CN115525076A - Atomic gas chamber temperature active disturbance rejection control method based on LSTM neural network - Google Patents

Atomic gas chamber temperature active disturbance rejection control method based on LSTM neural network Download PDF

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CN115525076A
CN115525076A CN202211223116.2A CN202211223116A CN115525076A CN 115525076 A CN115525076 A CN 115525076A CN 202211223116 A CN202211223116 A CN 202211223116A CN 115525076 A CN115525076 A CN 115525076A
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temperature
neural network
state
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周新秀
曹朝扬
沈振宇
谢文祥
崔培玲
毛琨
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Beihang University
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    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D23/00—Control of temperature
    • G05D23/19—Control of temperature characterised by the use of electric means
    • G05D23/20—Control of temperature characterised by the use of electric means with sensing elements having variation of electric or magnetic properties with change of temperature

Abstract

The invention discloses an atomic gas chamber temperature active disturbance rejection control method based on an LSTM neural network. And selecting the temperature of the atomic gas chamber as a controlled object, and constructing an atomic gas chamber active disturbance rejection control method based on an LSTM neural network. The temperature of the next moment is predicted by calculating the forgetting gate, the input gate, the memory unit and the output gate of the LSTM neural network in real time, the current temperature in the linear extended observer is replaced, and the corrected control quantity is obtained. The invention reduces the steady state error of the system, improves the performance indexes of temperature fluctuation, average absolute deviation, standard deviation, dispersion coefficient and the like of the air chamber, and further improves the stability of the scale factors of the atomic gyroscope and the atomic magnetometer.

Description

Atomic gas chamber temperature active disturbance rejection control method based on LSTM neural network
Technical Field
The invention belongs to the field of temperature control, and particularly relates to an atomic gas chamber temperature active disturbance rejection control method based on an LSTM neural network, which is used for realizing temperature control of an atomic gas chamber in a room temperature environment.
Background
The SERF atomic spin gyroscope is a new generation atomic gyroscope, has extremely high measurement accuracy theoretically, and is one of important development directions of future gyroscopes. The key component of the SERF gyroscope is an atomic gas chamber, and the scale factor stability of the gyroscope is closely related to the temperature stability of the atomic gas chamber. Because the temperature of the atomic gas chamber is easily interfered by the fluctuation of the ambient temperature, the temperature stability of the gas chamber is reduced, and therefore a proper temperature control method needs to be designed to ensure the temperature stability of the gas chamber. Relevant research institutions have already carried out certain research on high-precision temperature control strategies of the gas chamber, and under the condition of keeping the test environment stable, the high temperature control precision of the atomic gas chamber is achieved. In order to meet the requirements of miniaturization and outdoor work of the atomic gyroscope, the atomic gyroscope still can ensure high-precision temperature control in an outdoor environment. At the moment, the traditional PID control algorithm has the defects of static error and the like, and is not beneficial to improving the scale factor of the atomic gyroscope. Therefore, the research on the atomic gas chamber temperature control technology capable of adapting to the room-temperature working environment of the atomic gyroscope has important significance for improving performance indexes such as gas chamber temperature fluctuation, average absolute deviation, standard deviation, dispersion coefficient and the like.
Disclosure of Invention
Aiming at the problem that the temperature control precision of an atomic gas chamber under the influence of environmental temperature fluctuation and heat transfer delay by a PID control algorithm is insufficient, the invention provides an atomic gas chamber temperature active disturbance rejection control method based on an LSTM neural network, so that the steady-state error of a system is reduced, performance indexes such as gas chamber temperature fluctuation, mean absolute deviation, standard deviation, discrete coefficient and the like are improved, and the stability of scaling factors of an atomic gyro and an atomic magnetometer is further improved.
The invention takes an STM32F103 chip as a microcontroller of a temperature control circuit, measures the temperature of a gas chamber through a high-precision temperature sensor, an AD data acquisition module acquires and conditions signals of the temperature sensor, an A/D converter is utilized to convert analog signals obtained by measurement into digital signals for being processed by the STM32F103 chip, temperature data processing is carried out in the controller, namely, the temperature at the next moment is predicted through an LSTM neural network, and the temperature at the next moment is input into an ADRC extended state observer to obtain corresponding control signals. The DA data output module converts a digital control signal output by the microcontroller into an analog control signal through the digital-to-analog converter, outputs the analog control signal, inputs the analog control signal into the heating laser and controls the heating of the atomic gas chamber. Meanwhile, temperature data are monitored in real time at the PC end through the upper computer system and the data are stored.
The atomic gas chamber temperature active disturbance rejection control method based on the LSTM neural network predicts the gas chamber temperature at the next moment in real time through the LSTM neural network, inputs the gas chamber temperature into an ADRC extended state observer, obtains preliminary control quantity through ADRC nonlinear state error feedback, and can be changed into the control problem of unit gain of a double integrator in series through reducing the disturbance state.
The LSTM neural network prediction gas chamber temperature realization steps are as follows:
first, output h at last moment is utilized <t-1> And the present sequence data input x <t> Calculating to obtain a forgetting door f <t> Input door i <t> Neuron state at the previous time
Figure BDA0003878942160000021
As shown in formula:
Figure BDA0003878942160000022
Figure BDA0003878942160000023
Figure BDA0003878942160000024
second, combining the forget gate result and the input gate result, updating the current neuron state, wherein an h is Hadamard product:
C <t> ＝C <t-1> ⊙f <t> +i <t> ⊙a <t>
thirdly, the computation of the output gate comprises two parts, the first part is the hidden state h of the last input sequence <t-1> And the present sequence data x <t> Is calculated to obtain
Figure BDA0003878942160000025
Then, the calculation result is processed by sigmoid activation function to obtain o <t> (ii) a The second part is the state of the neuron C <t> And tanh activation function composition:
Figure BDA0003878942160000026
Figure BDA0003878942160000027
h <t> ＝o <t> ⊙tanh(C <t> )
the air chamber temperature control model uses a regression-based neural network, a sigmoid function is used as an activation function of an output layer, and the mathematical description of the model output is as follows;
Figure BDA0003878942160000028
o <t> ＝Vh <t> +c
where V and c are the weight and offset of the output layer. V has a size of out N, h <t> The size is Nx 1; c is out × 1; o. o <t> The size is out × 1;
Figure BDA0003878942160000031
the size is out × 1;
the observed disturbance of ADRC is a model-free observed disturbance, and by regarding the system as a series integral type and compensating the system to the series integral type, the portions that do not conform to the integral type are all considered as disturbances. The following formula:
Figure BDA0003878942160000032
i.e. the output of the system equals the disturbance f d And the sum of the system inputs bu.
Nonlinear state error feedback NLSEF uses a nonlinear function to convert two error signals (namely the error e between the set temperature and the observed temperature) 1 Error e of the derivative of the set temperature with the derivative of the observed temperature 2 ) Nonlinear combination is carried out to generate a primary control quantity u for the controlled object 0 。
u 0 ＝β 1 fal(e 1 ,α 1 ,δ)+β 2 fal(e 2 ,α 2 ,h)
In the formula, 0 < alpha 1 ＜1＜α 2 ，β 1 ＝k p ，β 2 ＝k d ；k p As an equivalent proportional link parameter, k d Is an equivalent differential link parameter.
Representative disturbance state variable f expanded in linear expansion observer d By z of ESO 3 Tracking, thereby simplifying the original object into a control problem of a double integrator connected with unit gain in series, and obtaining the final control quantity:
Figure BDA0003878942160000033
compared with the prior art, the invention has the advantages that:
(1) Aiming at the problem of insufficient temperature control precision in a room temperature environment, the temperature is predicted in real time through the LSTM neural network, and the temperature is controlled by using active disturbance rejection control, so that the steady-state error is reduced, and the performance of the system is improved.
(2) Compared with the existing PID temperature control method, the method can effectively reduce steady-state errors and improve performance indexes such as air chamber temperature fluctuation, average absolute deviation, standard deviation, dispersion coefficient and the like when dealing with larger environmental temperature fluctuation and heat transfer delay, thereby improving the stability of the scaling factors of the atomic gyroscope and the atomic magnetometer.
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FIG. 1 is a schematic diagram of a system framework of an atomic gas chamber temperature active disturbance rejection control method based on an LSTM neural network according to the present invention;
fig. 2 is a flowchart of the active disturbance rejection control.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
As shown in figure 1, the invention takes an STM32F103 chip 1 as a microcontroller of a temperature control circuit, the temperature of a gas chamber is measured by a high-precision temperature sensor 2, an AD data acquisition module 3 acquires and conditions a temperature sensor signal, an analog signal obtained by measurement is converted into a digital signal for being processed by the STM32F103 chip 1 by an A/D converter, temperature data processing is carried out in the microcontroller, namely the temperature at the next moment is predicted by an LSTM neural network, and the temperature at the next moment is input into an ADRC extended state observer to obtain a corresponding control signal. The DA data output module 4 converts a digital control signal output by the microcontroller into an analog control signal through a digital-to-analog converter, outputs the analog control signal, inputs the analog control signal into the heating laser 5, and controls the heating of the atomic gas chamber 6. Meanwhile, the temperature data is monitored in real time at the PC end through the upper computer system 7 and the data is stored.
The principle of the invention is as follows: and predicting the temperature of the air chamber at the next moment in real time through an LSTM neural network, inputting the temperature into an ADRC extended state observer, obtaining a preliminary control quantity through nonlinear state error feedback of the ADRC extended state observer, and reducing a disturbance state to obtain a control problem of a double integrator in series connection with a unit gain.
The LSTM neural network prediction gas chamber temperature realization steps are as follows:
first, output h at last moment is utilized <t-1> And the present sequence data input x <t> Calculating to obtain a forgetting door f <t> Input door i <t> Neuronal state at the previous moment
Figure BDA0003878942160000041
As shown in formula:
Figure BDA0003878942160000042
i <t> ＝σ(W i h <t-1> +U i x <t> +b i )
Figure BDA0003878942160000043
wherein, sigma (·) and tanh (·) are sigmoid function and hyperbolic tangent function respectively; w is a group of f 、U f 、W i 、U i 、W c 、 U c Weight being a linear relation, b f 、b i 、b c Is an offset. h is <t-1> Hidden state at the previous moment, x <t> Is the input of the present sequence data.
Second, combining the forget gate result and the input gate result, updating the current neuron state, wherein an h is Hadamard product:
C <t> ＝C <t-1> ⊙f <t> +i <t> ⊙a <t>
thirdly, the computation of the output gate comprises two parts, the first part is the hidden state h of the last input sequence <t-1> And the present sequence data x <t> Is calculated to obtain
Figure BDA0003878942160000051
Then, the calculation result is processed by sigmoid activation function to obtain o <t> (ii) a The second part is the state of the neuron C t＞ And tanh activation function composition:
o <t> ＝σ(W o h <t-1> +U o x <t> +b o )
h <t> ＝o <t> ⊙tanh(C <t> )
wherein o is <t> For output of the output gate, h <t> Is a hidden state at the current moment. W o 、U o Weight being a linear relation, b o To be offset, C <t> Is the current sequence neuron state.
The gas chamber temperature control model uses a regression-based neural network, a sigmoid function is used as an activation function of an output gate, and the mathematical description of the model output is as follows;
Figure BDA0003878942160000052
o <t> ＝Vh <t> +c
in the formula, V and c are the weight and bias of the output layer. V is out × N, h <t> The size is Nx 1; c is out × 1; o <t> The size is out × 1;
Figure BDA0003878942160000053
the size is out × 1;
the observed disturbance of the ADRC extended state observer is a model-free observed disturbance, and by regarding the system as a series integral type and compensating the system to the series integral type, the portions that do not conform to the integral type are all considered as disturbances. The following equation:
Figure BDA0003878942160000054
i.e. the output of the system
Figure BDA0003878942160000055
Equal to the disturbance f d And the sum of the system inputs bu.
Nonlinear state error feedback NLSEF uses a nonlinear function to convert two error signals (namely the error e between the set temperature and the observed temperature) 1 Error e of the derivative of the set temperature with the derivative of the observed temperature 2 ) Non-linear combination is carried out to generate a preliminary control quantity u for the controlled object 0 。
u 0 ＝β 1 fal(e 1 ,α 1 ,δ)+β 2 fal(e 2 ,α 2 ,h)
In the formula, 0 < alpha 1 ＜1＜α 2 ，β 1 ＝k p ，β 2 ＝k d ，k p As an equivalent proportional link parameter, k d Is an equivalent differential link parameter.
Representative disturbance state variable f expanded in linear expansion observer d Observed quantity z of temperature change acceleration of linear extended state observer 3 Tracking, thereby simplifying the original object into a control problem of a double integrator connected with unit gain in series, and obtaining the final control quantity:
Figure BDA0003878942160000061
wherein b is 0 Is an offset.
As shown in fig. 2, the active disturbance rejection control method of the atomic gas chamber temperature system based on the LSTM neural network of the present invention is specifically implemented as follows:
firstly, carrying out data modeling on a temperature control system and establishing an atomic gas chamber LSTM neural network model. The method comprises the steps of firstly obtaining gas chamber temperature data, heating power and environment temperature at historical moments, carrying out normalization processing on the data to obtain a training set, training a constructed LSTM model according to the training set to obtain a gas chamber temperature LSTM optimization prediction model, predicting the gas chamber temperature at the next moment, and generating a prediction result.
And secondly, constructing an ADRC active disturbance rejection controller, which comprises a tracking differentiator TD, an extended state observer ESO and a nonlinear state error feedback NLSEF. To facilitate parameter tuning, a linear extended state observer is used. To compensate for the effect of heat transfer delays on the temperature control system, the predicted temperature of the LSTM neural network is used instead of the current temperature in the linear expansion observer. The method comprises the following specific steps:
first the input x of the sample sequence <t> For heating power P, ambient temperature T 0 Upper time temperature T', output y <t> Is the temperature T of the gas chamber at the next moment, i.e. after the time deltat. In the atomic gas chamber LSTM neural network model, the input dimension in is 3 (namely the temperature, the heating power and the ambient temperature at the last moment), the number of the LSTMs is 50, the output dimension is 1 (namely the temperature of a gas chamber), the training frequency is 10000, the data size is 200000, the learning rate is 5e-4, and the training frequency is 500.
And secondly, an ADRC active disturbance rejection controller is set up, and because the temperature control required by the system belongs to constant temperature control and temperature tracking in the control process is not needed, a tracking differentiator in a conventional ADRC control algorithm is not needed.
Assuming that the chamber temperature control system is a second-order nonlinear system, as follows:
Figure BDA0003878942160000062
wherein w is unmodeled dynamics, d is external disturbances,
Figure BDA0003878942160000063
b is the adjustable parameter and u is the system input for the total disturbance of the system.
Let y = x 1 ,f＝x 3 The second order nonlinear system can be expressed in the form of the following ODE equation set:
Figure BDA0003878942160000064
x 1 for measuring temperature, x 2 Is the rate of change of temperature, x 3 For system disturbances, h is the rate of change of the system disturbance.
The original system is second order, the expansion is third order after the disturbance observation is added, and the discrete form of constructing the LESO is described as follows:
Figure BDA0003878942160000071
wherein z is 1 、z 2 、z 3 Respectively an observed quantity of temperature, an observed quantity of temperature change and an observed quantity of disturbance. Parameter beta 01 、β 02 、β 03 Designed according to the bandwidth of the observer, beta 01 ＝3ω 0 、
Figure BDA0003878942160000072
Wherein ω is 0 B is a compensation coefficient and is related to a model of the controlled object to expand the bandwidth of the state observer. e is the difference between the measured value and the actual value, and k is the discrete time.
The nonlinear error feedback control is constructed as follows:
u 0 ＝β 1 fal(e 1 ,α 1 ,δ)+β 2 fal(e 2 ,α 2 ,h)
in the formula, 0 < alpha 1 ＜1＜α 2 ，β 1 ＝k p ，β 2 ＝k d ，e 1 Estimating a difference between the controlled object and a set value; e.g. of the type 2 The difference, k, between the derivative estimated for the controlled object and the derivative of the set value p As an equivalent proportional link parameter, k d As equivalent differential element parameter, alpha 1 、α 2 δ is an adjustable parameter, and the fal () function has the form:
Figure BDA0003878942160000073
air chamber temperature matrix Y predicted by using atomic air chamber LSTM neural network model t Instead of the measured temperature y (k), the cell temperature is input into the linear extended observer in advance, so the mathematical description of the ADRC extended state observer can be written as:
Figure BDA0003878942160000074
wherein E is the difference between the observed temperature and the measured temperature, Z 1 、Z 2 、Z 3 Respectively an observed quantity matrix of temperature, an observed quantity matrix of temperature change and an observed quantity matrix of disturbance.
Writing a temperature control algorithm into an STM32F103 chip 1, using a platinum resistor with the model of PT1000 as a temperature sensor 2 of the system, reducing temperature measurement errors by using a low-temperature drift resistor on a circuit board, and simultaneously keeping stable interference of an atomic air chamber under an aerogel heat insulation membrane for heating test, wherein the temperature set value of the air chamber is 180 ℃. After the control process is started, the ADRC extended state observer is subjected to parameter adjustment, including that only the observer bandwidth omega needs to be adjusted due to the adoption of the linear state observer 0 In a certain range, the larger the control effect is, the better the control effect is, but the larger the control effect is, the system is possibly unstable, and the control effect is determined according to the transient response requirement; tuning for nonlinear state error feedback: parameter k p Increasing k in direct relation to tracking error p The tracking accuracy can be improved, but too much affects the dynamic performance, and may cause large oscillation to cause system instability. Parameter k d Increasing k in relation to the influence of the differentiated signal on the system d The response tracking speed can be improved. It should be noted that when the system reaches steady state, k is adjusted p 、k d The influence on the system is small.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (3)

1. An atomic gas chamber temperature active disturbance rejection control method based on an LSTM neural network is characterized by comprising the following steps: according to the environmental disturbance and the heat transfer delay of the atomic gas chamber temperature control, mathematical modeling is carried out through an LSTM neural network, the temperature at the next moment is predicted and input into an ADRC extended state observer, and the stability of the gas chamber temperature is improved by combining a temperature control algorithm of the ADRC extended state observer.
2. The LSTM neural network-based atomic gas cell temperature active disturbance rejection control method of claim 1, wherein: the mathematical modeling by the LSTM neural network includes:
the LSTM neural network is divided into four parts: the system comprises a forgetting gate, an input gate, a neuron state updating part and an output gate; t represents the t-th time, in is the input sequence x <t> N is the number of hidden layer LSTM cells and the hidden state h <t> ，C <t> Length of (d); the specific process of the forward calculation is as follows:
first, output h at last moment is utilized <t-1> And the present sequence data input x <t> And calculating to obtain a forgetting door f <t> Input door i <t> Neuronal state at the previous moment
Figure FDA0003878942150000011
As shown in formula:
Figure FDA0003878942150000012
i <t> ＝σ(W i h <t-1> +U i x <t> +b i )
Figure FDA0003878942150000013
wherein, sigma (·) and tanh (·) are sigmoid function and hyperbolic tangent function respectively; w f 、U f 、W i 、U i 、W c 、U c Weight being a linear relation, b f 、b i 、b c Is an offset; h is a total of <t-1> Is the hidden state at the previous moment, x <t> Input of the sequence data;
second, combining the forget gate result and the input gate result, updating the current neuron state, wherein an h is Hadamard product:
C <t> ＝C <t-1> ⊙f <t> +i <t> ⊙a <t>
wherein, C <t-1> For the last sequence neuron state, f <t> To forget the gate output, i <t> For input of gate output, a <t> Is a constant;
thirdly, the calculation of the output gate comprises two parts, the first part is the hidden state h of the last input sequence <t-1> And the present sequence data x <t> Calculating to obtain intermediate variable
Figure FDA0003878942150000014
Then, obtaining an output o of an output gate from the calculation result through a sigmoid activation function <t> (ii) a The second part is the state of the neuron C <t> And tanh activation function composition:
Figure FDA0003878942150000021
Figure FDA0003878942150000022
h <t> ＝o <t> ⊙tanh(C <t> )
wherein o is <t> For output of the output gate, h <t> Is a hidden state at the current moment; w is a group of o 、U o Weight being a linear relation, b o To be offset, C <t> Is the current sequence neuron state;
the mathematical model uses a regression-based neural network and a sigmoid function as an activation function of an output gate, and the mathematical description of the output of the model is as follows:
Figure FDA0003878942150000023
o <t> ＝Vh <t> +c
where out is the output sequence y <t> Dimension of (d); v, c are weight and bias of the output layer; h is <t> Is a hidden state at the current moment; v has a size of out N, h <t> Is of size Nx 1; c is out × 1; o <t> The size is out × 1;
Figure FDA0003878942150000024
the size is out × 1.
3. The LSTM neural network-based atomic gas cell temperature active disturbance rejection control method of claim 2, wherein: the active disturbance rejection control method comprises a linear extended state observer and a nonlinear state feedback error:
the linear extended state observer expands the total disturbance into a new state variable of the system, and reconstructs all states including the original state variable and the disturbance of the system by using the input and the output of the system, wherein the states are as follows:
Figure FDA0003878942150000025
wherein z is 1 、z 2 、z 3 Respectively the view of temperatureMeasurement, observed amount of temperature change, and observed amount of disturbance, e is an error of the observed amount and the measured amount, β 01 、β 02 、β 03 Is the coefficient, b is the compensation coefficient, u (k) is the system input;
the nonlinear state error feedback is used for controlling the error e between the set temperature and the observed temperature through a nonlinear function 1 Error e of the derivative of the set temperature with the derivative of the observed temperature 2 Non-linear combination is carried out to generate a preliminary control quantity u for the controlled object 0 ：
u 0 ＝β 1 fal(e 1 ,α 1 ,δ)+β 2 fal(e 2 ,α 2 ,h)
In the formula, 0 < alpha 1 ＜1＜α 2 ，β 1 ＝k p ，β 2 ＝k d ；k p As an equivalent proportional link parameter, k d As equivalent differential element parameter, alpha 1 、α 2 δ is an adjustable parameter, the fal () function is of the form:
Figure FDA0003878942150000031
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