Then divide the colonies according to the value of the empire cost function. The number of colonies of each empire is calculated according to the following formula: N.R. n =round{t n ×9N} Where: R n is the cost function value of the nth empire; is the cost function value of the empire with the largest cost function among all empires; R' n is the normalized cost of the nth empire; t n is the normalized power size of the nth empire; NR n It is the number of colonies in the empire. Round means rounding. Colonies move according to the following rules: x~U(0,β×d) θ~U(-γ,γ) Where: x represents the moving distance; d represents the distance between the colony and the empire; β is the moving parameter, and a value greater than 1 allows the colony to be close to the empire; θ is the random deviation angle; U(0,β×d),U(-γ,γ) represents uniform distribution in the interval; During the process of colony movement, if the cost function of a colony after the movement is less than that of the empire, the two identities will be exchanged, and other colonies will move towards the new empire; After the colony is moved, the colony with the largest cost function in the largest empire is the object of imperial competition. The sum of the cost functions of different empires and their colonies is weighted as the empire weight value, and the colony is randomly competed with the empire weight value as the probability. After the weakest colony is occupied, mutation is performed through the Gaussian probability distribution function. If the number of empires is less than 5N at this time, mutation is performed through the Cauchy probability distribution function; if the number of empires is not one, the process of colony movement and imperial competition is repeated; During the competition, if an empire loses all its colonies, the empire will perish. Finally, when only one empire remains, the algorithm ends and the angle value of the last empire is taken as the final initial position identification value.

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