A modeling method and system for temperature-dependent giant magnetostrictive actuator

Abstract

The present invention discloses a modeling method and system for a temperature-dependent giant magnetostrictive actuator, and relates to the technical field of giant magnetostrictive actuator modeling. Specific steps include: establishing an improved PI model at an initial temperature T0; identifying parameters in the improved PI model through a genetic algorithm; substituting the identified parameters into the initial envelope function of the improved PI model, and adding an identification parameter c on the basis of the envelope function to obtain a first envelope function; using a genetic algorithm to select the input current and output displacement of the giant magnetostrictive actuator at different temperatures to separately identify the identification parameter c; substituting the value of the identification parameter c into the first envelope function to obtain an expression for the temperature model, and completing the modeling. The present invention establishes a new temperature-dependent giant magnetostrictive model, which, compared to the classical PI model, can accurately describe the relationship between the input current and output displacement of the giant magnetostrictive actuator under temperature changes.

Description

Technical Field

[0001] The present invention relates to the technical field of giant magnetostrictive actuator modeling, and in particular to a modeling method and system for a temperature-dependent giant magnetostrictive actuator. Background Art

[0002] Giant magnetostrictive drive positioning systems based on giant magnetostrictive materials offer advantages such as fast response speed, high energy conversion rate, and nanometer-scale positioning accuracy. They are widely used in various fields such as precision driving and micro-nano processing. However, their complex hysteresis nonlinearity and temperature characteristics reduce the positioning accuracy of giant magnetostrictive precision drive systems. Conventional giant magnetostrictive drive modeling methods only consider the hysteresis characteristics of giant magnetostrictive materials, but fail to account for the temperature changes of giant magnetostrictive drives over long periods of operation. Therefore, establishing a new temperature-dependent giant magnetostrictive model to accurately describe the relationship between the input current and output displacement of the giant magnetostrictive drive under temperature changes is an urgent problem for those skilled in the art. Summary of the Invention

[0003] The object of the present invention is to provide a modeling method and system for a temperature-dependent giant magnetostrictive actuator to solve the problems raised in the background technology.

[0004] To achieve the above object, the present invention provides the following solution: a modeling method for a temperature-dependent giant magnetostrictive actuator, comprising the following specific steps:

[0005] Establish an improved PI model at the initial temperature T0;

[0006] Identifying parameters in the improved PI model by using a genetic algorithm;

[0007] Substituting the identified parameters into the initial envelope function of the improved PI model, and adding the identification parameter c to the envelope function to obtain a first envelope function;

[0008] A genetic algorithm is used to select the input current and output displacement of the giant magnetostrictive actuator at different temperatures to separately identify the identification parameter c;

[0009] Substitute the value of the identification parameter c into the first envelope function to obtain the expression of the temperature model, thereby completing the modeling.

[0010] Preferably, the continuous-time discretization expression of the improved PI model output is:

[0011]

[0012] Where m is the number of improved Play operators, N is the number of input data, u(k) is the input current at the kth moment, ri represents the threshold of the i-th improved Play operator, p(r i ) is the weight of the i-th improved Play operator; is a discrete improved Play operator, then the discrete improved Play operator is expressed as:

[0013] Initial moment:

[0014]

[0015] k moment:

[0016]

[0017] When the input amount increases monotonically or decreases monotonically, the envelope function in the improved Play operator is different, which can be expressed as:

[0018]

[0019] Among them, r i represents the threshold, r i =αi; weight Envelope function:

[0020]

[0021] Among them, a0, a1, a2, a3, b0, b1, b2, b3, α, ρ, and τ are parameters that need to be identified.

[0022] Preferably, the specific steps of identifying the parameters in the improved PI model by genetic algorithm are:

[0023] The solution parameters are expressed as real number vectors through real number coding, and the initialization population is established;

[0024] Calculating the fitness of each individual in the initialized population using a fitness function;

[0025] A fixed number of individuals are selected from the current population as parents according to the size of the fitness, and crossover and mutation operations are performed to identify the solution parameters.

[0026] Preferably, the fitness function is expressed as:

[0027]

[0028] Among them, y p is the theoretical output of the hysteresis model, y t is the actual output of GMA, N is the number of input data sets, F (V) is the sum of squared errors.

[0029] Preferably, the steps of the crossover operation are:

[0030] Among the two parent individuals, one or more crossover points are randomly selected;

[0031] Based on the crossover point, the genes in the crossover point are exchanged according to the set probability, that is, the crossover rate, to produce two new individuals;

[0032] Newly generated individuals are added to the population, replacing some of the existing individuals.

[0033] Preferably, the expression of the first envelope function is:

[0034]

[0035] Where c is a temperature-related parameter.

[0036] Preferably, the specific steps for identifying the temperature-related parameter c are:

[0037] Select the input current and output displacement of the giant magnetostrictive actuator at different temperatures to perform c parameter identification, and obtain the values of c parameters at different temperatures;

[0038] The nonlinear least squares fitting function is used to fit the values of the c parameter at different temperatures, and finally the fitting expression of the c parameter is obtained.

[0039] Preferably, the expression of the temperature model is:

[0040]

[0041] in, is the temperature model operator,

[0042] Initial moment:

[0043]

[0044] k moment:

[0045]

[0046] Among them, T gma is the surface temperature of the supermagnetic rod.

[0047] On the other hand, a modeling system for a temperature-dependent giant magnetostrictive actuator is provided, comprising an initial model building module, a parameter identification module, a parameter adding module, an identification module, and a modeling module; wherein,

[0048] The initial model building module is used to establish an improved PI model at an initial temperature T0;

[0049] The parameter identification module is used to identify the parameters in the improved PI model through a genetic algorithm;

[0050] The parameter adding module is used to substitute the identified parameters into the initial envelope function of the improved PI model, and add an identified parameter c on the basis of the envelope function to obtain a first envelope function;

[0051] The identification module is used to select the input current and output displacement of the giant magnetostrictive actuator at different temperatures using a genetic algorithm to separately identify the identification parameter c;

[0052] The modeling module is used to substitute the value of the identification parameter c into the first envelope function to obtain the expression of the temperature model and complete the modeling.

[0053] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects: establishing a new temperature-dependent giant magnetostrictive model, which can accurately describe the relationship between the input current and output displacement of the giant magnetostrictive drive under temperature change factors compared to the classical PI model. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0055] Figure 1 is a flow chart of the method of the present invention;

[0056] Figure 2 It is the genetic algorithm flow chart of the present invention;

[0057] Figure 3 This is a diagram showing the fitting effect of the temperature model output and the actual output of the present invention. DETAILED DESCRIPTION

[0058] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0059] The purpose of the present invention is to provide a modeling method for temperature-dependent giant magnetostrictive actuators, such as Figure 1 As shown, the specific steps include:

[0060] S1, establishing an improved PI model at the initial temperature T0;

[0061] S2, identify and improve the parameters in the PI model through genetic algorithm;

[0062] S3, substituting the identified parameters into the initial envelope function of the improved PI model, and adding the identified parameter c on the basis of the envelope function to obtain a first envelope function;

[0063] S4, using a genetic algorithm to select the input current and output displacement of the giant magnetostrictive actuator at different temperatures to separately identify the identification parameter c;

[0064] S5. Substitute the value of the identification parameter c into the first envelope function to obtain the expression of the temperature model, thereby completing the modeling.

[0065] Furthermore, the specific process of step S1 is as follows:

[0066] The present invention establishes an accurate model that can express the input current and output displacement at different temperatures for a giant magnetostrictive actuator at a single frequency.

[0067] Select a single frequency, here select the input current as y d =2sin(2πft)+2A, f=8hz, sinusoidal current input identifies the various parameters of the improved PI model at the initial temperature T0 degree (ambient temperature) of the giant magnetostrictive rod, and set the interval D m [0,T m ] is the domain of the input u(t), for any u(t)∈D m [0,T m ], assuming t j <t<t j+1 , interval D m [0,T m ] is divided into N subintervals, and the input u(t) is in each subinterval [t j ,t j+1 ] are monotonically continuous, and 0≤j≤N, j=0,1,2,….

[0068] In the initial state, the output of the improved Play operator is:

[0069]

[0070] At time t, the output of the improved Play operator is:

[0071]

[0072] Among them, r is the threshold of the improved Play operator, γ r (u(t)) is the envelope function of the rising segment of the improved play operator, γl (u(t)) is the envelope function of the descending segment of the improved play operator.

[0073] Then the continuous time expression of the improved PI model output is:

[0074]

[0075] Among them, p(r) is the weight function of the improved Play operator, and p0 is the weight function of the linear part.

[0076] To facilitate computer solution, the integral expression can be discretized as:

[0077]

[0078] Where m is the number of improved Play operators, N is the number of input data, u(k) is the input current at the kth moment, r i represents the threshold of the i-th improved Play operator, p(r i ) is the weight of the i-th improved Play operator; It is a discrete improved Play operator;

[0079] The discrete improved Play operator is expressed as:

[0080] Initial moment:

[0081] k moment:

[0082] When the input amount increases monotonically or decreases monotonically, the envelope function in the improved Play operator is different, which can be expressed as:

[0083]

[0084] Among them, r i represents the threshold, r i =αi; (7)

[0085] Weight

[0086] Envelope function:

[0087] Among them, a0, a1, a2, a3, b0, b1, b2, b3, α, ρ, and τ are parameters that need to be identified.

[0088] Once these 11 parameters are identified, an expression for the improved PI model at T0 is established. Step S2 is the process of identifying these 11 parameters using a genetic algorithm. Genetic algorithms are widely used in nonlinear optimization problems such as parameter identification. The greatest advantage of genetic algorithms is that their search process only targets the chromosomes formed by encoding the problem parameters, rather than the parameters themselves, thus avoiding the limitations of functional constraints.

[0089] Further, such as Figure 2 As shown, the specific process of step S2 is:

[0090] S21, expressing the solution parameters as real number vectors through real number coding, and establishing an initialization population;

[0091] Since the improved PI model has 11 parameters, each individual will contain 11 such chromosomes. The initial population size is set to 1000, that is, 1000 sets of values are randomly generated as the initial parameters of the solution space.

[0092] S22, using the fitness function to calculate the fitness of each individual in the initialized population;

[0093] In the present invention, the fitness function of the genetic algorithm is set to the inverse proportional function of the error square sum function, as follows:

[0094] Error sum of squares:

[0095] Fitness function:

[0096] Among them, y p is the theoretical output of the hysteresis model, y t is the actual output of GMA, N is the number of input data sets, F (V) is the sum of squared errors.

[0097] S23. Select a fixed number of individuals from the current population as parents according to the size of the fitness, perform crossover and mutation operations, and identify the solution parameters.

[0098] The parent generation is selected by the roulette selection method, that is, the probability of each being selected is proportional to the fitness level. The optimization goal of this invention is to find F (V) The minimum value of J (V) The larger it is, the greater the individual's fitness value is and the greater the probability of being selected.

[0099] Specifically, the steps of the crossover operation are:

[0100] S2311. Randomly select one or more crossover points between two parent individuals;

[0101] S2312. Based on the crossover point, the genes at the crossover point are exchanged according to the set probability, i.e., the crossover rate, to produce two new individuals.

[0102] S2313. Newly generated individuals are added to the population, replacing some of the existing individuals.

[0103] In the embodiment of the present invention, the real number crossover method is used to generate new individuals through linear combination, and two parent individuals b of the dth generation are selected. o (d) and c o (d) Use the following expression to calculate the d+1 generation individual b o (d+1) and c o (d+1);

[0104] c o (d+1)=b o (d)+(1-r)b o (d)

[0105] b o (d+1)=c o (d)+(1-g)c o (d); (12)

[0106] Where b and c are two individuals in the total population, r and g are random numbers in [0,1], d is the population iteration generation, d = 1, 2, ..., 1000, o is the position of the oth chromosome, o = 1, 2, ..., 11.

[0107] Specifically, the uniform mutation method is used in the mutation operation, which helps to introduce new diversity into the solution space and increase the possibility of finding a better solution. The specific steps are as follows:

[0108] S2321. Randomly select multiple individuals from the current population to perform mutation operation;

[0109] S2322. Specify certain mutation points in the gene sequence of the selected individual;

[0110] S2323. For each mutation point on the selected gene sequence, a value is randomly selected from the gene value range according to a set probability to replace the value in the original gene sequence.

[0111] The genetic algorithm parameter settings of the embodiment of the present invention are shown in Table 1.

[0112]

[0113] Table 1

[0114] Furthermore, through the above operation, 11 parameter values are finally identified, which are equivalent to 11 known constants in the subsequent identification process. Afterwards, an identification parameter c is added to the envelope function expression in (9), and formulas (4)(5)(6)(7)(8) remain unchanged.

[0115] The expression of the first envelope function is:

[0116]

[0117] Wherein, c is a temperature-related parameter. The c parameter is identified separately using the genetic algorithm in step S2. The input current and output displacement of the giant magnetostrictive actuator at different temperatures (T1, T2, T3, ...) are selected for c parameter identification. The values of the c parameter at different temperatures can be obtained. Then, a polynomial is used to fit the relational expression of the c parameter values at different temperatures. In the present invention, the nonlinear least squares method is used for fitting, and the nonlinear least squares fitting function is set as:

[0118] c(k)=p1x(k) 5 +p2x(k) 4 +p3x(k) 3 +p4x(k) 2 +p5x(k)+p6; (14)

[0119] Among them, p1, p2, p3, p4, p5, and p6 are 6 parameters to be identified, and x is the temperature change.

[0120] All the parameters that need to be identified in this embodiment of the present invention are shown in Table 2:

[0121]

[0122] Table 2

[0123] Equation (14) has expressed the temperature-dependent expression of the c parameter. Substituting it into the formula of the first envelope function, the envelope function is finally:

[0124]

[0125] Because x=(T gma -T0), x is the temperature change; (16)

[0126] Substituting Equation (16) into Equation (15) yields the envelope function of the temperature-dependent improved PI model:

[0127]

[0128] Where x is the temperature change, T gma is the surface temperature of the magnetorod, and T0 is the initial temperature.

[0129] Finally, the temperature-dependent improved PI model operator expression is:

[0130] Initial moment:

[0131]

[0132] k moment:

[0133]

[0134] The expression of the temperature model is:

[0135]

[0136] At any temperature, the input current is y = 2Sin (2Πft) + 2A (f = 8Hz) and the input and output data are selected. Here, the data when the giant magnetorots are 90 degrees is selected to verify the effect of the temperature-dependent model. The fitting results are as follows: Figure 3 , the root mean square error is 0.11208um, and the average error is 0.089671um. It can be seen that the fitting effect is very good and the temperature model is established successfully.

[0137] On the other hand, a modeling system for a temperature-dependent giant magnetostrictive actuator is provided, comprising an initial model building module, a parameter identification module, a parameter adding module, an identification module, and a modeling module; wherein,

[0138] An initial model building module is used to establish an improved PI model at the initial temperature T0;

[0139] Parameter identification module, used to identify and improve the parameters in the PI model through genetic algorithm;

[0140] A parameter adding module is used to substitute the identified parameters into the initial envelope function of the improved PI model, and add an identified parameter c on the basis of the envelope function to obtain a first envelope function;

[0141] an identification module, configured to use a genetic algorithm to select the input current and output displacement of the giant magnetostrictive actuator at different temperatures to separately identify the identification parameter c;

[0142] The modeling module is used to substitute the value of the identification parameter c into the first envelope function to obtain the expression of the temperature model and complete the modeling.

[0143] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The above examples are only intended to help understand the method and core concept of the present invention. At the same time, those skilled in the art will find that the specific implementation methods and application scopes may vary based on the concept of the present invention. In summary, the contents of this specification should not be construed as limiting the present invention.

Claims

1. A modeling method for a temperature-dependent giant magnetostrictive actuator, characterized in that: The specific steps include the following: Establish an improved PI model at the initial temperature T0; The continuous-time discretization expression of the improved PI model output is: Where m is the number of improved Play operators, N is the number of input data; r i represents the threshold of the i-th improved Play operator; r i =αi;p(r i ) is the weight of the i-th improved Play operator; is the discrete improved Play operator at the kth moment; The envelope function is expressed as: Among them, γ r (u(k))=a0u(k) 3 +a1u(k) 2 +a2u(k)+a3;γ l (u(k))=b0u(k) 3 +b1u(k) 2 +b2u(k)+b3; where a0, a1, a2, a3, b0, b1, b2, b3, α, ρ, and τ are parameters to be identified, and u(k) is the input current at the kth moment; the parameters in the improved PI model are identified by a genetic algorithm, which are equivalent to known constants in the subsequent identification process; the temperature-related parameter c(k) is added to the envelope function to obtain the first envelope function: A genetic algorithm is used to select the input current and output displacement of the giant magnetostrictive actuator at different temperatures to separately identify the temperature-related parameter c(k), and the values of c(k) at different temperatures are obtained; a nonlinear least squares fitting function is used to fit the values of c(k) at different temperatures: c(k) = p1x(k) 5 +p2x(k) 4 +p3x(k) 3 +p4x(k) 2 +p5x(k)+p6; where p1, p2, p3, p4, p5, p6 are 6 parameters to be identified, and x is the temperature change; Substitute the value of the temperature-related parameter c(k) into the first envelope function to obtain the final envelope function formula, and then replace x=(T gma -T0) is substituted into the final formula of the envelope function to obtain the envelope function of the temperature-dependent improved PI model, and the expression of the temperature model is obtained as follows: in, Improved Play operator for temperature model, k moment: Among them, T gma is the surface temperature of the magnetorod, Improve the envelope function of the PI model for temperature dependence.

2. The modeling method of a temperature-dependent giant magnetostrictive actuator according to claim 1, characterized in that: The specific steps of identifying the parameters in the improved PI model by genetic algorithm are as follows: The solution parameters are expressed as real number vectors through real number coding, and the initialization population is established; Calculating the fitness of each individual in the initialized population using a fitness function; A fixed number of individuals are selected from the current population as parents according to the size of the fitness, and crossover and mutation operations are performed to identify the solution parameters.

3. The modeling method of a temperature-dependent giant magnetostrictive actuator according to claim 2, characterized in that: The steps of the crossover operation are: Among the two parent individuals, one or more crossover points are randomly selected; Based on the crossover point, the genes in the crossover point are exchanged according to the set probability, that is, the crossover rate, to produce two new individuals; Newly generated individuals are added to the population, replacing some of the existing individuals.

4. A modeling system for a temperature-dependent giant magnetostrictive actuator, characterized in that: It includes initial model building module, parameter identification module, parameter adding module, identification module and modeling module; among them, The initial model building module is used to establish an improved PI model at an initial temperature T0; The continuous-time discretization expression of the improved PI model output is: Where m is the number of improved Play operators, N is the number of input data; r i represents the threshold of the i-th improved Play operator; r i =αi;p(r i ) is the weight of the i-th improved Play operator; is the discrete improved Play operator at the kth moment; The envelope function is expressed as: Among them, γ r (u(k))=a0u(k) 3 +a1u(k) 2 +a2u(k)+a3;γ l (u(k))=b0u(k) 3 +b1u(k) 2 +b2u(k)+b3; wherein a0, a1, a2, a3, b0, b1, b2, b3, α, ρ, τ are parameters to be identified, and u(k) is the input current at the kth moment; the parameter identification module is used to identify the parameters in the improved PI model through a genetic algorithm, which is equivalent to a known constant in the subsequent identification process; The parameter adding module is used to add the temperature-related parameter c(k) to the envelope function to obtain a first envelope function: The identification module is used to use a genetic algorithm to select the input current and output displacement of the giant magnetostrictive actuator at different temperatures to separately identify the temperature-related parameter c(k), thereby obtaining the values of c(k) at different temperatures; and to fit the values of c(k) at different temperatures using a nonlinear least squares fitting function: c(k) = p1x(k) 5 +p2x(k) 4 +p3x(k) 3 +p4x(k) 2 +p5x(k)+p6; where p1, p2, p3, p4, p5, p6 are 6 parameters to be identified, and x is the temperature change; The modeling module is used to substitute the value of the temperature-related parameter c(k) into the first envelope function to obtain the final formula of the envelope function, and then replace x=(T gma -T0) is substituted into the final formula of the envelope function to obtain the envelope function of the temperature-dependent improved PI model, and the expression of the temperature model is obtained as follows: in, Improved Play operator for temperature model, k moment: Among them, T gma is the surface temperature of the magnetorod, Improve the envelope function of the PI model for temperature dependence.

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