CN113238492A - Parameter identification method for ARMAX model of vane motor - Google Patents

Parameter identification method for ARMAX model of vane motor Download PDF

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CN113238492A
CN113238492A CN202110398512.8A CN202110398512A CN113238492A CN 113238492 A CN113238492 A CN 113238492A CN 202110398512 A CN202110398512 A CN 202110398512A CN 113238492 A CN113238492 A CN 113238492A
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model
identification
armax
continuous rotation
hydraulic servo
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王晓晶
师广强
李春辉
胡善良
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Harbin University of Science and Technology
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Abstract

The invention discloses a parameter identification method for an ARMAX model of a blade continuous rotation electro-hydraulic servo motor, belonging to the field of parameter identification, and the identification method comprises the following steps: 1. establishing an ARMAX identification model of a blade continuous rotation electro-hydraulic servo motor system; 2. determining the amplitude, frequency and sweep frequency time of an input signal; 3. determining the system order and the noise order of the ARMAX discrete model by adopting a final prediction error order-fixing method; 4. optimizing an ARMAX identification model of the blade continuous rotation motor by using an augmented least square method; 5. comparing the output data of the identification model with the actually acquired output data; 6. and verifying the accuracy of the identification model.

Description

Parameter identification method for ARMAX model of vane motor
Technical Field
The invention relates to the field of system parameter identification, in particular to a method for identifying parameters of an ARMAX model of a blade continuous rotation electro-hydraulic servo motor.
Background
The flight attitude simulation turntable is semi-physical simulation equipment with important national defense strategic significance and economic value, and the quality of the performance of the flight attitude simulation turntable is directly related to the fidelity of an aircraft simulation result. The blade continuous rotation electro-hydraulic servo motor has the advantages of large transmission torque, high response speed, high control precision, wide speed regulation range, high dynamic position rigidity and steady-state speed rigidity, strong anti-interference capability and the like.
The research on the continuous rotation electrohydraulic servo motor of the blade needs to identify relevant parameters, and at present, the identification of the parameters of the continuous rotation electrohydraulic servo motor of the blade does not always have an accurate mathematical model due to more parameter variables and the irregularity of parameter change, so that the parameter identification of a continuous rotation motor system by adopting a discrete identification system model is easier to obtain an accurate system model. The augmented least square method is a more common identification algorithm in system identification, and for an electro-hydraulic servo system, because the state space variable of the electro-hydraulic servo system has more parameters to be identified and the estimation precision required by the system is higher, the calculated amount is large; in addition, the electro-hydraulic servo system is a nonlinear system essentially, and the influence of nonlinear factors needs to be considered when a complete mathematical model of the electro-hydraulic servo system is constructed; the traditional blade continuous rotation electro-hydraulic servo motor identification usually ignores the complexity influence on identification caused by the uncertainty and nonlinearity of a system, so that the problems of low parameter fitting degree and low identification accuracy exist.
Therefore, the identification method which can simplify the mathematical model, optimize the calculation logic and save the calculation time on the premise of ensuring the accuracy is considered.
Disclosure of Invention
The invention provides a parameter identification method for an ARMAX model of a blade continuous rotation electro-hydraulic servo motor, which is used for identifying the process of the parameters of the blade continuous rotation electro-hydraulic servo motor and carrying out online real-time identification and optimization on the parameters by using an augmented least square method. The method effectively overcomes the influence of system nonlinearity and uncertain factors, thereby effectively improving the control precision of the electro-hydraulic servo system.
The technical scheme of the invention is as follows:
a parameter identification method for an ARMAX model of a blade continuous rotation electro-hydraulic servo motor is disclosed, and the basic idea is as follows: firstly, selecting and preprocessing input signals, secondly, determining the order of the ARMAX discrete model by using a final prediction error order method, thirdly, optimizing the ARMAX identification model of the blade continuous rotation motor by using an augmented least square method, and finally, verifying the identification result. The method specifically comprises the following steps:
the method comprises the following steps: establishing an ARMAX model expression:
A(z-1)z(k)＝z-dB(z-1)θ(k)+D(z-1)e(k) (1)
wherein D (z)-1) e (k) ═ epsilon (k); ε (k) is colored noise, D (z)-1) To generate output, θ (k) is the excitation signal, d is the delay times, e (k) is white noise, and { θ (k) }, { z (k) } are input and output for the identification model, respectively.
Step two: optimizing an ARMAX identification model of the continuous rotary motor by adopting an augmented least square method:
Figure BDA0003015042810000021
in the order of model na、nbAnd ndUnder the determined conditions, the parameter vector of the model is:
Figure BDA0003015042810000022
step three: unbiased estimation of β with augmented least squares estimation:
substituting the undetectable noise e (k-1), e (k-2), e (k-3) in the data vector h (k) to obtain:
Figure BDA0003015042810000023
when k is less than or equal to 0,
Figure BDA0003015042810000024
then when k > 0, then,
Figure BDA0003015042810000025
the values of (A) are:
Figure BDA0003015042810000026
step four: the augmented least squares recursion algorithm is as follows:
Figure BDA0003015042810000027
Figure BDA0003015042810000028
P(k)＝[I-K(k)hT(k)]P(k-1) (8)
where Λ (k) is a positive definite weighting matrix, k (k) is a gain matrix, and:
Figure BDA0003015042810000029
step five: establishing a state space model of a blade continuous rotation electro-hydraulic servo motor system:
after the identification data is processed, the identification data of the first 80s is subjected to system identification, and the data of the second 20s is used as model verification data. According to the obtained model order, obtaining a three-order discrete model as follows:
Figure BDA0003015042810000031
the transfer function from the discrete transfer function is:
Figure BDA0003015042810000032
step six: and identifying system parameters and verifying identification results.
The invention is mainly characterized in that:
1. according to the parameter identification method for the blade continuous rotation electro-hydraulic servo motor, the ARMAX parameter of the continuous rotation electro-hydraulic servo motor can be updated on line by using the current sampling input and output;
2. and accurate ARMAX model identification parameters can be provided in time when the model parameters change.
Drawings
FIG. 1 is a diagram of an input signal of an identification system.
FIG. 2 is a block diagram of an ARMAX recognition model.
FIG. 3 is a comparison graph of the recognition result and the actual result.
Fig. 4 is a graph of actual output versus swept output.
Fig. 5 is a comparison graph of the verification segment.
Detailed Description
The control method of the present invention will be described in detail with reference to the accompanying drawings.
The method comprises the following steps: as shown in FIG. 1, the initial frequency of the input signal of the recognition system, i.e., the sweep frequency signal, is 0.2Hz, with a peak value of 2 °.
Step two: as shown in FIG. 2, a block diagram of an ARMAX identification model with an excitation signal of θ (k) and colored noise ε (k) added to the output, A (z)-1)z(k)＝z-dB(z-1)θ(k)+D(z-1) e (k). Wherein D (z)-1) e (k) ═ epsilon (k), epsilon (k) is a linear system D (z) driven by white noise-1) And the output, D (z), produced-1) Does not affect the convergence of the transfer function. From fig. 2, the ARMAX model of the system dynamics is:
A(z-1)z(k)＝z-dB(z-1)θ(k)+D(z-1)e(k) (1)
in the formula: { θ (k) }, { z (k) } are respectively input and output of the identification model, d is the delay times, and e (k) is white noise; ε (k) is colored noise.
Step three: determining the order of the model by using a final prediction error order-determining method, listing FPE values of different orders, and taking na＝3，nb＝1，nd＝3。
Step four: optimizing an ARMAX identification model of the continuous rotary motor by adopting an augmented least square method:
Figure BDA0003015042810000041
in the order of model na、nbAnd ndHas been confirmedUnder certain conditions, the parameter vector of the model is:
Figure BDA0003015042810000042
step five: write (2) as augmented least squares format:
z(k)＝hT(k)β(k)+e(k) (4)
step six: carrying out unbiased estimation on beta by using an augmented least square estimation method, and substituting the undetectable noise e (k-1), e (k-2) and e (k-3) in the data vector h (k) to obtain:
Figure BDA0003015042810000043
when k is less than or equal to 0,
Figure BDA0003015042810000044
then when k > 0, then,
Figure BDA0003015042810000045
the values of (A) are:
Figure BDA0003015042810000046
step seven: the augmented least squares recursion algorithm is as follows:
Figure BDA0003015042810000047
Figure BDA0003015042810000048
P(k)＝[I-K(k)hT(k)]P(k-1) (9)
where Λ (k) is a positive definite weighting matrix, k (k) is a gain matrix, and:
Figure BDA0003015042810000049
step eight: establishing a state space model of the continuous rotation electro-hydraulic servo motor system:
after the identification data is processed, the identification data of the first 80s is subjected to system identification, and the data of the second 20s is used as model verification data. According to the obtained model order, obtaining a three-order discrete model as follows:
Figure BDA00030150428100000410
the transfer function from the discrete transfer function is:
Figure BDA0003015042810000051
step nine: and identifying system parameters and verifying identification results.
After the system parameters of the blade continuous rotation motor are identified according to the identification data, the comparison of the identification results shows that the fitting degree of the identification results and the system identification output results is 87.76%, as shown in fig. 3. The same sweep frequency signal is adopted for sweeping the frequency of the system after identification, the result after sweeping the frequency is compared with the actual identification result, and the comparison of the obtained sweep frequency result and the identification result shows that the fitting degree of the sweep frequency output and the identification output is 71.35 percent, as shown in fig. 4. Fig. 5 is a comparison graph of the verification segment.

Claims (7)

1. A parameter identification method for an ARMAX model of a blade continuous rotation electro-hydraulic servo motor is characterized by comprising the following steps:
the method comprises the following steps: establishing an ARMAX identification model of the blade continuous rotation electro-hydraulic servo motor system according to the identification data of the continuous rotation motor system;
step two: the selection of the input signal has great influence on the identification result, and an input signal capable of exciting a system must be selected;
step three: determining the system order and the noise order of the ARMAX discrete model by adopting a final prediction error order-fixing method;
step four: optimizing an ARMAX identification model of the continuous rotary motor by adopting an augmented least square method;
step five: and comparing the output data of the identification model with the actually acquired output data to verify the accuracy of the identification model.
2. The parameter identification method of the ARMAX model for the vane continuous rotation electro-hydraulic servo motor as claimed in claim 1, wherein the ARMAX identification model is established as follows:
A(z-1)z(k)＝z-dB(z-1)θ(k)+D(z-1) e (k), wherein D (z)-1)e(k)＝ε(k) (1)
In the formula: { θ (k) }, { z (k) } are respectively input and output of the identification model, d is the delay times, and e (k) is white noise; ε (k) is colored noise.
3. The parameter identification method for the ARMAX model of the blade continuous rotation electro-hydraulic servo motor as claimed in claim 1, wherein the augmented least squares model is established as follows:
Figure FDA0003015042800000011
in the order of model na、nbAnd ndUnder the determined conditions, the parameter vector of the model is:
Figure FDA0003015042800000012
4. the method for identifying the parameters of the ARMAX model of the blade continuous rotation electro-hydraulic servo motor as claimed in claim 3, wherein the β is estimated unbiased by using an augmented least squares estimation method:
substituting the undetectable noise e (k-1), e (k-2), e (k-3) in the data vector h (k) to obtain:
Figure FDA0003015042800000013
when k is less than or equal to 0,
Figure FDA0003015042800000014
then when k > 0, then,
Figure FDA0003015042800000015
the values of (A) are:
Figure FDA0003015042800000016
5. the method for identifying the parameters of the ARMAX model of the blade continuous rotation electro-hydraulic servo motor as claimed in claim 4, wherein the method comprises the following steps:
Figure FDA0003015042800000021
Figure FDA0003015042800000022
P(k)＝[I-K(k)hT(k)]P(k-1) (8)
where Λ (k) is a positive definite weighting matrix, k (k) is a gain matrix, and:
Figure FDA0003015042800000023
6. the parameter identification method for the ARMAX model of the blade continuous rotation electro-hydraulic servo motor is characterized in that the establishment of a state space model of a blade continuous rotation electro-hydraulic servo motor system is carried out;
after the identification data is processed, the identification data of the first 80s is subjected to system identification, and the data of the second 20s is used as model verification data. According to the obtained model order, obtaining a three-order discrete model as follows:
Figure FDA0003015042800000024
the transfer function from the discrete transfer function is:
Figure FDA0003015042800000025
7. the method for identifying parameters of the ARMAX model of the vane continuous rotation electro-hydraulic servo motor as claimed in claim 1, wherein the analysis identifies a degree of fit of the result to the output result.
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