CN112034710B - Online closed-loop frequency domain identification method and system for process object and computer readable storage medium - Google Patents

Online closed-loop frequency domain identification method and system for process object and computer readable storage medium Download PDF

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CN112034710B
CN112034710B CN202010893804.4A CN202010893804A CN112034710B CN 112034710 B CN112034710 B CN 112034710B CN 202010893804 A CN202010893804 A CN 202010893804A CN 112034710 B CN112034710 B CN 112034710B
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王亚刚
王阳
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Shanghai Xiaocong Technology Co ltd
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Abstract

The invention provides an online closed loop frequency domain identification method, a system and a computer readable storage medium of a process object, wherein the online closed loop frequency domain identification method comprises the following steps: performing laplace transform on the output signal y (t) and the input signal u (t) to obtain a laplace transform expression Y(s) of the output signal y (t) and a laplace transform expression U(s) of the input signal u (t); introducing an attenuation factor alpha to calculate to obtain a transfer function expression G(s) based on the Laplace transform expression U(s) and the Laplace transform expression Y(s); calculating the critical frequency omega based on the iterative formula and the transfer function expression G(s)c(ii) a Based on the transfer function expression G(s) and the critical frequency omegacAnd obtaining a first-order plus pure lag transfer function through a least square calculation method. By adopting the technical scheme, the important frequency response characteristics of the process object can be found, so that an accurate object model can be identified.

Description

Online closed-loop frequency domain identification method and system for process object and computer readable storage medium
Technical Field
The present invention relates to the field of control systems, and in particular, to a method and system for identifying a process object in an online closed-loop frequency domain, and a computer-readable storage medium.
Background
It is well known that object models are very important for the design and tuning of control systems. An appropriate controller can be conveniently designed as long as an object model with certain precision is available, so that the control effect can well meet the performance index. At present, two process model identification methods of open loop and closed loop exist in control application. However, in real life, many problems such as temperature control of the circulating fluidized bed boiler bed, wind field power generation, parameter identification of robot models, etc. cannot easily cut off the feedback loop of the process due to the requirement of the operation stability of the actual system, otherwise, the control may be out of control, which seriously affects the production, and thus the identification must be performed in a closed loop state. Thus, closed-loop identification is more practical in a sense.
In actual industrial control, a relay feedback method has been successfully applied to self-tuning of a controller, and can automatically obtain the critical frequency response characteristic of a process object. The technology is generally applicable to the initial operation and debugging phases of a control loop, and if a system is identified during operation, the running object model needs to be interrupted and switched to a test state to identify the object model. This is often inconvenient and in most cases not permitted on site.
According to the invention, the input and output signals generated in the normal operation process of the closed-loop control system loop are analyzed to find the important frequency response characteristics of the process object, so that an accurate object model is identified.
Disclosure of Invention
In order to overcome the technical defects, the present invention provides a method, a system and a computer readable storage medium for identifying a process object in an online closed-loop frequency domain.
The invention discloses an online closed-loop frequency domain identification method of a process object, which comprises the following steps:
performing laplace transform on the output signal y (t) and the input signal u (t) to obtain a laplace transform expression Y(s) of the output signal y (t) and a laplace transform expression U(s) of the input signal u (t);
introducing an attenuation factor alpha to calculate to obtain a transfer function expression G(s) based on the Laplace transform expression U(s) and the Laplace transform expression Y(s);
calculating the critical frequency omega based on the iterative formula and the transfer function expression G(s)c；
Based on the transfer function expression G(s) and the critical frequency ωcAnd obtaining a first-order plus pure lag transfer function through a least square calculation method.
Preferably, the step of performing laplace transform on the output signal y (t) and the input signal u (t) to obtain a laplace transform expression y(s) of the output signal y (t) and a laplace transform expression u(s) of the input signal u (t) comprises:
The laplace transform formula (1) is defined:
Figure GDA0003557979760000021
the laplace transforms u(s) and y(s) of the output signal y (t) and the input signal u (t) may be expressed as equation (2) and equation (3), respectively:
Figure GDA0003557979760000022
Figure GDA0003557979760000023
preferably, the step of calculating a transfer function expression g(s) by introducing the attenuation factor a based on the laplace transform expression u(s) and the laplace transform expression y(s) includes:
based on the transfer function expression g(s) represented by formula (4):
Figure GDA0003557979760000024
taking s as j ω + α, introducing an attenuation factor α, and calculating a solution formula (5):
Figure GDA0003557979760000025
preferably, e-αTcEqual to half the value of the step signal, where TcIs the time for the process object to reach the steady state response, α and TcSatisfies the relationship expressed by the following formula (6):
α＝ln(2)/Tc (6)
when the process object contains time-lag sections, α and TcSatisfies the relationship expressed by the following formula (7):
Figure GDA0003557979760000026
wherein T isLThe time after which the output signal lags.
Preferably, the critical frequency ω is calculated based on an iterative formula and a transfer function expression g(s)cComprises the following steps:
calculating the critical frequency omega according to the iterative formula (8)c：
Figure GDA0003557979760000031
Wherein ω and
Figure GDA0003557979760000032
are all set to 0 and,
Figure GDA0003557979760000033
expressed according to equation (9) as:
Figure GDA0003557979760000034
preferably, the expression G(s) is based on a transfer function and the critical frequency ωcThe step of obtaining the first-order plus pure lag transfer function by the least square calculation comprises:
A first order plus pure hysteresis model is employed according to equation (10):
Figure GDA0003557979760000035
where K is the static gain, T is the time constant, L is the pure lag coefficient, K, T, L is calculated according to equation (11) by applying a constant at ωnFrequency response point matching G (j ω + α) and G (j ω + α) of (n ═ 1, 2.. said., M) are obtained:
Figure GDA0003557979760000036
n＝1，2，…，M (11)。
preferably, for frequency ωnThe amplitude and phase relationships in equation (11) are represented by equation (12) and equation (13), respectivelyShown as follows:
ωn 2|G(ωn+α)|2T2+|G(ωn+α)|2(Tα+1)2＝K2e-2Lα (12)
Figure GDA0003557979760000037
wherein n is 1, 2.., M;
the magnitude relationship of equation (12) can be expressed by equation (14) as:
Φθ＝Γ (14)
wherein the content of the first and second substances,
Figure GDA0003557979760000041
Figure GDA0003557979760000042
θ in equation (14) is determined by equation (15):
θ＝(ΦTΦ)-1ΦTΓ (15)；
the time constant T is determined by θ and equation (16):
Figure GDA0003557979760000043
the pure hysteresis coefficient L is obtained by the phase relationship and equation (17):
Figure GDA0003557979760000044
the model parameter K is obtained by θ, the pure hysteresis coefficient L, and equation (18):
Figure GDA0003557979760000045
the invention also discloses an online closed loop frequency domain identification system of the process object, which comprises the following steps:
a transformation module, which performs laplace transformation on the output signal y (t) and the input signal u (t) to obtain a laplace transformation expression U(s) of the output signal y (t) and a laplace transformation expression Y(s) of the input signal u (i);
a calculation module for calculating a transfer function expression G(s) by introducing an attenuation factor alpha based on the Laplace transform expression U(s) and the Laplace transform expression Y(s), and calculating a critical frequency omega based on an iterative formula and the transfer function expression G(s) c；
An acquisition module based on the transfer function expression G(s) and the critical frequency omegacAnd obtaining a first-order plus pure lag transfer function through a least square calculation method.
The invention also discloses a computer readable storage medium having stored thereon a computer program which, when executed by a processor, performs the steps of any of the above.
After the technical scheme is adopted, compared with the prior art, the method has the following beneficial effects:
1. the required input and output data are collected under the normal operation state of the industrial control system without the prior knowledge of any process object, so that the frequency response characteristic of the system can be calculated;
2. a first-order plus pure hysteresis model is obtained by calculation through a least square method, the original running state of a control system is not required to be changed, the model can be directly used for setting parameters of the control system, and the method has good practical significance;
3. the attenuation factor alpha can directly calculate and analyze the input and output signals generated when the system normally operates, so as to obtain an identification model of the process object.
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FIG. 1 is a diagram illustrating a Nyquist curve under a first identification model;
FIG. 2 is a diagram illustrating a Nyquist curve under a second identification model;
FIG. 3 is a diagram illustrating a Nyquist curve under the third identification model.
Detailed Description
The advantages of the invention are further illustrated in the following description of specific embodiments in conjunction with the accompanying drawings.
Reference will now be made in detail to the exemplary embodiments, examples of which are illustrated in the accompanying drawings. When the following description refers to the accompanying drawings, like numbers in different drawings represent the same or similar elements unless otherwise indicated. The implementations described in the exemplary embodiments below are not intended to represent all implementations consistent with the present disclosure. Rather, they are merely examples of apparatus and methods consistent with certain aspects of the present disclosure, as detailed in the appended claims.
The terminology used in the present disclosure is for the purpose of describing particular embodiments only and is not intended to be limiting of the disclosure. As used in this disclosure and the appended claims, the singular forms "a," "an," and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It should also be understood that the term "and/or" as used herein refers to and encompasses any and all possible combinations of one or more of the associated listed items.
It is to be understood that although the terms first, second, third, etc. may be used herein to describe various information, such information should not be limited to these terms. These terms are only used to distinguish one type of information from another. For example, first information may also be referred to as second information, and similarly, second information may also be referred to as first information, without departing from the scope of the present disclosure. The word "if" as used herein may be interpreted as "at … …" or "when … …" or "in response to a determination", depending on the context.
In the description of the present invention, it is to be understood that the terms "longitudinal", "lateral", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", and the like, indicate orientations or positional relationships based on those shown in the drawings, and are used merely for convenience of description and for simplicity of description, and do not indicate or imply that the referenced devices or elements must have a particular orientation, be constructed in a particular orientation, and be operated, and thus, are not to be construed as limiting the present invention.
In the description of the present invention, unless otherwise specified and limited, it is to be noted that the terms "mounted," "connected," and "connected" are to be interpreted broadly, and may be, for example, a mechanical connection or an electrical connection, a communication between two elements, a direct connection, or an indirect connection via an intermediate medium, and specific meanings of the terms may be understood by those skilled in the art according to specific situations.
In the following description, suffixes such as "module", "component", or "unit" used to denote elements are used only for facilitating the explanation of the present invention, and have no specific meaning in themselves. Thus, "module" and "component" may be used in a mixture.
Generally, the change signals between two stable states of the object to be recognized include important frequency domain dynamics, but these signals are not always absolute integrable, so it is considered to use laplace transform, i.e., laplace transform of the output signal y (t) and the input signal u (t) to obtain the laplace transform expression y(s) of the output signal y (t) and the laplace transform expression u(s) of the input signal u (t). Specifically, the output signal y (t) and the input signal u (t) are subjected to laplace transform to obtain formula (1):
Figure GDA0003557979760000061
the laplace transforms u(s) and y(s) of the output signal y (t) and the input signal u (t) may be expressed as equation (2) and equation (3), respectively:
Figure GDA0003557979760000062
Figure GDA0003557979760000063
then, based on the laplace transform expression u(s) and the laplace transform expression y(s), a transfer function expression g(s) is calculated by introducing an attenuation factor α, and specifically, based on the transfer function expression g(s) expressed by the formula (4):
Figure GDA0003557979760000064
for a general input signal u (t) and output signal y (t), steady-state values thereof are non-zero constants, and direct integration calculation cannot converge, so that s is taken as j ω + α, an attenuation factor α is introduced, and a solution formula (5) is calculated:
Figure GDA0003557979760000071
due to e-αtFor a monotonically decreasing function of the variable t, let u (t) e -αtAnd y (t) e-αtDecays to a value close to zero over a certain time, so that the signal integral converges.
Simulation experiments show that step signals are input to the process objects, and when the process objects reach steady-state response, e-αTcEqual to half of the step signal value, the identification result is good and can well cover the dynamic frequency characteristic, therefore, e is taken-αTcEqual to half the value of the step signal, where TcIs the time for the process object to reach the steady state response, α and TcSatisfies the relationship expressed by the following formula (6):
α＝ln(2)/Tc (6)
when the process object contains time-lag sections, α and TcSatisfies the relationship expressed by the following formula (7):
Figure GDA0003557979760000072
wherein T isLThe time after which the output signal lags.
If the object model converges, since the system mainly affects the stability of the system in the low frequency band and the middle frequency band, and hardly affects the stability of the system in the high frequency band, the critical frequency point omega from zero to the objectcIs its important frequency range. For this, the critical frequency ω will be calculated based on the iterative formula and the transfer function expression g(s)c. Specifically, the critical frequency ω is calculated according to the iterative formula (8)c：
Figure GDA0003557979760000073
Wherein ω and
Figure GDA0003557979760000074
are all set to 0 and,
Figure GDA0003557979760000075
expressed according to equation (9) as:
Figure GDA0003557979760000076
finally, based on the transfer function expression G(s) and the critical frequency ω cAnd obtaining a first-order plus pure lag transfer function through a least square calculation method. Specifically, a first order plus pure hysteresis model is employed according to equation (10):
Figure GDA0003557979760000077
where K is the static gain, T is the time constant, L is the pure lag coefficient, K, T, L is calculated according to equation (11) by applying a constant at ωnFrequency response point matching G (j ω + α) and G (j ω + α) of (n ═ 1, 2.. said., M) are obtained:
Figure GDA0003557979760000078
n＝1，2，…，M (11)。
for frequency omeganThe amplitude and phase relationships in equation (11) are expressed by equation (12) and equation (13), respectively:
ωn 2|G(ωn+α)|2T2+|G(ωn+α)|2(Tα+1)2＝K2e-2Lα (12)
Figure GDA0003557979760000081
wherein n is 1, 2.., M;
the magnitude relationship of equation (12) can be expressed by equation (14) as:
Φθ＝Γ (14)
wherein the content of the first and second substances,
Figure GDA0003557979760000082
Figure GDA0003557979760000083
θ in equation (14) is determined by equation (15) using a linear least squares method:
θ＝(ΦTΦ)-1ΦTΓ (15)；
the time constant T is determined by θ and equation (16):
Figure GDA0003557979760000084
the pure hysteresis coefficient L is obtained by the phase relationship and equation (17):
Figure GDA0003557979760000085
the model parameter K is obtained by θ, the pure hysteresis coefficient L, and equation (18):
Figure GDA0003557979760000091
the invention also discloses an online closed loop frequency domain identification system of the process object, which comprises the following steps:
a transformation module, which performs laplace transformation on the output signal y (t) and the input signal u (t) to obtain a laplace transformation expression Y(s) of the output signal y (t) and a laplace transformation expression U(s) of the input signal u (t);
A calculation module for calculating a transfer function expression G(s) by introducing an attenuation factor alpha based on the Laplace transform expression U(s) and the Laplace transform expression Y(s), and calculating a critical frequency omega based on an iterative formula and the transfer function expression G(s)c；
An acquisition module based on the transfer function expression G(s) and the critical frequency omegacAnd obtaining a first-order plus pure lag transfer function through a least square calculation method.
The invention further discloses a computer readable storage medium having a computer program stored thereon, which computer program, when being executed by a processor, realizes the steps of any of the above.
The method uses MATLAB simulation software, selects the frequency response point number M to be 30, carries out identification simulation on different types of models, and verifies the effectiveness of the method by analyzing the Nyquist curve.
To test the reliability and accuracy of the inventive method, a Signal-to-Noise Ratio SNR (Signal-Noise Ratio) was added to the simulation experiment, defined as follows
Figure GDA0003557979760000092
Assume a higher order model as follows
Figure GDA0003557979760000093
When the SNR is 10%, using the identification method of the present invention, the α value is calculated to be 0.0161, and the final first-order plus pure hysteresis model is:
Figure GDA0003557979760000094
the nyquist curve for model one is shown in fig. 1.
The second high-order time-lag model is assumed as follows:
Figure GDA0003557979760000095
when the SNR is 10%, the identification method of the present invention is used to calculate the α value to be 0.068, and the finally obtained first-order plus pure hysteresis model is:
Figure GDA0003557979760000101
the nyquist curve of model two is shown in fig. 2.
The high-order large-time-lag model III is assumed as follows:
Figure GDA0003557979760000102
when the SNR is 10%, the α value is calculated to be 0.081 using the identification method of the present invention, and the finally obtained first-order plus pure hysteresis model is:
Figure GDA0003557979760000103
the nyquist curve for model three is shown in fig. 3.
In fig. 1 to 3, the dotted line represents the simulation result of the method of the present invention, and the solid line represents the simulation result of the actual object. The simulation result shows that the identification method of the invention has higher identification precision even in a noisy environment, is suitable for different types of object models, and has good identification precision and applicability.
It should be noted that the embodiments of the present invention have been described in terms of preferred embodiments, and not by way of limitation, and that those skilled in the art can make modifications and variations of the embodiments described above without departing from the spirit of the invention.

Claims (6)

1. An online closed-loop frequency domain identification method of a process object is characterized by comprising the following steps:
performing laplace transform on the output signal y (t) and the input signal u (t) to obtain a laplace transform expression Y(s) of the output signal y (t) and a laplace transform expression U(s) of the input signal u (t);
introducing an attenuation factor alpha to calculate to obtain a transfer function expression G(s) based on the Laplace transform expression U(s) and the Laplace transform expression Y(s);
calculating the critical frequency omega based on the iterative formula and the transfer function expression G(s)c；
Based on the transfer function expression G(s) and the critical frequency omegacObtaining a first order plus pure lag transfer function by a least squares calculation, wherein
The step of performing laplace transform on the output signal y (t) and the input signal u (t) to obtain a laplace transform expression y(s) of the output signal y (t) and a laplace transform expression u(s) of the input signal u (t) comprises:
the laplace transform formula (1) is defined:
Figure FDA0003557979750000011
the laplace transforms u(s) and y(s) of the input signal u (t) and the output signal y (t) may be expressed as equation (2) and equation (3), respectively:
Figure FDA0003557979750000012
Figure FDA0003557979750000013
based on the Laplace transform expression U(s) and the Laplace transform expression Y(s), the step of introducing the attenuation factor alpha to calculate and obtain a transfer function expression G(s) comprises the following steps:
Based on a transfer function expression g(s) represented by formula (4):
Figure FDA0003557979750000014
taking s as j ω + α, introducing an attenuation factor α, and calculating a solution formula (5):
Figure FDA0003557979750000021
e-αTcequal to half the value of the step signal, where TcIs the time for the process object to reach the steady state response, α and TcSatisfies the relationship expressed by the following formula (6):
α＝ln(2)/Tc (6)
when the process object contains time-lag sections, α and TcSatisfies the relationship expressed by the following formula (7):
Figure FDA0003557979750000022
wherein T isLThe time after which the output signal lags.
2. The on-line closed-loop frequency domain identification method of claim 1,
calculating the critical frequency omega based on the iterative formula and the transfer function expression G(s)cComprises the following steps:
calculating the critical frequency omega according to the iterative formula (8)c：
Figure FDA0003557979750000023
Wherein ω and
Figure FDA0003557979750000024
are all set to 0 and,
Figure FDA0003557979750000025
expressed according to equation (9) as:
Figure FDA0003557979750000026
3. the on-line closed-loop frequency domain identification method of claim 2,
based on the transfer function expression G(s) and the critical frequency omegacThe step of obtaining the first-order plus pure lag transfer function by the least square calculation comprises:
a first order plus pure hysteresis model is employed according to equation (10):
Figure FDA0003557979750000027
where K is the static gain, T is the time constant, L is the pure lag coefficient, K, T, L is calculated according to equation (11) by applying a constant at ωnFrequency response point matching G (j ω + α) and G (j ω + α) of (n ═ 1, 2.. said., M) are obtained:
Figure FDA0003557979750000028
4. The on-line closed-loop frequency domain identification method of claim 3,
for frequency omeganThe amplitude and phase relationships in equation (11) are expressed by equation (12) and equation (13), respectively, as:
ωn 2|G(ωn+α)|2T2+|G(ωn+α)|2(Tα+1)2＝K2e-2Lα (12)
Figure FDA0003557979750000031
wherein n is 1, 2., M;
the magnitude relationship of equation (12) can be expressed by equation (14) as:
Φθ＝Γ (14)
wherein the content of the first and second substances,
Figure FDA0003557979750000032
Figure FDA0003557979750000033
θ in equation (14) is determined by equation (15):
θ＝(ΦTΦ)-1ΦTΓ (15)；
the time constant T is determined by θ and equation (16):
Figure FDA0003557979750000034
the pure hysteresis coefficient L is obtained by the phase relationship and equation (17):
Figure FDA0003557979750000035
the model parameter K is obtained by θ, the pure hysteresis coefficient L, and equation (18):
Figure FDA0003557979750000036
5. an online closed-loop frequency domain identification system of a process object, the online closed-loop frequency domain identification system comprising:
a transformation module, which performs laplace transformation on the output signal y (t) and the input signal u (t) to obtain a laplace transformation expression Y(s) of the output signal y (t) and a laplace transformation expression U(s) of the input signal u (t);
a calculation module for calculating a transfer function expression G(s) by introducing an attenuation factor alpha based on the Laplace transform expression U(s) and the Laplace transform expression Y(s), and calculating a critical frequency omega based on an iterative formula and the transfer function expression G(s) c；
An acquisition module based on the transfer function expression G(s) and the critical frequency omegacObtaining a first order plus pure lag transfer function by a least squares calculation wherein
The transform module defines the laplace transform formula (1):
Figure FDA0003557979750000041
the laplace transforms u(s) and y(s) of the input signal u (t) and the output signal y (t) may be expressed as equation (2) and equation (3), respectively:
Figure FDA0003557979750000042
Figure FDA0003557979750000043
the calculation module is based on a transfer function expression G(s) expressed by formula (4):
Figure FDA0003557979750000044
the obtaining module takes s as j omega + alpha, introduces an attenuation factor alpha, and calculates a solution formula (5):
Figure FDA0003557979750000045
e-αTcequal to half the value of the step signal, where TcIs the time for the process object to reach the steady state response, α and TcSatisfies the relationship expressed by the following formula (6):
α＝ln(2)/Tc (6)
when the process object contains time-lag sections, α and TcSatisfies the relationship expressed by the following formula (7):
Figure FDA0003557979750000046
wherein T isLThe time after which the output signal lags.
6. A computer-readable storage medium, on which a computer program is stored, which, when being executed by a processor, carries out the steps of any of claims 1-4.
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