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

Abstract

The application discloses a method for identifying initial position of a permanent magnet synchronous motor based on double-distribution empire competition, and belongs to the field of sensorless control of the permanent magnet synchronous motor. A function of initial position angle of the motor rotor with zero rotating speed is constructed; the function of initial position angle is converted into an initial position angle cost function; a gradient value is calculated, substituted into a formula of a conjugate gradient method, and an identification interval is determined; a state with the minimum cost function is selected as an empire, and the remaining states are divided into various empires to generate an initial empire group; a state with the minimum cost function is selected as an empire, and the remaining states are selected as colonies; a state with the minimum cost function is selected as an empire in the empire group, and the remaining states are selected as colonies, and a colony with the highest cost function is removed; iteration is repeated, when the number of the empire group is reduced to half of the initial number, the colonies are subjected to Cauchy distribution; when only one state is left, an estimated angle value of the state is taken as a final initial angle identification result. The application is used for initial position identification of the permanent magnet synchronous motor.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of permanent magnet synchronous motor position sensorless control, and particularly relates to a permanent magnet synchronous motor initial position identification method based on double-distribution empire competition. BACKGROUND

[0002] Permanent magnet synchronous motors have good dynamic performance, high starting torque and energy density, and are therefore widely used in the industrial field. However, the permanent magnet synchronous motor vector control system must use accurate information of the motor rotor position, and the use of a position sensor will bring a series of problems, such as size, weight and cost increase, and reduced motor control reliability in extreme environments. To achieve good starting performance, the initial position of the permanent magnet synchronous motor needs to be accurately obtained, and if the initial position is unknown, the motor may cause shaking, reverse rotation or even failure to start during starting. Therefore, it is of great significance to identify the rotor position of the permanent magnet synchronous motor under zero-speed conditions.

[0003] Currently, the rapidity of initial position identification is still a difficult problem to be solved. To avoid the slow initial position identification caused by the position error through the PI regulator to obtain the estimated position, a cost function can be constructed according to the motor voltage equation, the conjugate gradient method is used to preliminarily search the angle, and then the double-distribution mutation empire competition method is used to finely search the angle, so that the initial position is quickly obtained in one calculation period. If there is a lack of rapid method for initial position estimation, the application of permanent magnet synchronous motor position sensorless control in fast starting scenarios will be limited. SUMMARY

[0004] The application aims to solve the problem of rapid initial position identification of the permanent magnet synchronous motor, and provides a permanent magnet synchronous motor initial position identification method based on double-distribution empire competition.

[0005] The double distribution refers to the use of Gaussian and Cauchy distributions in different stages of empire competition.

[0006] The method of the application uses the motor voltage equation to construct a cost function, and quickly searches the angle through the double-distribution empire competition method, which effectively avoids the problem of long calculation time of the initial position using the PI regulator, and has good application prospects in the use scenarios of fast starting of the motor.

[0007] To achieve the above-mentioned purposes, the technical solutions adopted by the application are as follows:

[0008] The permanent magnet synchronous motor initial position identification method based on double-distribution empire competition comprises the following steps:

[0009] Step one: based on the voltage equation in the static state, a motor rotor initial position angle function is constructed under the premise of the rotating speed equaling to zero;

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

[0011] Step three: 0 is selected as the initial value for optimization, the gradient value of the initial position angle cost function obtained in step two is calculated, and the identification interval is determined by substituting the value into the formula of the conjugate gradient method;

[0012] Step four: in the identification interval, 10N angle values are randomly generated as initial states, N of which are selected as the minimum cost function states as the empire, and N is greater than 5; the remaining states are proportionally divided into each empire to generate an initial empire group; in each empire group, the state with the minimum cost function is selected as the empire again, and the remaining states are selected as the colonies, so that the angle values of the colonies are randomly changed near the initial angle according to the Gaussian distribution; after the change, the state with the minimum cost function is selected again in the empire group, and the remaining states are selected as the colonies, and the colony with the highest cost function is removed from the empire group; repeated iteration is performed, and when the number of empire groups is reduced to half of the initial number, the colonies are randomly changed near the initial angle according to the Cauchy distribution; when only one state remains, the estimated angle value is taken as the final initial angle identification result.

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

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

[0015]

[0016] In the formula, u α ,u β represents the motor voltage in the static coordinate axis system; R s represents the stator resistance; i α ,i β represents the motor current in the static coordinate axis system; L a ,L b represents the inductance matrix; ψ f represents the permanent magnet flux linkage; θ e ,ω e respectively represent the motor electrical angle and electrical angular velocity; T s represents the calculation period; k represents the time period; Δi α ,Δi βThe change of the motor current in the adjacent time in the stationary coordinate system is represented by the following expression:

[0017]

[0018] In the formula, T pk is a coordinate transformation matrix;

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

[0020]

[0021] In the formula, ω respectively represent the estimated motor electrical angle and the estimated electrical angular velocity; represents the inductance matrix, represents the coordinate transformation matrix, and the specific expressions are as follows:

[0022]

[0023]

[0024] In the formula, L d , L q represent the cross-axis and direct-axis inductances of the motor.

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

[0026] The cost function with the regularization term is as follows:

[0027]

[0028] In the formula, k1 and k2 are constants;

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

[0030]

[0031] In the formula, ω1 represents a rotation speed threshold.

[0032] Further, in step three, the determination process of the identification interval is as follows:

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

[0034] Further, in step three, 0 is selected as the initial value of optimization, the gradient value of the initial position angle cost function obtained in step two is calculated, and the conjugate gradient method formula is calculated to determine the identification interval; Specifically:

[0035] In each calculation period, the constructed cost function is taken as the objective function, the threshold value is selected as ε, and the search is started from an arbitrary initial point At this time, the iteration number k = 1, and the search is carried out along the negative gradient direction:

[0036]

[0037] In the formula: 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 let:

[0039]

[0040] In the formula: is the estimated angle of the second iteration, λ1 is the coefficient, which is calculated by ; is the estimated angle of the first iteration;

[0041] If , stop, otherwise continue to calculate α from k =||g k+1 || 2 / ||g k || 2 , let:

[0042] p k+1 = -g k+1 + α k p k ,

[0043] In the formula: g k+1 represents the gradient direction at the k+1 iteration, α k represents the optimization direction coefficient, and p k represents the optimization direction at the k iteration;

[0044] Continue iteration from until ||g k ||≤ε, stop the search, and take as the initialization range of the imperial competition algorithm; λ k is the coefficient at the k iteration.

[0045] Further, step four is specifically:

[0046] Step 3: Randomly generate 10N countries as initial countries in the range obtained in step 2, select the first N countries with the minimum cost function as empires, and the remaining countries as colonies. Then, divide the colonies according to the size of the empire cost function value, and calculate the number of colonies for each empire according to the following formula:

[0047]

[0048] N.R. n = round{t n ×9N}

[0049] In the formula: R n is the cost function value of the nth empire; is the cost function value of the largest empire among all empires; R' n is the standardized cost of the nth empire; t n is the standardized power size of the nth empire; N.R. n is the number of initial colonies corresponding to the empire; round represents rounding;

[0050] The colonies move according to the following rules:

[0051] x ~ U(0, β × d)

[0052] θ ~ U(-γ, γ)

[0053] In the formula: x represents the moving distance; d represents the distance between the colony and the empire; β is the moving parameter, which is greater than 1 to make the colony closer to the empire; θ is the random deviation angle; U(0, β × d), U(-γ, γ) represent uniform distribution in the interval;

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

[0055] After the colonies move, the colony with the largest cost function in the largest empire is the object of competition for the empire. The sum of the cost functions of different empires and their colonies is weighted as the empire weight value. The weakest colony is occupied by the empire, and then the colony is mutated by a Gaussian probability distribution function. If the number of empires is less than 5N, the colony is mutated by a Cauchy probability distribution function. If the number of empires is not one, the colony movement and empire competition process is repeated.

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

[0057] The beneficial effects of the present application relative to the prior art are: the present application adopts a double-distribution empire competition method to optimize the cost function constructed according to the voltage equation under the alpha-beta axis system, compared with the existing method, the initial position of the permanent magnet synchronous motor is quickly identified, and the application of the position control algorithm in the fast start scenario is provided with wide possibility. BRIEF DESCRIPTION OF DRAWINGS

[0058] Figure 1 is a flowchart of the double-distribution empire competition-based permanent magnet synchronous motor initial position identification method of the present application. DETAILED DESCRIPTION

[0059] Specific implementation one: as shown in the embodiment, a double-distribution empire competition-based permanent magnet synchronous motor initial position identification method is disclosed, the method comprises the following steps: Figure 1

[0060] Step one: based on the voltage equation under the static state, an initial position angle function of the motor rotor is constructed under the premise that the rotating speed is equal to zero; specifically:

[0061] The voltage equation of the permanent magnet synchronous motor under the alpha-beta axis system is obtained based on the discretization of the Euler equation:

[0062]

[0063] In the formula: u α ,u β represents the motor voltage under the static coordinate axis system; R s represents the stator resistance; i α ,i β represents the motor current under the static coordinate axis system; L a ,L b represents the inductance matrix; ψ f represents the permanent magnet flux linkage; θ e ,ω e respectively represent the motor electrical angle and electrical angular velocity; T s represents the calculation period; k represents the time period; Δi α ,Δi β represents the change of the motor current under the static coordinate axis system at adjacent time, and its expression is:

[0064]

[0065] In the formula: T pk is a coordinate transformation matrix;

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

[0067] ​

[0068] In the formula: respectively represent the estimated motor electrical angle and the estimated electrical angular velocity;

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

[0070]

[0071] In the formula: L d , L q represents the cross-axis and direct-axis inductance of the motor.

[0072] Since the initial position angle cost function designed in the step can be solved by using the optimization method to directly obtain the initial position value, the initial position recognition can be completed within the calculation period of a digital signal processor, and the problem that the initial position value cannot be obtained by using the PI regulator in the traditional initial position recognition algorithm for multiple periods is solved, and the starting time of the position sensorless motor is effectively shortened.

[0073] Step two: based on the function optimization theory, based on the convex function method of 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 the regularization term is:

[0075]

[0076] In the formula: k1, k2 are constants;

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

[0078]

[0079] In the formula: ω1 represents the speed threshold.

[0080] Step three: selecting 0 as the initial value of optimization, calculating the gradient value of the initial position angle cost function obtained in step two, and substituting it into the formula of the conjugate gradient method to determine the identification interval; specifically:

[0081] In each calculation period, the constructed cost function is taken as the objective function, the threshold is selected as ε, and the search is started from an arbitrary initial point At this time, the iteration number k = 1, and the search is carried out 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 bound of the identification interval, and the last estimated angle value minus the threshold is used as the lower bound of the identification interval.

[0091] Step four: Randomly generate 10N angle values as initial states in the identification interval, select N states with minimum cost function as empires, and N is greater than 5; divide the remaining states into empires in proportion to the interval to generate initial empire groups; in each empire group, select the state with minimum cost function as empire again, and the remaining states as colonies, and make the angle values of the colonies change randomly around their initial angles according to Gaussian distribution; after the change, select the state with minimum cost function as empire again in the empire group, and the remaining states as colonies, and remove the colony with the highest cost function from the empire group; repeat the iteration, and when the number of empire groups decreases to half of the initial number, make the colonies change randomly around their initial angles according to Cauchy distribution; when only one state remains, take its estimated angle value as the final initial angle identification result; specifically:

[0092] Randomly generate 10N states in the range obtained in step three as initial states, select the first N states with minimum cost function as empires, and the remaining states as colonies, then divide the colonies according to the empire cost function value, and the number of colonies of each empire is calculated according to the following formula:

[0093]

[0094] N.R. n = round{t n ×9N}

[0095] In the formula: R n is the cost function value of the nth empire; is the cost function value of the empire with the maximum cost function among all empires; R' n is the standardized cost of the nth empire; t n is the standardized power of the nth empire; N.R. n is the number of initial colonies corresponding to the empire; round represents rounding;

[0096] The colonies move according to the following rules:

[0097] x ~ U(0, β × d)

[0098] θ ~ U(-γ, γ)

[0099] In the formula: x represents the moving distance; d represents the distance between the colony and the empire; β is the moving parameter, which is greater than 1 to make the colony approach the empire; θ is the random deviation angle; U(0, β × d), U(-γ, γ) represent uniform distribution in the interval;

[0100] During the movement of the colonies, if the cost function of a colony after moving is less than that of the empire, exchange their identities, and other colonies move towards the new empire.

[0101] After the colony moves, the colony with the largest cost function in the largest empire is taken as the target of competition among the empires, and the sum of the cost functions of the different empires and their colonies is weighted as the empire weight value, the colony is randomly competed for according to the empire weight value as a probability, after the weakest colony is occupied, mutation is performed through a Gaussian probability distribution function, if the number of empires is less than 5N, mutation is performed through a Cauchy probability distribution function; if the number of empires is not one, the colony moving and empire competition process is repeatedly executed;

[0102] In the competition process, if a certain empire loses all the colonies, the empire is extinct, finally, when only one empire is left, the algorithm ends, and the angle value of the last empire is taken as the final initial position recognition value.

[0103] The above merely describes the preferred specific embodiments of the present application, but the protection scope of the present application is not limited thereto, any person skilled in the art can make equivalent replacements or changes to the technical scheme and the inventive concept of the present application within the technical scope disclosed by the present application, which should be covered within the protection scope of the present application.

Claims

1. A method for initial position identification of a permanent magnet synchronous motor based on dual-distributed imperial competition, characterized by: 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; 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: Represents the motor voltage in the stationary coordinate system; represents the stator resistance; Represents the motor current in the stationary coordinate system; represents the inductance matrix; represents the permanent magnet flux; Represent the motor electrical angle and electrical angular velocity respectively; represents the calculation cycle; k represents the number of time cycles; Represents the change in motor current in the stationary coordinate system at adjacent moments, and its expression is: Where: 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: Represents the DC-axis inductance of the motor; Step 2: Based on function optimization theory, the convex function method based on d-axis high-frequency voltage injection and regularization term is used to convert the initial position angle function into an initial position angle cost function; specifically: The cost function with regularization is: Where: is a constant; The amplitude modulation function based on d-axis high-frequency voltage injection is: Where: represents the speed threshold; 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; The method selects 0 as the initial value for optimization, calculates the gradient value of the initial position angle cost function obtained in step 2, substitutes it into the conjugate gradient method formula, and determines the identification interval; specifically: In each calculation cycle, the constructed cost function is used as the objective function, and the threshold is selected as , from any initial point Start, at this time the number of iterations k=1, search along the negative gradient direction: ， Where: represents the gradient direction at the first iteration, represents the gradient value of the cost function, Represents the optimization direction in the first iteration; like , then stop, otherwise set: Where: is the estimated angle for the second iteration, As coefficients, by setting Calculated; is the estimated angle of the first iteration; like , then stop, otherwise Continue calculation ,make: ， Where: represents the gradient direction at the k+1th iteration, represents the optimization direction coefficient, Indicates the optimization direction at the kth iteration; Depend on Continue iterating until Stop searching when As the initialization scope of the imperial competition algorithm; 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 bound of the identification interval, and the last estimated angle value minus the threshold is used as the lower bound of the identification interval; Step 4: Within the identification interval, randomly generate 10N angle values ​​as initial countries, select N countries with the smallest cost functions as empires, and the value of N is greater than 5; divide the remaining countries into empires in proportion to the interval to generate initial empire groups; within 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 values ​​of the colonies vary randomly around their initial angles according to the Gaussian distribution; after the change, select the country with the smallest cost function as the empire again within the empire group, and the rest as colonies, and remove the colonies 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 colonies follow the Cauchy distribution and vary randomly around their initial angles; 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 dual-distributed imperial competition according to claim 1 is characterized in that: Step 4 is as follows: Randomly generate 10N countries within the range obtained in step 3 as the initial countries. Select the first N countries with the smallest cost function as empires, and the remaining countries 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: Where: is the cost function value of the nth empire; is the cost function value of the empire that maximizes the cost function; is the normalized cost of the nth empire; is the normalized power size of the nth empire; The number of colonies in the empire at the beginning; round means rounding; Colonies move according to the following rules: Where: Indicates the moving distance; It indicates the distance between colonies and empires; is the movement parameter, a value greater than 1 allows the colony to move closer to the empire; is the random deviation angle; Indicates uniform distribution within the interval; During the colony movement process, if the cost function of a colony after the movement is less than that of the empire, the two identities will be exchanged, and the other colonies will move towards the new empire. After the colonies are moved, the colonies with the highest cost function in the largest empire become the targets of imperial competition. The sum of the cost functions of different empires and their colonies is weighted as the empire weight value, and colonies are randomly competed for with the empire weight value as the probability. After the weakest colony is occupied, mutation is performed using the Gaussian probability distribution function. If the number of empires at this time is less than 5N, mutation is performed using the Cauchy probability distribution function. If the number of empires is more than one, the colony movement and imperial competition process 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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