CN111897212A - Multi-model combined modeling method of magnetic control shape memory alloy actuator - Google Patents

Multi-model combined modeling method of magnetic control shape memory alloy actuator Download PDF

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CN111897212A
CN111897212A CN202010516434.2A CN202010516434A CN111897212A CN 111897212 A CN111897212 A CN 111897212A CN 202010516434 A CN202010516434 A CN 202010516434A CN 111897212 A CN111897212 A CN 111897212A
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narmax
shape memory
memory alloy
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周淼磊
于业伟
徐瑞
张晨
高巍
韩志武
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Jilin University
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Abstract

A multi-model combined modeling method of a magnetic control shape memory alloy actuator belongs to the technical field of control. The invention aims to construct an NARMAX structure model, which can improve the capability of describing multi-value mapping hysteresis by the NARMAX model and simultaneously enable a Bouc-wen model to describe highly asymmetric hysteresis to become a possible multi-model combined modeling method for the magnetic control shape memory alloy actuator. The method comprises the following steps: establishing an NARMAX structural model capable of describing the multi-value mapping hysteresis of the magnetic control shape memory alloy actuator; an unknown nonlinear function of the NARMAX structure model is built by utilizing a wavelet neural network, and the NARMAX structure model which can update model parameters on line and adapt to the complex dynamic hysteresis characteristics of the magnetic control shape memory alloy actuator is built. The invention effectively promotes the application of the intelligent material actuating mechanism in the high-precision manufacturing industry, and can adjust the model parameters on line to adapt to the complex dynamic hysteresis characteristic of the magnetic control shape memory alloy actuator.

Description

Multi-model combined modeling method of magnetic control shape memory alloy actuator
Technical Field
The invention belongs to the technical field of control.
Background
Because of the advantages of generating huge macroscopic strain and shape memory effect and the like under the action of a magnetic field, the actuator taking the magnetic control shape memory alloy material as a core device has wide application value and prospect in the field of micro-nano technology. However, due to the inherent complex hysteresis nonlinearity of the magnetic shape memory alloy material, the further application of the magnetic shape memory alloy actuator in the field of high-precision positioning is seriously influenced. Compared with the traditional intelligent material actuator, such as a piezoelectric ceramic actuator and a giant magnetostrictive actuator, the hysteresis loop of the magnetic control shape memory alloy actuator has the characteristics of high saturation and strong asymmetry, and the shape of the hysteresis loop can change along with the change of the amplitude, the frequency and the waveform of an input signal of the actuator. In addition, temperature is also an important factor affecting the shape of the hysteresis ring. Therefore, the hysteresis nonlinear modeling of the magnetron shape memory alloy actuator is a very challenging task and is receiving more and more attention.
At present, models for describing the hysteresis nonlinearity of the magnetron shape memory alloy actuator are mainly classified into phenomenological models such as KP model, PI model, Bouc-wen model and phenomenological models such as Jiles-Atherton model. The model can effectively describe the hysteresis nonlinearity of the magnetic control shape memory alloy actuator, but has the defects of complex calculation process, low modeling precision, incapability of adapting to the dynamic change of a system and the like. The NARMAX model is a nonlinear black box model and has good description capability on complex nonlinear systems. In order to enable the NARMAX model to better describe the hysteresis nonlinearity of the magnetic control shape memory alloy actuator with multi-value mapping, introducing an exogenous variable function is an effective method. The Bocu-Wen model is a commonly used hysteresis model due to its simple structure, and by selecting different model parameters, the Bocu-Wen model can describe different hysteresis characteristics. However, the conventional Bouc-Wen model cannot describe highly asymmetric hysteresis, and therefore is difficult to use to describe the hysteresis exhibited by a magnetically controlled shape memory alloy actuator.
Disclosure of Invention
The invention aims to introduce the entire Bouc-wen model as an exogenous variable function into an NARMAX model to construct an NARMAX structure model, so that the capability of the NARMAX model in describing multi-value mapping hysteresis can be improved, and the Bouc-wen model can be a multi-model combined modeling method of a magnetic control shape memory alloy actuator capable of describing highly asymmetric hysteresis.
The method comprises the following steps:
step 1: a multi-model combined modeling method for introducing a Bouc-wen model into an NARMAX model as an exogenous variable is provided, and an NARMAX structure model capable of describing the multi-value mapping hysteresis of the magnetic control shape memory alloy actuator is established;
the NARMAX structural model expression with exogenous variables is as follows:
Figure BDA0002530301430000011
where k is the discrete time of the system, N is an unknown nonlinear function, y*(k) And h (k-1) represents the output value and the exogenous variable of the NARMAX structure model, respectively, v (k-1) and y (k-1) represent the input and output values of the magnetically controlled shape memory alloy actuator, respectively,
Figure BDA0002530301430000013
nv、nhand nyDenotes the memory delay of v, h and y, respectively, p ═ nv+nh+nyFor the total delay of the system, an exogenous variable h is represented by a Bouc-wen model, and a function expression of the Bouc-wen model is as follows:
Figure BDA0002530301430000012
wherein,
Figure BDA0002530301430000021
representing the derivative with time, alpha, beta, gamma and d are parameters of the Bouc-wen model;
for convenience, the NARMAX structural model is adapted to polynomial form, the expression being as follows:
Figure BDA0002530301430000022
wherein, theta is a polynomial coefficient,
Figure BDA0002530301430000023
is the i-th of the model input xpThe value of the input to the term,
Figure BDA0002530301430000029
a matrix term formed by coefficients, q is a model order, and n is (p + q)! P! q! -1 is the total number of terms,
Figure BDA0002530301430000025
is an autoregressive moving average term
Step 2: an unknown nonlinear function of the NARMAX structure model is built by utilizing a wavelet neural network, and the NARMAX structure model which can update model parameters on line and adapt to the complex dynamic hysteresis characteristics of the magnetic control shape memory alloy actuator is built;
the expression of the wavelet neural network is as follows:
Figure BDA0002530301430000026
wherein O (k) is the output value of the wavelet neural network, omegaijThe weight value of the connection between the ith neuron of the input layer and the jth neuron of the hidden layer, omegajThe weight value, eta, of the connection between the jth neuron of the hidden layer and the neuron of the output layeriThe input quantity of the ith neuron of the input layer, m and n are the numbers of the neurons of the input layer and the hidden layer respectively, ajAnd bjRespectively representing the scaling and translation parameters of the wavelet function of the jth neuron of the hidden layer,
Figure BDA0002530301430000027
for the Morlet wavelet function, the expression is as follows:
Figure BDA0002530301430000028
the method comprises the steps that I is an input value of a wavelet function, e is a constant, when a wavelet neural network is adopted to construct a nonlinear function of an NARMAX structure model, the input quantity of the neural network is an autoregressive moving average term of the NARMAX structure model, the calculation complexity and the modeling precision are comprehensively considered, the number of neurons in a hidden layer is selected to be 7, the number of neurons in an output layer is 1, the initial weight of the neural network is set to be a random value from 0 to 1, and a gradient descent method is adopted in an optimization algorithm.
The hysteresis model of the magnetic control shape memory alloy actuator, which is established by a multi-model combined modeling method, overcomes the defects of the traditional single model in describing the hysteresis nonlinearity of the magnetic control shape memory alloy actuator, provides a new idea for the modeling of a complex nonlinear system, and can effectively promote the application of an intelligent material actuator in the high-precision manufacturing industry. Aiming at the defects of the traditional single model in describing the hysteresis nonlinearity of the magnetic control shape memory alloy actuator, the invention provides a combined modeling method for establishing an NARMAX structural model by combining an NARMAX model and a Bouc-wen model, and a wavelet neural network is adopted to construct a nonlinear function of the NARMAX structural model. The established NARMAX structure model combines the advantages of the NARMAX model and the Bouc-wen model, and the model parameters can be adjusted on line to adapt to the complex dynamic hysteresis characteristic of the magnetic control shape memory alloy actuator.
Drawings
FIG. 1 is a schematic block diagram of a NARMAX structure model based on a wavelet neural network;
FIG. 2 is a schematic illustration of an experimental platform;
FIG. 3 is a graph comparing the output of the model at an input signal frequency of 0.3Hz (24 deg.C);
FIG. 4 is a graph comparing the output of the actuator at an input signal frequency of 0.3Hz (24 deg.C);
FIG. 5 is a graph comparing the output of the model at an input signal frequency of 1Hz (24 deg.C);
FIG. 6 is a graph comparing the output results of the actuator at an input signal frequency of 1Hz (24 deg.C);
FIG. 7 is a graph comparing the output of the model at an input signal frequency of 3Hz (24 deg.C);
FIG. 8 is a graph comparing the output of the actuator at an input signal frequency of 3Hz (24 deg.C);
FIG. 9 is a graph comparing the output of the model at 10 ℃ with the same frequency input;
FIG. 10 is a graph comparing actuator output at 10 ℃ with the same frequency input;
FIG. 11 is a graph comparing the output of the model at 30 ℃ with the same frequency input;
FIG. 12 is a graph comparing actuator output at 30 ℃ with the same frequency input.
Detailed Description
The invention comprises the following steps:
step 1: a multi-model combined modeling method for introducing a Bouc-wen model into an NARMAX model as an exogenous variable is provided, and the NARMAX structure model capable of describing the multi-value mapping hysteresis of the magnetic control shape memory alloy actuator is established.
The NARMAX structural model expression with exogenous variables is as follows:
Figure BDA0002530301430000031
where k is the discrete time of the system, N is an unknown nonlinear function, y*(k) And h (k-1) represents the output value and the exogenous variable of the NARMAX structure model, respectively, v (k-1) and y (k-1) represent the input and output values of the magnetically controlled shape memory alloy actuator, respectively,
Figure BDA0002530301430000034
nv、nhand nyDenotes the memory delay of v, h and y, respectively, p ═ nv+nh+nyIs the total delay of the system.
The exogenous variable h is represented by a Bouc-wen model, and a Bouc-wen model function is expressed as follows:
Figure BDA0002530301430000032
wherein,
Figure BDA0002530301430000033
representing the derivative with time, α, β, γ and d are parameters of the Bouc-wen model.
For convenience, the NARMAX structural model is adapted to polynomial form, the expression being as follows:
Figure BDA0002530301430000041
wherein, theta is a polynomial coefficient,
Figure BDA0002530301430000042
is the i-th of the model input xpThe value of the input to the term,
Figure BDA0002530301430000043
a matrix term formed by coefficients, q is a model order, and n is (p + q)! P! q! -1 is the total number of terms,
Figure BDA0002530301430000044
is an autoregressive moving average term.
Step 2: an unknown nonlinear function of the NARMAX structure model is built by utilizing a wavelet neural network, and the NARMAX structure model which can update model parameters on line and adapt to the complex dynamic hysteresis characteristics of the magnetic control shape memory alloy actuator is built.
The expression of the wavelet neural network is as follows:
Figure BDA0002530301430000045
wherein O (k) is the output value of the wavelet neural network, omegaijThe weight value of the connection between the ith neuron of the input layer and the jth neuron of the hidden layer, omegajThe weight value, eta, of the connection between the jth neuron of the hidden layer and the neuron of the output layeriThe input quantity of the ith neuron of the input layer is m and n are the numbers of the neurons of the input layer and the hidden layer respectively. a isjAnd bjRespectively representing the scale and translation parameters of the wavelet function of the jth neuron of the hidden layer.
Figure BDA0002530301430000046
As a function of Morlet wavelet, tableThe expression is as follows:
Figure BDA0002530301430000047
wherein, I is the input value of the wavelet function, and e is a constant. When a wavelet neural network is adopted to construct a nonlinear function of the NARMAX structure model, the input of the neural network is an autoregressive moving average term of the NARMAX structure model, a structural block diagram is shown in FIG. 1, the calculation complexity and the modeling precision are comprehensively considered, the number of neurons in a hidden layer is selected to be 7, and the number of neurons in an output layer is 1.
The initial weight of the neural network is set to be a random value from 0 to 1, the optimization algorithm adopts a gradient descent method, and the updating rule formula for obtaining the neural network parameters according to the gradient descent method is as follows:
wij(k)＝wij(k-1)-ηd_wij+μ[wij(k-1)-wij(k-2)](6)
wj(k)＝wj(k-1)-ηd_wj+μ[wj(k-1)-wj(k-2)](7)
Figure BDA0002530301430000048
Figure BDA0002530301430000049
aj(k)＝aj(k-1)-ηd_aj+μ[aj(k-1)-aj(k-2)](10)
bj(k)＝bj(k-1)-ηd_bj+μ[bj(k-1)-bj(k-2)](11)
Figure BDA0002530301430000051
Figure BDA0002530301430000052
Figure BDA0002530301430000053
Figure BDA0002530301430000054
wherein d _ wij、d_wj、d_ajAnd d _ bjAre respectively a parameter wij、wj、ajAnd bjE (k) is an error function, e*(k) For modeling errors, Ij(k) Is the input value of the jth neuron of the hidden layer.
The modeling method of the present invention was then experimentally verified.
The description capability of the proposed model on the hysteresis nonlinearity of the magnetic control shape memory alloy actuator is tested under different frequency input signals and temperatures. The experimental platform is shown in fig. 2, and the computer controls the output displacement of the actuator by controlling the output signal of the programmable direct-current power supply. The high-precision micrometer is used for measuring the output displacement value of the actuator and transmitting the measured displacement signal back to the computer through the data acquisition card. Comparing the hysteresis modeling result of the NARMAX structure model based on the RBF neural network, the NARMAX structure model based on the wavelet neural network can well describe the dynamic characteristics of the actuator. In addition, under different temperature conditions, the NARMAX structure model based on the wavelet neural network has higher modeling precision. 3-5 are graphs comparing modeling results and errors of an actuator based on NARMAX structural models of a wavelet neural network and an RBF neural network under the condition of different frequency input signals at 24 ℃. 6-7 are graphs comparing the results and errors of actuator modeling based on NARMAX structure models of wavelet neural network and RBF neural network under different temperature conditions when signals with the same frequency are input.
Table 1 shows the comparison of the root mean square error and the maximum modeling error for the above cases.
Figure BDA0002530301430000055
Table 1 shows the performance index comparison between the NARMAX structure model based on the RBF neural network and the NARMAX structure model based on the wavelet neural network under different frequency input signals and temperatures.

Claims (1)

1. A multi-model combined modeling method of a magnetic control shape memory alloy actuator is characterized in that: the method comprises the following steps:
step 1: a multi-model combined modeling method for introducing a Bouc-wen model into an NARMAX model as an exogenous variable is provided, and an NARMAX structure model capable of describing the multi-value mapping hysteresis of the magnetic control shape memory alloy actuator is established;
the NARMAX structural model expression with exogenous variables is as follows:
Figure FDA0002530301420000011
where k is the discrete time of the system, N is an unknown nonlinear function, y*(k) And h (k-1) represents the output value and the exogenous variable of the NARMAX structure model, respectively, v (k-1) and y (k-1) represent the input and output values of the magnetically controlled shape memory alloy actuator, respectively,
Figure FDA0002530301420000012
nv、nhand nyDenotes the memory delay of v, h and y, respectively, p ═ nv+nh+nyFor the total delay of the system, an exogenous variable h is represented by a Bouc-wen model, and a function expression of the Bouc-wen model is as follows:
Figure FDA0002530301420000013
wherein,
Figure FDA0002530301420000014
representing the derivative with time, alpha, beta, gamma and d are parameters of the Bouc-wen model;
for convenience, the NARMAX structural model is adapted to polynomial form, the expression being as follows:
Figure FDA0002530301420000015
wherein, theta is a polynomial coefficient,
Figure FDA0002530301420000016
is the i-th of the model input xpThe value of the input to the term,
Figure FDA0002530301420000019
a matrix term formed by coefficients, q is a model order, and n is (p + q)! P! q! -1 is the total number of terms,
Figure FDA0002530301420000018
is an autoregressive moving average term
Step 2: an unknown nonlinear function of the NARMAX structure model is built by utilizing a wavelet neural network, and the NARMAX structure model which can update model parameters on line and adapt to the complex dynamic hysteresis characteristics of the magnetic control shape memory alloy actuator is built;
the expression of the wavelet neural network is as follows:
Figure FDA0002530301420000021
wherein O (k) is the output value of the wavelet neural network, omegaijThe weight value of the connection between the ith neuron of the input layer and the jth neuron of the hidden layer, omegajThe weight value, eta, of the connection between the jth neuron of the hidden layer and the neuron of the output layeriThe input quantity of the ith neuron of the input layer, m and n are the numbers of the neurons of the input layer and the hidden layer respectively, ajAnd bjRespectively representing the scaling and translation parameters of the wavelet function of the jth neuron of the hidden layer,
Figure FDA0002530301420000022
for the Morlet wavelet function, the expression is as follows:
Figure FDA0002530301420000023
the method comprises the steps that I is an input value of a wavelet function, e is a constant, when a wavelet neural network is adopted to construct a nonlinear function of an NARMAX structure model, the input quantity of the neural network is an autoregressive moving average term of the NARMAX structure model, the calculation complexity and the modeling precision are comprehensively considered, the number of neurons in a hidden layer is selected to be 7, the number of neurons in an output layer is 1, the initial weight of the neural network is set to be a random value from 0 to 1, and a gradient descent method is adopted in an optimization algorithm.
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