Comprehensive dynamics nonlinear modeling method for magnetic control shape memory alloy actuator

Abstract

The invention discloses a comprehensive dynamics nonlinear modeling method of a magnetic control shape memory alloy actuator, and relates to the field of nonlinear modeling of intelligent materials and driving mechanisms thereof. According to the method, a constitutive model and a redirection model of the alloy are established, a kinetic model is established according to mechanical characteristics of a magnetic control shape memory alloy actuator, and an MFCPI hysteresis model is established according to hysteresis characteristics of the alloy actuator. On the basis of models established for different characteristics of the magnetic control shape memory alloy actuator, a mathematical expression of a comprehensive dynamic nonlinear model of a magnetic control shape memory alloy actuator system is obtained, so that the relationship between physical quantities and model parameters of the actuator system is defined; therefore, high-precision modeling of the magnetic control shape memory alloy actuator system is realized. According to the method, a foundation is laid for high-quality modeling and control application of the magnetic control shape memory alloy actuator, the method is closer to engineering requirements, and technical development and wide application of the alloy actuator in the field of micro-positioning can be promoted.

Description

Technical Field

[0001] The present invention relates to the field of nonlinear modeling of smart materials and driving mechanisms thereof, and in particular to a comprehensive dynamic nonlinear modeling method of a magnetically controlled shape memory alloy actuator. Background Art

[0002] Magnetic shape memory alloy actuators represent a class of precision actuators driven by smart materials. Due to their advantages of large travel and strong active and passive deformation capabilities, they have great application potential in the fields of ultra-precision machining and medical devices. Therefore, system modeling of magnetic shape memory alloy actuators is a necessary basis for controller design and engineering application of the actuators. However, there is hysteresis nonlinearity between the input and output of magnetic shape memory alloy actuators. This nonlinear behavior has complex characteristics such as frequency dependence, load dependence, asymmetry and strong saturation, which brings certain challenges to the modeling and control of actuators.

[0003] For precision motion systems such as magnetically controlled shape memory alloy actuators, when designing advanced intelligent control frameworks for them, it is necessary to accurately reflect the dynamic model of the actuator. At present, the modeling methods of magnetically controlled shape memory alloy actuators mainly include Prandtl-Ishlinskii (PI) model, Duhem model, NARMAX model and neural network model. However, it should be noted that for operator models such as PI model and differential equation models such as Duhem model, according to their modeling principles, these two types of models can only describe the hysteresis nonlinearity of magnetically controlled shape memory alloy actuators, and cannot characterize the dynamic behavior of the entire actuator system. As for NARMAX model and neural network model, the establishment of these two types of models is based on the measured input and output data of the actuator. Although the system output of the actuator can be fitted with high precision, the change mechanism of the magnetically controlled shape memory alloy inside the actuator system under the action of the magnetic field and the mechanical characteristics of the actuator system cannot be described by these two types of models.

[0004] In summary, there is a gap in the existing technology in the modeling method of the entire system dynamic behavior of the magnetically controlled shape memory alloy actuator, so research in this area is needed. Summary of the invention

[0005] In order to solve the problem that the prior art does not take into account the dynamic behavior of the overall system of the magnetically controlled shape memory alloy actuator, cannot provide the relationship between the internal physical quantities of the actuator system and the model parameters, and thus cannot accurately reflect the characteristics of the controlled object, the present invention provides a comprehensive dynamic nonlinear modeling method for the magnetically controlled shape memory alloy actuator.

[0006] The present invention is realized by the following technical scheme: a comprehensive dynamic nonlinear modeling method of a magnetically controlled shape memory alloy actuator, comprising the following steps:

[0007] S1: Based on the interaction between stress and strain of magnetically controlled shape memory alloy under the action of magnetic field, a constitutive model of magnetically controlled shape memory alloy is established to reveal the relationship between magnetic field, stress and strain; the details are as follows:

[0008] The established constitutive model of magnetically controlled shape memory alloy is shown in formula (1):

[0009]

[0010] Among them, σ, χ and are the stress, strain and magnetic field to which the magnetic shape memory alloy is subjected; ε is the Young's modulus of the magnetic shape memory alloy; Ω is the transformation tensor; Ψ is a function related to the magnetostrictive properties of the magnetic shape memory alloy; ζ is the martensite fraction.

[0011] S2: Based on the physical properties of martensite variants in magnetically controlled shape memory alloys, a reorientation model is established for magnetically controlled shape memory alloys; the details are as follows:

[0012] Since the system output of the magnetically controlled shape memory alloy actuator is different under different external loads, it means that the model parameters obtained under different loads are different. Therefore, the physical properties of the martensite variant in the magnetically controlled shape memory alloy will be affected by the combined effects of stress and magnetic field, so the reorientation model of the magnetically controlled shape memory alloy is described as:

[0013]

[0014] in, and σ are the volume fractions of magnetic field preferred martensite and stress preferred martensite, respectively; the value of ζ is determined according to the thermodynamic driving force and the volume fraction of martensite variants;

[0015] In the reorientation model, the external magnetic field causes ζ σ Reduce while This deformation process is caused by the twin boundary movement between martensite variants in the magnetically controlled shape memory alloy. and σ Must meet Therefore, formula (2) is rewritten as:

[0016]

[0017] S3: According to the mechanical characteristics of the magnetically controlled shape memory alloy actuator, a dynamic model is constructed for it; the details are as follows:

[0018] The mechanical characteristics of the magnetically controlled shape memory alloy actuator are described as a mass-damper-spring model, which is obtained according to Newton's laws of motion:

[0019]

[0020] in, a c is the cross-sectional area of ​​the magnetically controlled shape memory alloy; is the conversion force; a m ,a d ,a s are the mass, damping coefficient and stiffness coefficient in the mass-damper-spring model respectively; yes The initial value of .

[0021] S4: Analyze the hysteresis nonlinearity of magnetically controlled shape memory alloy actuators and establish a multi-factor coupling Prandtl–Ishlinskii model (MFCPI), namely the MFCPI model; the details are as follows:

[0022] In order to describe the hysteresis nonlinearity, the expression of the PI model used in the existing method is as follows:

[0023]

[0024] in, is the output of the hysteresis model; m is the number of Play operators; b(ξ) is a density function used to characterize the influence of each operator on the shape of the hysteresis loop; ξ is the threshold of the PI model; is the Play operator, and its mathematical expression is as follows:

[0025]

[0026] Among them, the time interval [0,t M ] is divided into M parts, and 0 = t0 < t1 < ... < t m ; In each subinterval [t p ,t p+1 ], the input signal v(t) satisfies monotonicity;

[0027] Since the hysteresis nonlinearity of the magnetically controlled shape memory alloy actuator has strong saturation, asymmetry, frequency-related and load-related characteristics, the PI model described in equation (5) cannot effectively describe the hysteresis characteristics of the magnetically controlled shape memory alloy actuator. In the present invention, in order to accurately describe the hysteresis nonlinearity of the magnetically controlled shape memory alloy actuator, a dynamic threshold is designed. and the envelope function η l ,ηr Specifically, since the hysteresis nonlinearity of the magnetically controlled shape memory alloy actuator is affected by the excitation signal frequency and external load, the dynamic threshold The design is as follows:

[0028]

[0029] in, is a frequency-dependent function; γ2=α3exp(-μ m ) is a load-related function; α1, α2, α3 are positive design parameters; μ m is the mass of the external load applied to the magnetically controlled shape memory alloy actuator;

[0030] Since the hysteresis nonlinearity of the magnetically controlled shape memory alloy actuator also has the characteristics of asymmetry and strong saturation, the nonlinear envelope function is defined as:

[0031]

[0032] Among them, η l (v),η r (v) is a strictly continuous and monotonically increasing function; c0>0, c1>0, c2, d0>0, d1>0, d2 are the model parameters to be identified;

[0033] Considering that the output displacement of the magnetically controlled shape memory alloy actuator is a positive number, the value range of the Play operator is Combining equations (7) and (8), the proposed dynamic Play operator The mathematical expression is:

[0034]

[0035] The MFCPI model is composed of the superposition of dynamic Play operators, and its mathematical expression is as follows:

[0036]

[0037] S5: Based on the models established for different characteristics of the magnetically controlled shape memory alloy actuator in steps S1-S4, a mathematical expression of the comprehensive dynamic nonlinear model of the magnetically controlled shape memory alloy actuator system is obtained to clarify the relationship between the physical quantities of the actuator system and the model parameters, so as to achieve high-precision modeling of the magnetically controlled shape memory alloy actuator system. The details are as follows:

[0038] During the operation of the magnetically controlled shape memory alloy actuator, when current v is applied to the coil, a magnetic field is generated. Therefore, for an external magnetic field use To describe, is a function used to describe electromagnetic transformation;

[0039] Considering the strain rate and the initial length r of the magnetically controlled shape memory alloy satisfies Combining equation (1) and equation (3), we can get:

[0040]

[0041] The three variables l, and σ is defined as:

[0042]

[0043] According to the definition in formula (12), combined with formulas (4), (10) and (11), the comprehensive dynamic nonlinear model of the magnetically controlled shape memory alloy actuator is established as follows:

[0044]

[0045] in, is the hysteresis nonlinearity, which is described by the MFCPI model established by formula (10).

[0046] Based on the models established for different characteristics of the magnetically controlled shape memory alloy actuator in steps S1-S4, the mathematical expression of the comprehensive dynamic nonlinear model of the magnetically controlled shape memory alloy actuator system as shown in formula (13) is finally obtained. The comprehensive dynamic model established in the present invention can clarify the relationship between the physical quantities and model parameters of the actuator system, laying the foundation for realizing high-precision modeling of the magnetically controlled shape memory alloy actuator system.

[0047] Compared with the prior art, the present invention has the following beneficial effects: the comprehensive dynamic nonlinear modeling method of a magnetically controlled shape memory alloy actuator provided by the present invention provides a comprehensive dynamic nonlinear model form that fully describes the magnetically controlled shape memory alloy actuator system, and has the following three advantages: First, by analyzing the physical properties of the magnetically controlled shape memory alloy under the action of a magnetic field, a constitutive model and a redirection model are constructed for the alloy. The constructed model clarifies the relationship between the external magnetic field and the physical changes inside the alloy, and explicitly characterizes the internal physical properties of the alloy using the tool of mathematical expressions. Second, the present invention designs a dynamic Play operator that can represent frequency-related and load-related characteristics for the complex hysteresis nonlinearity of the magnetically controlled shape memory alloy actuator, and constructs an MFCPI model in combination with a nonlinear envelope function. The constructed MFCPI model makes up for the deficiency that the existing PI model cannot describe the load-related hysteresis nonlinearity. Third, based on the physical properties of the alloy, the mechanical properties of the system and the hysteresis characteristics, the present invention derives a comprehensive dynamic nonlinear model of the magnetically controlled shape memory alloy actuator, which fully describes the dynamic characteristics of the actuator system in the form of a third-order differential equation. The method of the present invention lays a foundation for high-quality modeling and control applications of magnetically controlled shape memory alloy actuators and is closer to engineering needs. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 It is a schematic diagram of the comprehensive dynamic nonlinear modeling method of the magnetically controlled shape memory alloy actuator of the present invention.

[0049] Figure 2 It is a schematic diagram of frequency-dependent and load-dependent dynamic Play operators of the MFCPI hysteresis model constructed by the present invention under different frequencies and different loads.

[0050] Figure 3 It is a schematic diagram of an experimental device of the magnetically controlled shape memory alloy actuator of the present invention.

[0051] Figure 4 It is a schematic diagram of the principle of the experimental device of the magnetically controlled shape memory alloy actuator of the present invention.

[0052] Figure 5 It is a comparison diagram of the model output curve of the present invention with a 0.5 Hz sinusoidal signal input under no-load condition and the actual output curve of the actuator.

[0053] Figure 6 It is an error diagram of the model output curve of the present invention with a 0.5 Hz sinusoidal signal input under no-load condition and the actual output of the actuator.

[0054] Figure 7 It is a comparison diagram of the model output curve of the present invention with a 2 Hz sinusoidal signal input under no-load condition and the actual output curve of the actuator.

[0055] Figure 8 It is an error diagram of the model output curve of the present invention with a 2 Hz sinusoidal signal as input and the actual output of the actuator under no-load condition.

[0056] Fig. 9 It is a comparison diagram of the model output curve of the present invention with a 1 Hz sinusoidal signal input under load (100 g) and the actual output curve of the actuator.

[0057] Fig.10 It is an error diagram of the model output curve of the present invention with a 1 Hz sinusoidal signal input under load (200 g) and the actual output of the actuator.

[0058] Fig.11 It is a comparison diagram of the model output curve of the present invention with a 1 Hz sinusoidal signal input under load (200 g) and the actual output curve of the actuator.

[0059] Fig.12 It is an error diagram of the model output curve of the present invention with a 1 Hz sinusoidal signal input under load (200 g) and the actual output of the actuator. DETAILED DESCRIPTION

[0060] The present invention is further described below in conjunction with specific embodiments.

[0061] A comprehensive dynamic nonlinear modeling method for magnetically controlled shape memory alloy actuators, such as Figure 1 As shown, the following steps are included:

[0062] S1: Based on the interaction between stress and strain of magnetically controlled shape memory alloy under the action of magnetic field, a constitutive model of magnetically controlled shape memory alloy is established to reveal the relationship between magnetic field, stress and strain; the details are as follows:

[0063] The established constitutive model of magnetically controlled shape memory alloy is shown in formula (1):

[0064]

[0065] Among them, σ, χ and are the stress, strain and magnetic field to which the magnetic shape memory alloy is subjected; ε is the Young's modulus of the magnetic shape memory alloy; Ω is the transformation tensor; Ψ is a function related to the magnetostrictive properties of the magnetic shape memory alloy; ζ is the martensite fraction.

[0066] S2: Based on the physical properties of martensite variants in magnetically controlled shape memory alloys, a reorientation model is established for magnetically controlled shape memory alloys; the details are as follows:

[0067] Since the system output of the magnetically controlled shape memory alloy actuator is different under different external loads, it means that the model parameters obtained under different loads are different. Therefore, the physical properties of the martensite variant in the magnetically controlled shape memory alloy will be affected by the combined effects of stress and magnetic field, so the reorientation model of the magnetically controlled shape memory alloy is described as:

[0068]

[0069] in, and σ are the volume fractions of magnetic field preferred martensite and stress preferred martensite, respectively; the value of ζ is determined according to the thermodynamic driving force and the volume fraction of martensite variants;

[0070] In the reorientation model, the external magnetic field causes ζ σ Reduce while This deformation process is caused by the twin boundary movement between martensite variants in the magnetically controlled shape memory alloy. and σ Must meet Therefore, formula (2) is rewritten as:

[0071]

[0072] S3: According to the mechanical characteristics of the magnetically controlled shape memory alloy actuator, a dynamic model is constructed for it; the details are as follows:

[0073] The mechanical characteristics of the magnetically controlled shape memory alloy actuator are described as a mass-damper-spring model, which is obtained according to Newton's laws of motion:

[0074]

[0075] in, a c is the cross-sectional area of ​​the magnetically controlled shape memory alloy; is the conversion force; a m ,a d ,a s are the mass, damping coefficient and stiffness coefficient in the mass-damper-spring model respectively; yes The initial value of .

[0076] S4: Analyze the hysteresis nonlinearity of magnetically controlled shape memory alloy actuators and establish a multi-factor coupled Prandtl–Ishlinskii model, namely the MFCPI model; the details are as follows:

[0077] In order to describe the hysteresis nonlinearity, the expression of the PI model used in the existing method is as follows:

[0078]

[0079] in, is the output of the hysteresis model; m is the number of Play operators; b(ξ) is a density function used to characterize the influence of each operator on the shape of the hysteresis loop; ξ is the threshold of the PI model; is the Play operator, and its mathematical expression is as follows:

[0080]

[0081] Among them, the time interval [0,t M ] is divided into M parts, and 0 = t0 < t1 < ... < t m ; In each subinterval [t p ,t p+1 ], the input signal v(t) satisfies monotonicity;

[0082] Since the hysteresis nonlinearity of the magnetically controlled shape memory alloy actuator has strong saturation, asymmetry, frequency-related and load-related characteristics, the PI model described in equation (5) cannot effectively describe the hysteresis characteristics of the magnetically controlled shape memory alloy actuator. In the present invention, in order to accurately describe the hysteresis nonlinearity of the magnetically controlled shape memory alloy actuator, a dynamic threshold is designed. and the envelope function η l ,η r Specifically, since the hysteresis nonlinearity of the magnetically controlled shape memory alloy actuator is affected by the excitation signal frequency and external load, the dynamic threshold The design is as follows:

[0083]

[0084] in, is a frequency-dependent function; γ2=α3exp(-μ m ) is a load-related function; α1, α2, α3 are positive design parameters; μ m is the mass of the external load applied to the magnetically controlled shape memory alloy actuator;

[0085] Since the hysteresis nonlinearity of the magnetically controlled shape memory alloy actuator also has the characteristics of asymmetry and strong saturation, the nonlinear envelope function is defined as:

[0086]

[0087] Among them, η l (v),η r (v) is a strictly continuous and monotonically increasing function; c0>0, c1>0, c2, d0>0, d1>0, d2 are the model parameters to be identified;

[0088] Considering that the output displacement of the magnetically controlled shape memory alloy actuator is a positive number, the value range of the Play operator is Combining equations (7) and (8), the proposed dynamic Play operator The mathematical expression of is as follows, and the operator diagram is as follows Figure 2 As shown:

[0089]

[0090] The MFCPI model is composed of the superposition of dynamic Play operators, and its mathematical expression is as follows:

[0091]

[0092] S5: Based on the models established for different characteristics of the magnetically controlled shape memory alloy actuator in steps S1-S4, a mathematical expression of the comprehensive dynamic nonlinear model of the magnetically controlled shape memory alloy actuator system is obtained to clarify the relationship between the physical quantities of the actuator system and the model parameters, so as to achieve high-precision modeling of the magnetically controlled shape memory alloy actuator system. The details are as follows:

[0093] During the operation of the magnetically controlled shape memory alloy actuator, when current v is applied to the coil, a magnetic field is generated. Therefore, for an external magnetic field use To describe, is a function used to describe electromagnetic transformation;

[0094] Considering the strain rate and the initial length r of the magnetically controlled shape memory alloy satisfies Combining equation (1) and equation (3), we can get:

[0095]

[0096] The three variables l, and σ is defined as:

[0097]

[0098] According to the definition in formula (12), combined with formulas (4), (10) and (11), the comprehensive dynamic nonlinear model of the magnetically controlled shape memory alloy actuator is established as follows:

[0099]

[0100] in, is the hysteresis nonlinearity, which is described by the MFCPI model established by formula (10).

[0101] The following specific examples verify the beneficial effects of the above method.

[0102] Example 1: Taking the magnetically controlled shape memory alloy actuator system as an example, the comprehensive dynamic nonlinear modeling method constructed by the present invention is used to analyze the magnetically controlled shape memory alloy actuator system under no-load conditions. Figure 3 The experimental platform shown is modeled to verify the effectiveness of the proposed method.

[0103] ① Experimental platform: Figure 3 The experimental platform shown in the figure is used to verify the effectiveness of the modeling method. The working principle diagram of the experimental platform based on magnetically controlled shape memory alloy actuator is shown in Figure 4 As shown. The hardware facilities of the experimental platform include computers, data acquisition cards, power supplies, linear displacement sensors, magnetically controlled shape memory alloy actuators and vibration isolation tables. The computer is equipped with Matlab / Simulink software, which gives the current signal used to drive the magnetically controlled shape memory alloy actuator. This signal is converted by D / A in the data acquisition card, input to the power supply, and processed by the power supply to give an analog signal to drive the actuator to move. The actuator generates an output displacement under the action of the driving signal. The displacement is measured by a linear displacement sensor, and after A / D conversion by the data acquisition card, it is transmitted back to the computer for data analysis and processing.

[0104] ② Set the driving signal and model parameters: Select sinusoidal signals with the same amplitude and different frequencies (0.5 Hz and 2 Hz, respectively) as the signal to drive the magnetically controlled shape memory alloy actuator, and set the sampling frequency to 10 kHz. The identified model parameters are:

[0105] b0=0.9204, b1=0.0641, b2=0.9278, b3=0.0482, b4=0.6284, b5=0.9063, b6=0.7161,

[0106] b7=0.9254,b8=0.4790,b9=0.0241,b 10 =0.8001,b 11 =0.0740, α1=0.5178, α2=0.2666,

[0107] α3=0.5860, c0=0.5852, c1=0.4715, c2=0.0222, d0=0.6915, d1=0.4486, d2=0.0219

[0108] The modeling results of the modeling method of the present invention obtained by experiment are as follows Figure 5-Figure 8 As shown. Figure 5 It can be seen that the model output curve constructed by the present invention can well fit the actual output curve of the actuator. Figure 5Subtracting the model output and the actual output shown gives Figure 6 The modeling error curve is shown in Figure 2. Figure 6 It can be seen that when the driving signal is a 0.5 Hz sinusoidal signal, the modeling error of the proposed model is between [-12, 40] μm, which is 3% to 10% of the actual output of the actuator. Figure 7 and Figure 8 They are the comparison diagram of the model output curve and the actual output curve of the actuator when the driving signal is a 2Hz sinusoidal signal, and the error diagram between the output curve and the actual output of the actuator. Figure 7 High-precision fitting of the model curve and the actual output curve Figure 8 The error curve in can also prove the effectiveness of the proposed model.

[0109] Example 2: Taking the magnetically controlled shape memory alloy actuator system as an example, the comprehensive dynamic nonlinear modeling method constructed by the present invention is used to analyze the Figure 3 The experimental platform shown is modeled to verify the effectiveness of the proposed method. The driving signal is set to a sinusoidal signal with the same amplitude and frequency (frequency is 1 Hz) to drive the magnetically controlled shape memory alloy actuator under 100g and 200g load conditions. Other settings are the same as in Example 1.

[0110] Under different loads, the modeling results of the modeling method of the present invention obtained through experiments are as follows: Figure 9-12 As shown. Fig. 9 and 11 It can be seen that under the load of 100g and 200g, the output curve of the model constructed by the present invention can well fit the actual output curve of the actuator. Fig. 9 and Fig.11 Subtracting the model output and the actual output shown gives Fig.10 and Fig.12 The modeling error curve is shown in FIG. It can be seen from the error curve that under the influence of the load, the maximum output displacement and hysteresis characteristics of the magnetically controlled shape memory alloy actuator have changed, and the modeling method described in the present invention can well fit the measured output under different loads under the action of the dynamic Play operator, and the modeling error can be maintained at about [-20,12] μm, which verifies the effectiveness of the proposed model.

[0111] The scope of protection claimed by the present invention is not limited to the above specific embodiments. For those skilled in the art, the present invention may have various deformations and changes. Any modifications, improvements and equivalent substitutions made within the concept and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A comprehensive dynamic nonlinear modeling method for a magnetically controlled shape memory alloy actuator, characterized in that: The steps include: S1: Based on the interaction between stress and strain of magnetically controlled shape memory alloy under the action of magnetic field, a constitutive model of magnetically controlled shape memory alloy is established to reveal the relationship between magnetic field, stress and strain; S2: Based on the physical properties of martensite variants in magnetically controlled shape memory alloys, a reorientation model is established for magnetically controlled shape memory alloys; S3: Construct a dynamic model for the magnetically controlled shape memory alloy actuator based on its mechanical characteristics; S4: Analyze the hysteresis nonlinearity of magnetically controlled shape memory alloy actuators and establish a multi-factor coupled Prandtl–Ishlinskii model, namely the MFCPI model; S5: Based on the models established for different characteristics of the magnetically controlled shape memory alloy actuator in steps S1-S4, a mathematical expression of a comprehensive dynamic nonlinear model of the magnetically controlled shape memory alloy actuator system is obtained to clarify the relationship between the physical quantities of the actuator system and the model parameters, so as to achieve high-precision modeling of the magnetically controlled shape memory alloy actuator system.

2. The comprehensive dynamic nonlinear modeling method of a magnetically controlled shape memory alloy actuator according to claim 1, characterized in that: Step S1 is specifically as follows: The established constitutive model of magnetically controlled shape memory alloy is shown in formula (1): Among them, σ, χ and are the stress, strain and magnetic field to which the magnetic shape memory alloy is subjected; ε is the Young's modulus of the magnetic shape memory alloy; Ω is the transformation tensor; Ψ is a function related to the magnetostrictive properties of the magnetic shape memory alloy; ζ is the martensite fraction.

3. The comprehensive dynamic nonlinear modeling method of a magnetically controlled shape memory alloy actuator according to claim 2, characterized in that: Step S2 is specifically as follows: Since the system output of the magnetically controlled shape memory alloy actuator is different under different external loads, it means that the model parameters obtained under different loads are different. Therefore, the physical properties of the martensite variant in the magnetically controlled shape memory alloy will be affected by the combined effects of stress and magnetic field, so the reorientation model of the magnetically controlled shape memory alloy is described as: in, and σ are the volume fractions of magnetic field preferred martensite and stress preferred martensite, respectively; the value of ζ is determined according to the thermodynamic driving force and the volume fraction of martensite variants; In the reorientation model, the external magnetic field causes ζ σ Reduce while This deformation process is caused by the twin boundary movement between martensite variants in the magnetically controlled shape memory alloy. and σ Must meet Therefore, formula (2) is rewritten as:

4. The comprehensive dynamic nonlinear modeling method of a magnetically controlled shape memory alloy actuator according to claim 3, characterized in that: Step S3 is as follows: The mechanical characteristics of the magnetically controlled shape memory alloy actuator are described as a mass-damper-spring model, which is obtained according to Newton's laws of motion: in, a c is the cross-sectional area of ​​the magnetically controlled shape memory alloy; is the conversion force; a m ,a d ,a s are the mass, damping coefficient and stiffness coefficient in the mass-damper-spring model respectively; yes The initial value of .

5. The comprehensive dynamic nonlinear modeling method of a magnetically controlled shape memory alloy actuator according to claim 4, characterized in that: Step S4 is specifically as follows: In order to describe the hysteresis nonlinearity, the expression of the PI model used in the existing method is as follows: in, is the output of the hysteresis model; m is the number of Play operators; b(ξ) is a density function used to characterize the influence of each operator on the shape of the hysteresis loop; ξ is the threshold of the PI model; is the Play operator, and its mathematical expression is as follows: Among them, the time interval [0,t M ] is divided into M parts, and 0 = t0 < t1 < ... < t m ; In each subinterval [t p ,t p+1 ], the input signal v(t) satisfies monotonicity; Since the hysteresis nonlinearity of the magnetically controlled shape memory alloy actuator has strong saturation, asymmetry, frequency-dependent and load-dependent characteristics, the PI model described in equation (5) cannot effectively describe the hysteresis characteristics of the magnetically controlled shape memory alloy actuator. In order to accurately describe the hysteresis nonlinearity of the magnetically controlled shape memory alloy actuator, a dynamic threshold is designed. and the envelope function η l ,η r Specifically, since the hysteresis nonlinearity of the magnetically controlled shape memory alloy actuator is affected by the excitation signal frequency and external load, the dynamic threshold The design is as follows: in, is a frequency-dependent function; γ2=α3exp(-μ m ) is a load-related function; α1, α2, α3 are positive design parameters; μ m is the mass of the external load applied to the magnetically controlled shape memory alloy actuator; Since the hysteresis nonlinearity of the magnetically controlled shape memory alloy actuator also has the characteristics of asymmetry and strong saturation, the nonlinear envelope function is defined as: Among them, η l (v),η r (v) is a strictly continuous and monotonically increasing function; c0>0, c1>0, c2, d0>0, d1>0, d2 are the model parameters to be identified; Considering that the output displacement of the magnetically controlled shape memory alloy actuator is a positive number, the value range of the Play operator is Combining equations (7) and (8), the proposed dynamic Play operator The mathematical expression is: The MFCPI model is composed of the superposition of dynamic Play operators, and its mathematical expression is as follows:

6. The comprehensive dynamic nonlinear modeling method of a magnetically controlled shape memory alloy actuator according to claim 5, characterized in that: Step S5 is specifically as follows: During the operation of the magnetically controlled shape memory alloy actuator, when current v is applied to the coil, a magnetic field is generated. Therefore, for an external magnetic field use To describe, is a function used to describe electromagnetic transformation; Considering the strain rate and the initial length r of the magnetically controlled shape memory alloy satisfies Combining equation (1) and equation (3), we can get: The three variables l, and σ is defined as: According to the definition in formula (12), combined with formulas (4), (10) and (11), the comprehensive dynamic nonlinear model of the magnetically controlled shape memory alloy actuator is established as follows: in, is the hysteresis nonlinearity, which is described by the MFCPI model established by formula (10).

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