CN113885322A - Dual-controller closed-loop system identification method based on slope response - Google Patents

Dual-controller closed-loop system identification method based on slope response Download PDF

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CN113885322A
CN113885322A CN202111150993.7A CN202111150993A CN113885322A CN 113885322 A CN113885322 A CN 113885322A CN 202111150993 A CN202111150993 A CN 202111150993A CN 113885322 A CN113885322 A CN 113885322A
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CN113885322B (en
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刘艳红
吴振龙
张赞
张宽
李朋真
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Zhengzhou University
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Abstract

The invention provides a dual-controller closed-loop system identification method based on slope response, and belongs to the technical field of automatic control. Subtracting the steady state value before the slope change of the set value from the set value of the closed-loop system and the output sequence set obtained by extraction to obtain the set value and an output first-stage sequence set, and obtaining the set value and an output second-stage sequence set by the set value and the output first-stage sequence set through mathematical calculation; and combining the known delay time constant of the object to be identified, the parameters of the series feedback controller, the set value and the output second-level sequence set, and calculating to obtain the parameters to be identified of the first-order inertia and pure delay system. The method can obtain the parameters to be identified of the second-order inertia and pure delay system through proper transformation. The method can identify the controlled object containing the double controllers, provides a model for control strategy design and optimization, and has certain application potential.

Description

Dual-controller closed-loop system identification method based on slope response
Technical Field
The invention belongs to the technical field of automatic control, and particularly relates to a dual-controller closed-loop system identification method based on slope response.
Background
With the increase of the industrial automation level, the requirement on the control performance is higher and higher. In order to improve the control performance of the system, how to design the control strategy and optimize the parameters of the control strategy becomes more important. However, control strategy design and parameter optimization requires a known system model. In order to ensure the safe operation of the system, the open-loop test is generally not allowed in the industrial production, although the identification method of the open-loop test is mature, the automatic input state needs to be changed into the manual operation state in the open-loop identification process, the continuity of the industrial production is interrupted, and certain cost increase is brought. In addition, in an industrial process, a series controller system exists, and the series controller system has two controllers, so that the current research on how to obtain a model of the series controller system under a closed-loop condition is relatively deficient. In addition, since the set value generally changes at a certain rate when changing, and the change of the set value is not a step response in a strict sense but a ramp response, it is necessary to research a dual-controller closed-loop system identification method based on the ramp response. In the industrial process, most processes can be described by a transfer function system of first-order inertia plus pure delay or second-order inertia plus delay, and as the time constant of delay can be directly obtained according to the relation of input and output data of a closed-loop system, other parameters in the first-order inertia or the second-order inertia need to be identified.
Therefore, the closed-loop identification method for the slope data and the output data of the closed-loop system in the industrial process based on the double-controller system is provided, the problem of the closed-loop identification method of the double-controller system can be solved, a model basis is provided for further control strategy design and parameter optimization, and an advanced control method is implemented, so that the method has a strong industrial application value and a strong application prospect.
Disclosure of Invention
The invention aims to solve the problem of closed-loop identification of a system containing double controllers, and provides a dual-controller closed-loop system identification method based on slope response.
The invention provides a dual-controller closed-loop system identification method based on slope response in a first aspect, which comprises the following steps:
1) describing an object to be identified by adopting a transfer function of first-order inertia plus pure delay, wherein the mathematical expression of the object to be identified is as follows:
Figure BDA0003287093370000011
wherein G(s) is a transfer function of the object, s and tau are respectively a differential operator and a delay time constant known by the object to be identified, a1 and a2The parameter to be identified is the object to be identified;
2) extracting a set value sequence set R of a closed-loop system consisting of an object to be identified, two feedback controllers and a feedforward controller in the same time period before and after the slope change of the set value0And output sequence set Y0；
3) The steady state value of the closed loop system before the set value is changed in a slope is rssSetting value sequence set R extracted in step 2)0And output sequence set Y0Subtracting a steady state value r from each of the datassRespectively obtaining a first-level sequence set R of a set value1And outputting the first level sequence set Y1；
4) The amplitude value of the slope response of the set value of the closed loop system is l, the slope is gamma, and the maximum integer not exceeding tau/delta T is defined as
Figure BDA00032870933700000210
The maximum integer not exceeding (tau + l/gamma)/delta T is xi; for the set value obtained in the step 3), a first-level sequence set R is obtained1The data in the sequence table is subjected to algebraic transformation to obtain a set value second-level sequence set R01、R11、R21、R31 and R41The data of (1); set value second level sequence set R01、R11、R21、R31 and R41The data length of the medium data is n;
5) for the output primary sequence set Y obtained in the step 3)1The data in (2) is calculated to obtain an output second-level sequence set Y01、Y10、Y11、Y21、Y31 and Y41The data of (1); second level sequence set Y01、Y10、Y11、Y21、Y31 and Y41The data length of the medium data is n;
6) two series feedback controllers in the closed loop system are respectively Gc1(s) and Gc2(s)；
For the set value obtained in the step 4), a second-level sequence set R is obtained01、R11、R21、R31 and R41The data in (5) and the output second level sequence set Y obtained in step 5)01、Y10、Y11、Y21、Y31 and Y41In combination with a feedback controller Gc1(s) and Gc2Parameters in(s) are subjected to algebraic transformation to obtain a sequence set theta1 and θ2The data of (1);
7) the sequence set theta obtained in the step 6) is added1 and θ2Transforming to obtain a sequence set theta; the mathematical calculation of the sequence set θ is as follows:
Figure BDA0003287093370000021
wherein
Figure BDA0003287093370000022
And
Figure BDA0003287093370000023
respectively a sequence set theta1Transposed and sequence set θ of2Transposing;
8) parameter a to be identified of object to be identified1 and a2Composed parameter vector
Figure BDA0003287093370000024
Outputting the first-level sequence set Y obtained by the step 3)1And calculating the sequence set theta obtained in the step 7);
coefficient a to be identified of object to be identified1 and a2Composed parameter vector
Figure BDA0003287093370000025
Parameter vector
Figure BDA0003287093370000026
The form of (A) is as follows:
Figure BDA0003287093370000027
parameter vector
Figure BDA0003287093370000028
The calculation formula of (a) is as follows:
Figure BDA0003287093370000029
wherein ,
Figure BDA0003287093370000031
θT and Y1 TAre respectively parameter vectors
Figure BDA0003287093370000034
Transpose of (2), transpose of sequence set θ, and output first level sequence set Y1Transpose of (θ)Tθ)-1Is thetaTMatrix inversion of theta;
thereby identifying the parameter a to be identified of the object to be identified1 and a2And obtaining a transfer function of the object to be identified and optimizing a control strategy of the object to be identified.
The invention provides a dual-controller closed-loop system identification method based on slope response, which aims at an object to be identified by second-order inertia plus pure delay and comprises the following steps:
1) describing an object to be identified by adopting a transfer function of second-order inertia plus pure delay, wherein the mathematical expression of the object to be identified is as follows:
Figure BDA0003287093370000032
wherein G(s) is a transfer function of the object, s and tau are respectively a differential operator and a delay time constant known by the object to be identified, a1、a2 and a3The parameter to be identified is the object to be identified;
2) extracting a set value sequence set R of a closed-loop system consisting of an object to be identified, two feedback controllers and a feedforward controller in the same time period before and after the slope change of the set value0And output sequence set Y0；
3) The steady state value of the closed loop system before the set value is changed in a slope is rssSetting value sequence set R extracted in step 2)0And output sequence set Y0Subtracting a steady state value r from each of the datassRespectively obtaining a first-level sequence set R of a set value1And outputting the first level sequence set Y1；
4) The amplitude value of the slope response of the set value of the closed loop system is l, the slope is gamma, and the maximum integer not exceeding tau/delta T is defined as
Figure BDA0003287093370000033
The maximum integer not exceeding (tau + l/gamma)/delta T is xi; for the set value obtained in the step 3), a first-level sequence set R is obtained1The data in the sequence table is subjected to algebraic transformation to obtain a set value second-level sequence set R11、R21、R31、R41 and R51The data of (1); set value second level sequence set R11、R21、R31、R41 and R51The data length of the medium data is n;
5) for the output primary sequence set Y obtained in the step 3)1The data in (2) is calculated to obtain an output second-level sequence set Y10、Y20、Y11、Y21、Y31、Y41 and Y51The data of (1); second level sequence set Y10、Y20、Y11、Y21、Y31、Y41 and Y51The data length of the medium data is n;
6) two series feedback controllers in a closed loop systemAre each Gc1(s) and Gc2(s), feedback controller Gc1(s) and Gc2The mathematical expressions of(s) are respectively as follows:
Figure BDA0003287093370000041
Figure BDA0003287093370000042
wherein ,kp1、ki1 and kd1Is a feedback controller Gc1(s) known parameters, respectively Gc1(s) a proportional gain coefficient, an integral gain coefficient, and a differential gain coefficient; wherein k isp2、ki2 and kd2Is a feedback controller Gc2(s) known parameters, respectively Gc2(s) a proportional gain coefficient, an integral gain coefficient, and a differential gain coefficient;
for the set value obtained in the step 4), a second-level sequence set R is obtained11、R21、R31、R41 and R51The data in (5) and the output second level sequence set Y obtained in step 5)10、Y20、Y11、Y21、Y31、Y41 and Y51In combination with a feedback controller Gc1(s) and Gc2Parameters in(s) are subjected to algebraic transformation to obtain a sequence set theta1、θ2 and θ3The data of (1);
7) the sequence set theta obtained in the step 6) is added1、θ2 and θ3Transforming to obtain a sequence set theta; the mathematical calculation of the sequence set θ is as follows:
Figure BDA0003287093370000043
wherein ,
Figure BDA0003287093370000044
and
Figure BDA0003287093370000045
respectively a sequence set theta1Transposed, sequence set θ of2Transposed and sequence set θ of3Transposing;
8) parameter a to be identified of object to be identified1、a2 and a3Composed parameter vector
Figure BDA0003287093370000046
Outputting the first-level sequence set Y obtained by the step 3)1And calculating the sequence set theta obtained in the step 7);
coefficient a to be identified of object to be identified1、a2 and a3Composed parameter vector
Figure BDA0003287093370000047
Parameter vector
Figure BDA0003287093370000048
The form of (A) is as follows:
Figure BDA0003287093370000049
parameter vector
Figure BDA00032870933700000410
The calculation formula of (a) is as follows:
Figure BDA00032870933700000411
wherein ,
Figure BDA00032870933700000412
θT and Y1 TAre respectively parameter vectors
Figure BDA00032870933700000413
Transpose of (2), transpose of sequence set θ, and output first level sequence set Y1Transpose of (θ)Tθ)-1Is thetaTMatrix inversion of theta;
thereby identifying the parameter a to be identified of the object to be identified1、a2 and a3And obtaining a transfer function of the object to be identified and optimizing a control strategy of the object to be identified.
The invention provides a dual-controller closed-loop system, which comprises two feedback controllers and an object to be identified, wherein the two feedback controllers and the object to be identified are sequentially connected in series.
The method can identify the controlled object as a continuous system of first-order inertia plus pure delay or second-order inertia plus pure delay or delay time constant of a system to be identified based on the sequence set of the set value of the closed-loop system and the output sequence set, two feedback controllers and the delay time constant of the system to be identified, can effectively avoid the operation of the system for open-loop identification, can be directly applied to the design and parameter optimization of a control strategy, provides a model base for the implementation of an advanced control method, and has strong industrial application value and application prospect.
Drawings
FIG. 1 is a closed loop control system for a dual controller.
FIG. 2 is a set of values, an output sequence set, and a trend of the output of the recognition model in example 3.
Detailed Description
Example 1
The embodiment provides a dual-controller closed-loop system identification method based on slope response, which comprises the following steps:
1) describing an object to be identified by adopting a transfer function of first-order inertia plus pure delay, wherein the mathematical expression of the object to be identified is as follows:
Figure BDA0003287093370000051
whereinG(s) is the transfer function of the object, s and tau are the known delay time constants of the differential operator and the object to be identified, respectively, a1 and a2The parameter to be identified is the object to be identified; the delay time constant of the object to be identified is generally more than or equal to 0 and less than or equal to 100.
2) Extracting a set value sequence set R of a closed-loop system consisting of an object to be identified, two feedback controllers and a feedforward controller in the same time period before and after the slope change of the set value0And output sequence set Y0The data length is n +1, and the sampling period is delta T; set value sequence set R0And output sequence set Y0The form of (A) is as follows:
R0＝[r0(1),…,r0(i),…,r0(n+1)]
Y0＝[y0(1),…,y0(i),…,y0(n+1)]；
wherein i represents the position of the data in the sequence set, and i is more than or equal to 1 and less than or equal to n + 1; r is0(1)、r0(i) and r0(n +1) are the first data, the ith data and the (n +1) th data of the set value sequence set respectively; y is0(1)、y0(i) and y0(n +1) are the first data, the ith data and the (n +1) th data of the output sequence set respectively; the extracted data length is generally 400-n.100000, and the sampling period of a typical industrial process is generally 0.01 s.DELTA.T.ltoreq.10 s.
3) The steady state value of the closed loop system before the set value is changed in a slope is rssSetting value sequence set R extracted in step 2)0And output sequence set Y0Subtracting a steady state value r from each of the datassRespectively obtaining a first-level sequence set R of a set value1And outputting the first level sequence set Y1；
Set value first order sequence set R1And outputting the first level sequence set Y1Each of the data can be calculated by:
r1(1)＝r0(1)-rss
r1(i)＝r0(i)-rss
r1(n+1)＝r0(n+1)-rss
y1(1)＝y0(1)-rss
y1(i)＝y0(i)-rss
y1(n+1)＝y0(n+1)-rss；
wherein ,r1(1)、r1(i) and r1(n +1) are respectively set values of a first-level sequence set R1The first data, the ith data, and the n +1 th data; y is1(1)、y1(i) and y1(n +1) are respectively output first-stage sequence sets Y1The first data, the ith data, and the n +1 th data; the steady state value of the closed loop system at the beginning stage of data extraction is determined according to the actual physical quantity, and is generally equal to or more than 0.01 and less than rss≤1000；
Set value first order sequence set R1And outputting the first level sequence set Y1In the form of:
R1＝[r1(1),…,r1(i),…,r1(n+1)]
Y1＝[y1(1),…,y1(i),…,y1(n+1)]。
4) the amplitude value of the slope response of the set value of the closed loop system is l, the slope is gamma, and the maximum integer not exceeding tau/delta T is defined as
Figure BDA0003287093370000062
The maximum integer not exceeding (τ + l γ)/Δ T is ξ; for the set value obtained in the step 3), a first-level sequence set R is obtained1The data in the sequence table is subjected to algebraic transformation to obtain a set value second-level sequence set R01、R11、R21、R31 and R41The data of (1); set value second level sequence set R01、R11、R21、R31 and R41The data length of the medium data is n; generally comprises
Figure BDA0003287093370000063
L is more than or equal to 1 and less than or equal to 1000, gamma is more than or equal to 0.001 and less than or equal to 10000, and xi is more than or equal to 1 and less than or equal to 1000;
set value second level sequence set R01、R11、R21、R31 and R41The mathematical calculation of the data in (1) is as follows:
Figure BDA0003287093370000061
Figure BDA0003287093370000071
Figure BDA0003287093370000072
Figure BDA0003287093370000073
Figure BDA0003287093370000074
wherein ,r01(i)、r11(i)、r21(i)、r31(i) and r41(i) Set value second level sequence set R01、R11、R21、R31 and R41The ith data in (1); set value second level sequence set R01、R11、R21、R31 and R41In the form of:
R01＝[r01(1),…,r01(i),…,r01(n)]
R11＝[r11(1),…,r11(i),…,r11(n)]
R21＝[r21(1),…,r21(i),…,r21(n)]
R31＝[r31(1),…,r31(i),…,r31(n)]
R41＝[r41(1),…,r41(i),…,r41(n)]。
5) for the output primary sequence set Y obtained in the step 3)1The data in (2) is calculated to obtain an output second-level sequence set Y01、Y10、Y11、Y21、Y31 and Y41The data of (1); second level sequence set Y01、Y10、Y11、Y21、Y31 and Y41The data length of the medium data is n;
outputting a second level sequence set Y01、Y10、Y11、Y21、Y31 and Y41The data in (1) are obtained by the following formula:
Figure BDA0003287093370000081
Figure BDA0003287093370000082
Figure BDA0003287093370000083
Figure BDA0003287093370000084
Figure BDA0003287093370000085
Figure BDA0003287093370000086
wherein j is the position of the data in the sequence set which exceeds i, and j is more than or equal to 1 and less than or equal to i; y is01(i)、y10(i)、y11(i)、y21(i)、y31(i) and y41(i) Respectively, outputting a second level sequence set Y01、Y10、Y11、Y21、Y31 and Y41The ith data in (1); outputting a second level sequence set Y01、Y10、Y11、Y21、Y31 and Y41In the form of:
Y01＝[y01(1),…,y01(i),…,y01(n)]
Y10＝[y10(1),…,y10(i),…,y10(n)]
Y11＝[y11(1),…,y11(i),…,y11(n)]
Y21＝[y21(1),…,y21(i),…,y21(n)]
Y31＝[y31(1),…,y31(i),…,y31(n)]
Y41＝[y41(1),…,y41(i),…,y41(n)]。
6) two series feedback controllers in the closed loop system are respectively Gc1(s) and Gc2(s), feedback controller Gc1(s) and Gc2The mathematical expressions of(s) are respectively as follows:
Figure BDA0003287093370000087
Figure BDA0003287093370000091
wherein ,kp1、ki1 and kd1Is a feedback controller Gc1(s) known parameters, respectively Gc1(s) a proportional gain coefficient, an integral gain coefficient, and a differential gain coefficient; wherein k isp2、ki2 and kd2Is a feedback controller Gc2(s) known parameters, respectively Gc2(s) a proportional gain coefficient, an integral gain coefficient, and a differential gain coefficient; feedback controllerGc1The parameter(s) is generally-105≤kp1≤105、-105≤ki1≤105 and -105≤kd1≤105(ii) a Feedback controller Gc2The parameter(s) is generally-105≤kp2≤105、-105≤ki2≤105 and -105≤kd2≤105；
For the set value obtained in the step 4), a second-level sequence set R is obtained01、R11、R21、R31 and R41The data in (5) and the output second level sequence set Y obtained in step 5)01、Y10、Y11、Y21、Y31 and Y41In combination with a feedback controller Gc1(s) and Gc2Parameters in(s) are subjected to algebraic transformation to obtain a sequence set theta1 and θ2The data of (1);
sequence set theta1 and θ2The mathematical calculation of the data in (1) is as follows:
θ1(i)＝kd1kd2r01(i)+(kp1kd2+kd1kp2)r11(i)+(kp1kp2+ki1kd2+kd1ki2)r21(i)+(kp1ki2+ki1kp2)r31(i)+ki1ki2r41(i)-kd1kd2y01(i)-(kp1kd2+kd1kp2)y11(i)-(kp1kp2+ki1kd2+kd1ki2)y21(i)-(kp1ki2+ki1kp2)y31(i)-ki1ki2y41(i)
θ2(i)＝-y10(i)；
wherein ,θ1(i) and θ2(i) Are respectively a sequence set theta1 and θ2The ith data in (1); sequence set theta1 and θ2Form (1) ofRespectively as follows:
θ1＝[θ1(1),…,θ1(i),…,θ1(n)]
θ2＝[θ2(1),…,θ2(i),…,θ2(n)]。
7) the sequence set theta obtained in the step 6) is added1 and θ2Transforming to obtain a sequence set theta; the mathematical calculation of the sequence set θ is as follows:
Figure BDA0003287093370000092
wherein
Figure BDA0003287093370000093
And
Figure BDA0003287093370000094
respectively a sequence set theta1Transposed and sequence set θ of2The transposing of (1).
8) Parameter a to be identified of object to be identified1 and a2Composed parameter vector
Figure BDA0003287093370000095
The output first-level sequence set Y obtained by the step 3)1And calculating the sequence set theta obtained in the step 7);
coefficient a to be identified of object to be identified1 and a2Composed parameter vector
Figure BDA0003287093370000096
Parameter vector
Figure BDA0003287093370000097
The form of (A) is as follows:
Figure BDA0003287093370000101
parameter vector
Figure BDA0003287093370000102
The calculation formula of (a) is as follows:
Figure BDA0003287093370000103
wherein ,
Figure BDA0003287093370000104
θT and Y1 TAre respectively parameter vectors
Figure BDA0003287093370000105
Transpose of (2), transpose of sequence set θ, and output first level sequence set Y1Transpose of (θ)Tθ)-1Is thetaTMatrix inversion of θ.
9) Completing the steps 1) -8) can complete a feedforward-considered series controller closed-loop system identification method, which can identify the parameter a to be identified of the object to be identified1 and a2Combining the known delay time constant tau of the object to be identified in the step 1) to obtain a transfer function of the object to be identified; and analyzing the dynamic characteristics of the object according to the obtained transfer function, and optimizing the control strategy of the object to be identified.
According to the steps, the implementation of the dual-controller closed-loop system identification method based on the ramp response can be completed.
Example 2
The embodiment provides a dual-controller closed-loop system identification method based on slope response for a second-order inertia plus pure delay object to be identified, which comprises the following steps:
1) describing an object to be identified by adopting a transfer function of second-order inertia plus pure delay, wherein the mathematical expression of the object to be identified is as follows:
Figure BDA0003287093370000106
wherein G(s) is a transfer function of the object, and s and τ areDifferential operator and known delay time constant of object to be identified, a1、a2 and a3The parameter to be identified is the object to be identified; the delay time constant of the object to be identified is generally more than or equal to 0 and less than or equal to 100.
2) Extracting a set value sequence set R of a closed-loop system consisting of an object to be identified, two feedback controllers and a feedforward controller in the same time period before and after the slope change of the set value0And output sequence set Y0The data length is n, and the sampling period is delta T; set value sequence set R0And output sequence set Y0The form of (A) is as follows:
R0＝[r0(1),…,r0(i),…,r0(n)]
Y0＝[y0(1),…,y0(i),…,y0(n)]；
wherein i represents the position of the data in the sequence set, and i is more than or equal to 1 and less than or equal to n; r is0(1)、r0(i) and r0(n) the first data, the ith data and the nth data of the set value sequence set respectively; y is0(1)、y0(i) and y0(n) the first data, the ith data and the nth data of the output sequence set respectively; (ii) a The extracted data length is generally 400-n.100000, and the sampling period of a typical industrial process is generally 0.01 s.DELTA.T.ltoreq.10 s.
3) The steady state value of the closed loop system before the set value is changed in a slope is rssSetting value sequence set R extracted in step 2)0And output sequence set Y0Subtracting a steady state value r from each of the datassRespectively obtaining a first-level sequence set R of a set value1And outputting the first level sequence set Y1；
Set value first order sequence set R1And outputting the first level sequence set Y1Each of the data can be calculated by:
r1(1)＝r0(1)-rss
r1(i)＝r0(i)-rss
r1(n)＝r0(n)-rss
y1(1)＝y0(1)-rss
y1(i)＝y0(i)-rss
y1(n)＝y0(n)-rss；
wherein ,r1(1)、r1(i) and r1(n) first-level sequence sets R respectively being set values1The first data, the ith data and the nth data of (a); y is1(1)、y1(i) and y1(n) respectively output first level sequence set Y1The first data, the ith data and the nth data of (a); the steady state value of the closed loop system at the beginning stage of data extraction is determined according to the actual physical quantity, and is generally equal to or more than 0.01 and less than rss≤1000；
Set value first order sequence set R1And outputting the first level sequence set Y1In the form of:
R1＝[r1(1),…,r1(i),…,r1(n)]
Y1＝[y1(1),…,y1(i),…,y1(n)]。
4) the amplitude value of the slope response of the set value of the closed loop system is l, the slope is gamma, and the maximum integer not exceeding tau/delta T is defined as
Figure BDA0003287093370000111
The maximum integer not exceeding (τ + l γ)/Δ T is ξ; for the set value obtained in the step 3), a first-level sequence set R is obtained1The data in the sequence table is subjected to algebraic transformation to obtain a set value second-level sequence set R11、R21、R31、R41 and R51The data of (1); set value second level sequence set R11、R21、R31、R41 and R51The data length of the medium data is n; generally comprises
Figure BDA0003287093370000112
L is more than or equal to 1 and less than or equal to 1000, gamma is more than or equal to 0.001 and less than or equal to 10000, and xi is more than or equal to 1 and less than or equal to 1000;
set value second level sequence set R11、R21、R31、R41 and R51The mathematical calculation of the data in (1) is as follows:
Figure BDA0003287093370000121
Figure BDA0003287093370000122
Figure BDA0003287093370000123
Figure BDA0003287093370000124
Figure BDA0003287093370000125
wherein ,r11(i)、r21(i)、r31(i)、r41(i) and r51(i) Set value second level sequence set R11、R21、R31、R41 and R51The ith data in (1); set value second level sequence set R11、R21、R31、R41 and R51In the form of:
R11＝[r11(1),…,r11(i),…,r11(n)]
R21＝[r21(1),…,r21(i),…,r21(n)]
R31＝[r31(1),…,r31(i),…,r31(n)]
R41＝[r41(1),…,r41(i),…,r41(n)]
R51＝[r51(1),…,r51(i),…,r51(n)]。
5) for the output primary sequence set Y obtained in the step 3)1The data in (2) is calculated to obtain an output second-level sequence set Y10、Y20、Y11、Y21、Y31、Y41 and Y51The data of (1); second level sequence set Y10、Y20、Y11、Y21、Y31、Y41 and Y51The data length of the medium data is n;
outputting a second level sequence set Y10、Y20、Y11、Y21、Y31、Y41 and Y51The data in (1) can be obtained by the following formula:
Figure BDA0003287093370000131
Figure BDA0003287093370000132
Figure BDA0003287093370000133
Figure BDA0003287093370000134
Figure BDA0003287093370000135
Figure BDA0003287093370000136
Figure BDA0003287093370000137
wherein j is the position of the data in the sequence set which exceeds i, and j is more than or equal to 1 and less than or equal to i; y is10(i)、y20(i)、y11(i)、y21(i)、y31(i)、y41(i) and y51(i) Respectively, outputting a second level sequence set Y10、Y20、Y11、Y21、Y31、Y41 and Y51The ith data in (1); outputting a second level sequence set Y10、Y20、Y11、Y21、Y31、Y41 and Y51In the form of:
Y10＝[y10(1),…,y10(i),…,y10(n)]
Y20＝[y20(1),…,y20(i),…,y20(n)]
Y11＝[y11(1),…,y11(i),…,y11(n)]
Y21＝[y21(1),…,y21(i),…,y21(n)]
Y31＝[y31(1),…,y31(i),…,y31(n)]
Y41＝[y41(1),…,y41(i),…,y41(n)]
Y51＝[y51(1),…,y51(i),…,y51(n)]。
6) two series feedback controllers in the closed loop system are respectively Gc1(s) and Gc2(s), feedback controller Gc1(s) and Gc2The mathematical expressions of(s) are respectively as follows:
Figure BDA0003287093370000141
Figure BDA0003287093370000142
wherein ,kp1、ki1 and kd1Is reversedFeed controller Gc1(s) known parameters, respectively Gc1(s) a proportional gain coefficient, an integral gain coefficient, and a differential gain coefficient; wherein k isp2、ki2 and kd2Is a feedback controller Gc2(s) known parameters, respectively Gc2(s) a proportional gain coefficient, an integral gain coefficient, and a differential gain coefficient; feedback controller Gc1The parameter(s) is generally-105≤kp1≤105、-105≤ki1≤105 and -105≤kd1≤105(ii) a Feedback controller Gc2The parameter(s) is generally-105≤kp2≤105、-105≤ki2≤105 and -105≤kd2≤105；
For the set value obtained in the step 4), a second-level sequence set R is obtained11、R21、R31、R41 and R51The data in (5) and the output second level sequence set Y obtained in step 5)10、Y20、Y11、Y21、Y31、Y41 and Y51In combination with a feedback controller Gc1(s) and Gc2Parameters in(s) are subjected to algebraic transformation to obtain a sequence set theta1、θ2 and θ3The data of (1);
sequence set theta1、θ2 and θ3The mathematical calculation of the data in (1) is as follows:
θ1(i)＝kd1kd2r11(i)+(kp1kd2+kd1kp2)r21(i)+(kp1kp2+ki1kd2+kd1ki2)r31(i)+(kp1ki2+ki1kp2)r41(i)+ki1ki2r51(i)-kd1kd2y11(i)-(kp1kd2+kd1kp2)y21(i)-(kp1kp2+ki1kd2+kd1ki2)y31(i)-(kp1ki2+ki1kp2)y41(i)-ki1ki2y51(i)
θ2(i)＝-y10(i)
θ3(i)＝-y20(i)；
wherein ,θ1(i)、θ2(i) and θ3(i) Are respectively a sequence set theta1、θ2 and θ3The ith data in (1); sequence set theta1、θ2 and θ3In the form of:
θ1＝[θ1(1),…,θ1(i),…,θ1(n)]
θ2＝[θ2(1),…,θ2(i),…,θ2(n)]
θ3＝[θ3(1),…,θ3(i),…,θ3(n)]。
7) the sequence set theta obtained in the step 6) is added1、θ2 and θ3Transforming to obtain a sequence set theta; the mathematical calculation of the sequence set θ is as follows:
Figure BDA0003287093370000151
wherein ,
Figure BDA0003287093370000152
and
Figure BDA0003287093370000153
respectively a sequence set theta1Transposed, sequence set θ of2Transposed and sequence set θ of3The transposing of (1).
8) Parameter a to be identified of object to be identified1、a2 and a3Composed parameter vector
Figure BDA0003287093370000154
The output first-level sequence set Y obtained by the step 3)1And the sequence obtained in step 7)Calculating a column set theta;
coefficient a to be identified of object to be identified1、a2 and a3Composed parameter vector
Figure BDA0003287093370000155
Parameter vector
Figure BDA0003287093370000156
The form of (A) is as follows:
Figure BDA0003287093370000157
parameter vector
Figure BDA0003287093370000158
The calculation formula of (a) is as follows:
Figure BDA0003287093370000159
wherein ,
Figure BDA00032870933700001510
θT and Y1 TAre respectively parameter vectors
Figure BDA00032870933700001511
Transpose of (2), transpose of sequence set θ, and output first level sequence set Y1Transpose of (θ)Tθ)-1Is thetaTMatrix inversion of θ.
9) Completing the steps 1) -8) can complete a feedforward-considered series controller closed-loop system identification method, which can identify the parameter a to be identified of the object to be identified1、a2 and a3Combining the known delay time constant tau of the object to be identified in the step 1) to obtain a transfer function of the object to be identified; and analyzing the dynamic characteristics of the object according to the obtained transfer function, and optimizing the control strategy of the object to be identified.
According to the steps, the implementation of the dual-controller closed-loop system identification method based on the slope response aiming at the second-order inertia plus the pure delay to-be-identified object can be completed.
Example 3
The technical superiority of the invention is illustrated by simulation:
1) describing an object to be identified by adopting a transfer function of first-order inertia plus pure delay, wherein the mathematical expression of the object to be identified is as follows:
Figure BDA0003287093370000161
wherein G(s) is a transfer function of the object, s and tau are respectively a differential operator and a delay time constant known by the object to be identified, a1 and a2The parameter to be identified is the object to be identified; in the embodiment, the delay time constant of the object to be recognized is τ 6.
2) Extracting a set value sequence set R of a closed-loop system consisting of an object to be identified, two feedback controllers and a feedforward controller in the same time period before and after the slope change of the set value0And output sequence set Y0The data length is n +1, and the sampling period is delta T; set value sequence set R0And output sequence set Y0The form of (A) is as follows:
R0＝[r0(1),…,r0(i),…,r0(n+1)]
Y0＝[y0(1),…,y0(i),…,y0(n+1)]；
wherein i represents the position of the data in the sequence set, and i is more than or equal to 1 and less than or equal to n + 1; r is0(1)、r0(i) and r0(n +1) are the first data, the ith data and the (n +1) th data of the set value sequence set respectively; y is0(1)、y0(i) and y0(n +1) are the first data, the ith data and the (n +1) th data of the output sequence set respectively; the data length extracted in this embodiment is n-4000, and the sampling period in this embodiment is Δ T-1 s.
3) The steady state value of the closed loop system before the set value is changed in a slope is rssSetting value sequence set R extracted in step 2)0And output sequence set Y0Subtracting a steady state value r from each of the datassRespectively obtaining a first-level sequence set R of a set value1And outputting the first level sequence set Y1；
Set value first order sequence set R1And outputting the first level sequence set Y1Each of the data can be calculated by:
r1(1)＝r0(1)-rss
r1(i)＝r0(i)-rss
r1(n+1)＝r0(n+1)-rss
y1(1)＝y0(1)-rss
y1(i)＝y0(i)-rss
y1(n+1)＝y0(n+1)-rss；
wherein ,r1(1)、r1(i) and r1(n +1) are respectively set values of a first-level sequence set R1The first data, the ith data, and the n +1 th data; y is1(1)、y1(i) and y1(n +1) are respectively output first-stage sequence sets Y1The first data, the ith data, and the n +1 th data; in this embodiment, the steady state value of the closed loop system before the set value slope response is rss＝0；
Set value first order sequence set R1And outputting the first level sequence set Y1In the form of:
R1＝[r1(1),…,r1(i),…,r1(n+1)]
Y1＝[y1(1),…,y1(i),…,y1(n+1)]。
4) the amplitude value of the slope response of the set value of the closed loop system is l, the slope is gamma, and the maximum integer not exceeding tau/delta T is defined as
Figure BDA0003287093370000175
Not exceeding (tau + l/gamma)/delta TThe maximum integer is xi; for the set value obtained in the step 3), a first-level sequence set R is obtained1The data in the sequence table is subjected to algebraic transformation to obtain a set value second-level sequence set R01、R11、R21、R31 and R41The data of (1); set value second level sequence set R01、R11、R21、R31 and R41Data length n in the present embodiment is 3000; in this embodiment, the maximum integer not exceeding τ/Δ T is
Figure BDA0003287093370000176
l ═ 5, γ ═ 0.005, and ξ ═ 1006;
set value second level sequence set R01、R11、R21、R31 and R41The mathematical calculation of the data in (1) is as follows:
Figure BDA0003287093370000171
Figure BDA0003287093370000172
Figure BDA0003287093370000173
Figure BDA0003287093370000174
Figure BDA0003287093370000181
wherein ,r01(i)、r11(i)、r21(i)、r31(i) and r41(i) Set value second level sequence set R01、R11、R21、R31 and R41The ith data in (1); set valueSecond level sequence set R01、R11、R21、R31 and R41In the form of:
R01＝[r01(1),…,r01(i),…,r01(n)]
R11＝[r11(1),…,r11(i),…,r11(n)]
R21＝[r21(1),…,r21(i),…,r21(n)]
R31＝[r31(1),…,r31(i),…,r31(n)]
R41＝[r41(1),…,r41(i),…,r41(n)]。
5) for the output primary sequence set Y obtained in the step 3)1The data in (2) is calculated to obtain an output second-level sequence set Y01、Y10、Y11、Y21、Y31 and Y41The data of (1); second level sequence set Y01、Y10、Y11、Y21、Y31 and Y41The data length of the medium data is n;
outputting a second level sequence set Y01、Y10、Y11、Y21、Y31 and Y41The data can be obtained as follows:
Figure BDA0003287093370000182
Figure BDA0003287093370000183
Figure BDA0003287093370000184
Figure BDA0003287093370000185
Figure BDA0003287093370000186
Figure BDA0003287093370000191
wherein j is the position of the data in the sequence set which exceeds i, and j is more than or equal to 1 and less than or equal to i; y is01(i)、y10(i)、y11(i)、y21(i)、y31(i) and y41(i) Respectively, outputting a second level sequence set Y01、Y10、Y11、Y21、Y31 and Y41The ith data in (1); outputting a second level sequence set Y01、Y10、Y11、Y21、Y31 and Y41In the form of:
Y01＝[y01(1),…,y01(i),…,y01(n)]
Y10＝[y10(1),…,y10(i),…,y10(n)]
Y11＝[y11(1),…,y11(i),…,y11(n)]
Y21＝[y21(1),…,y21(i),…,y21(n)]
Y31＝[y31(1),…,y31(i),…,y31(n)]
Y41＝[y41(1),…,y41(i),…,y41(n)]。
6) two series feedback controllers in the closed loop system are respectively Gc1(s) and Gc2(s), feedback controller Gc1(s) and Gc2The mathematical expressions of(s) are respectively as follows:
Figure BDA0003287093370000192
Figure BDA0003287093370000193
wherein ,kp1、ki1 and kd1Is a feedback controller Gc1(s) known parameters, respectively Gc1(s) a proportional gain coefficient, an integral gain coefficient, and a differential gain coefficient; wherein k isp2、ki2 and kd2Is a feedback controller Gc2(s) known parameters, respectively Gc2(s) a proportional gain coefficient, an integral gain coefficient, and a differential gain coefficient; in this example kp1＝0.03、ki10.015 and kd1＝0；kp2＝1、ki20.001 and kd2＝0；
For the set value obtained in the step 4), a second-level sequence set R is obtained01、R11、R21、R31 and R41The data and the output second level sequence set Y obtained in the step 5)01、Y10、Y11、Y21、Y31 and Y41In combination with a feedback controller Gc1(s) and Gc2Parameters in(s) are subjected to algebraic transformation to obtain a sequence set theta1 and θ2The data of (1);
sequence set theta1 and θ2The mathematical calculation of the data in (1) is as follows:
θ1(i)＝kd1kd2r01(i)+(kp1kd2+kd1kp2)r11(i)+(kp1kp2+ki1kd2+kd1ki2)r21(i)+(kp1ki2+ki1kp2)r31(i)+ki1ki2r41(i)-kd1kd2y01(i)-(kp1kd2+kd1kp2)y11(i)-(kp1kp2+ki1kd2+kd1ki2)y21(i)-(kp1ki2+ki1kp2)y31(i)-ki1ki2y41(i)
θ2(i)＝-y10(i)；
wherein ,θ1(i) and θ2(i) Are respectively a sequence set theta1 and θ2The ith data in (1); sequence set theta1 and θ2In the form of:
θ1＝[θ1(1),…,θ1(i),…,θ1(n)]
θ2＝[θ2(1),…,θ2(i),…,θ2(n)]。
7) the sequence set theta obtained in the step 6) is added1 and θ2Transforming to obtain a sequence set theta; the mathematical calculation of the sequence set θ is as follows:
Figure BDA0003287093370000201
wherein ,
Figure BDA0003287093370000202
and
Figure BDA0003287093370000203
respectively a sequence set theta1Transposed and sequence set θ of2The transposing of (1).
8) Parameter a to be identified of object to be identified1 and a2Composed parameter vector
Figure BDA0003287093370000204
The output first-level sequence set Y obtained by the step 3)1And calculating the sequence set theta obtained in the step 7);
coefficient a to be identified of object to be identified1 and a2Composed parameter vector
Figure BDA0003287093370000205
Parameter vector
Figure BDA0003287093370000206
The form of (A) is as follows:
Figure BDA0003287093370000207
parameter vector
Figure BDA0003287093370000208
The calculation formula of (a) is as follows:
Figure BDA0003287093370000209
wherein ,
Figure BDA00032870933700002010
θT and Y1 TAre respectively parameter vectors
Figure BDA00032870933700002011
Transpose of (2), transpose of sequence set θ, and output first level sequence set Y1Transpose of (θ)Tθ)-1Is thetaTMatrix inversion of theta; in this example a10.0417 and a2＝0.0333。
9) Completing the steps 1) -8) can complete a feedforward-considered series controller closed-loop system identification method, which can identify the parameter a to be identified of the object to be identified1 and a2Combining the known delay time constant tau of the object to be identified in the step 1) to obtain a transfer function of the object to be identified; the dynamic characteristics of the object can be analyzed according to the obtained transfer function, and the control strategy of the object to be identified is optimized; in this embodiment, the transfer function of the object to be recognized is
Figure BDA00032870933700002012
Fig. 2 shows the trend of the set value sequence set, the output sequence set, and the output sequence set of the identification model in the embodiment, the dotted line shows the trend of the set value sequence set, the dotted line shows the trend of the output sequence set, and the solid line shows the output trend of the identification model in the embodiment under the excitation of the first set of the set value in the closed loop structure of fig. 1. The identified model can keep consistent with the trend of the output sequence set according to the trend result, and the dynamic characteristic of the closed-loop system can be well reflected. The effectiveness of the method provided by the invention is demonstrated, and the model identified based on the method can provide a model basis for further controller design, control optimization and advanced control method implementation, and has strong practicability and wide industrial application prospect.
Example 4
The embodiment provides a dual-controller closed-loop system, which comprises two feedback controllers and an object to be identified, wherein the two feedback controllers and the object to be identified are sequentially connected in series, and the identification method of the object to be identified of the dual-controller closed-loop system adopts the dual-controller closed-loop system identification method based on slope response.
In the above embodiments, the descriptions of the respective embodiments have respective emphasis, and reference may be made to the related descriptions of other embodiments for parts that are not described or illustrated in a certain embodiment.
Those of ordinary skill in the art will appreciate that the various illustrative elements and algorithm steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware or combinations of computer software and electronic hardware. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the implementation. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present application.
In the embodiments provided in the present application, it should be understood that the disclosed apparatus/terminal and method may be implemented in other ways. For example, the above-described device/terminal embodiments are merely illustrative, and for example, the division of the above-described modules is only one logical division, and other divisions may be realized in practice, for example, a plurality of units or components may be combined or integrated into another system, or some features may be omitted, or not executed. In addition, the shown or discussed mutual coupling or direct coupling or communication connection may be an indirect coupling or communication connection through some interfaces, devices or units, and may be in an electrical, mechanical or other form.
In addition, functional units in the embodiments of the present application may be integrated into one processing unit, or each unit may exist alone physically, or two or more units are integrated into one unit. The integrated unit can be realized in a form of hardware, and can also be realized in a form of a software functional unit.
The integrated module may be stored in a computer-readable storage medium if it is implemented in the form of a software functional unit and sold or used as a separate product. Based on such understanding, all or part of the flow in the method of the embodiments described above may be implemented by a computer program, which may be stored in a computer-readable storage medium and can implement the steps of the embodiments of the methods described above when the computer program is executed by a processor. The computer program includes computer program code, and the computer program code may be in a source code form, an object code form, an executable file or some intermediate form.
The computer readable medium may include: any entity or device capable of carrying the above-described computer program code, recording medium, usb disk, removable hard disk, magnetic disk, optical disk, computer Memory, Read-Only Memory (ROM), Random Access Memory (RAM), electrical carrier signal, telecommunications signal, software distribution medium, and the like.
The above description is only for the specific embodiments of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can easily conceive of the changes or substitutions within the technical scope of the present invention, and all the changes or substitutions should be covered within the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the appended claims.

Claims (3)

1. A dual-controller closed-loop system identification method based on slope response is characterized by comprising the following steps:
1) describing an object to be identified by adopting a transfer function of first-order inertia plus pure delay, wherein the mathematical expression of the object to be identified is as follows:
Figure FDA0003287093360000011
wherein G(s) is a transfer function of the object, s and tau are respectively a differential operator and a delay time constant known by the object to be identified, a1 and a2The parameter to be identified is the object to be identified;
2) extracting a set value sequence set R of a closed-loop system consisting of an object to be identified, two feedback controllers and a feedforward controller in the same time period before and after the slope change of the set value0And output sequence set Y0The data length is n +1, and the sampling period is delta T; set value sequence set R0And output sequence set Y0The form of (A) is as follows:
R0＝[r0(1),…,r0(i),…,r0(n+1)]
Y0＝[y0(1),…,y0(i),…,y0(n+1)]；
wherein i represents the position of the data in the sequence set, and i is more than or equal to 1 and less than or equal to n + 1; r is0(1)、r0(i) and r0(n +1) are the first data, the ith data and the (n +1) th data of the set value sequence set respectively; y is0(1)、y0(i) and y0(n +1) are the first data, the ith data and the (n +1) th data of the output sequence set respectively;
3) the steady state value of the closed loop system before the set value is changed in a slope is rssSetting value sequence set R extracted in step 2)0And output sequence set Y0Subtracting a steady state value r from each of the datassRespectively obtaining a first-level sequence set R of a set value1And outputting the first level sequence set Y1；
Set value first order sequence set R1And outputting the first level sequence set Y1Each calculated by the following formula:
r1(1)＝r0(1)-rss
r1(i)＝r0(i)-rss
r1(n+1)＝r0(n+1)-rss
y1(1)＝y0(1)-rss
y1(i)＝y0(i)-rss
y1(n+1)＝y0(n+1)-rss；
wherein ,r1(1)、r1(i) and r1(n +1) are respectively set values of a first-level sequence set R1The first data, the ith data, and the n +1 th data; y is1(1)、y1(i) and y1(n +1) are respectively output first-stage sequence sets Y1The first data, the ith data, and the n +1 th data;
set value first order sequence set R1And outputting the first level sequence set Y1In the form of:
R1＝[r1(1),…,r1(i),…,r1(n+1)]；Y1＝[y1(1),…,y1(i),…,y1(n+1)]；
4) the amplitude value of the slope response of the set value of the closed loop system is l, the slope is gamma, and the maximum integer not exceeding tau/delta T is defined as
Figure FDA0003287093360000025
The maximum integer not exceeding (tau + l/gamma)/delta T is xi;
for the set value obtained in the step 3), a first-level sequence set R is obtained1The data in the sequence table is subjected to algebraic transformation to obtain a set value second-level sequence set R01、R11、R21、R31 and R41The data of (1); set value second level sequence set R01、R11、R21、R31 and R41The data length of the medium data is n;
set value second level sequence set R01、R11、R21、R31 and R41The mathematical calculation of the data in (1) is as follows:
Figure FDA0003287093360000021
Figure FDA0003287093360000022
Figure FDA0003287093360000023
Figure FDA0003287093360000024
Figure FDA0003287093360000031
wherein ,r01(i)、r11(i)、r21(i)、r31(i) and r41(i) Set value second level sequence set R01、R11、R21、R31 and R41The ith data in (1); set value second level sequence set R01、R11、R21、R31 and R41In the form of:
R01＝[r01(1),…,r01(i),…,r01(n)]
R11＝[r11(1),…,r11(i),…,r11(n)]
R21＝[r21(1),…,r21(i),…,r21(n)]
R31＝[r31(1),…,r31(i),…,r31(n)]
R41＝[r41(1),…,r41(i),…,r41(n)]；
5) for the output primary sequence set Y obtained in the step 3)1The data in (2) is calculated to obtain an output second-level sequence set Y01、Y10、Y11、Y21、Y31 and Y41The data of (1); second level sequence set Y01、Y10、Y11、Y21、Y31 and Y41The data length of the medium data is n;
outputting a second level sequence set Y01、Y10、Y11、Y21、Y31 and Y41The data in (1) are obtained by the following formula:
Figure FDA0003287093360000032
Figure FDA0003287093360000033
Figure FDA0003287093360000034
Figure FDA0003287093360000035
Figure FDA0003287093360000036
Figure FDA0003287093360000041
wherein j is the position of the data in the sequence set which exceeds i, and j is more than or equal to 1 and less than or equal to i; y is01(i)、y10(i)、y11(i)、y21(i)、y31(i) and y41(i) Respectively, outputting a second level sequence set Y01、Y10、Y11、Y21、Y31 and Y41The ith data in (1); outputting a second level sequence set Y01、Y10、Y11、Y21、Y31 and Y41In the form of:
Y01＝[y01(1),…,y01(i),…,y01(n)]
Y10＝[y10(1),…,y10(i),…,y10(n)]
Y11＝[y11(1),…,y11(i),…,y11(n)]
Y21＝[y21(1),…,y21(i),…,y21(n)]
Y31＝[y31(1),…,y31(i),…,y31(n)]
Y41＝[y41(1),…,y41(i),…,y41(n)]；
6) two series feedback controllers in the closed loop system are respectively Gc1(s) and Gc2(s), feedback controller Gc1(s) and Gc2The mathematical expressions of(s) are respectively as follows:
Figure FDA0003287093360000042
Figure FDA0003287093360000043
wherein ,kp1、ki1 and kd1Is a feedback controller Gc1(s) known parameters, respectively Gc1Proportional gain coefficient and integral of(s)A gain factor and a differential gain factor; wherein k isp2、ki2 and kd2Is a feedback controller Gc2(s) known parameters, respectively Gc2(s) a proportional gain coefficient, an integral gain coefficient, and a differential gain coefficient;
for the set value obtained in the step 4), a second-level sequence set R is obtained01、R11、R21、R31 and R41The data in (5) and the output second level sequence set Y obtained in step 5)01、Y10、Y11、Y21、Y31 and Y41In combination with a feedback controller Gc1(s) and Gc2Parameters in(s) are subjected to algebraic transformation to obtain a sequence set theta1 and θ2The data of (1);
sequence set theta1 and θ2The mathematical calculation of the data in (1) is as follows:
θ1(i)＝kd1kd2r01(i)+(kp1kd2+kd1kp2)r11(i)+(kp1kp2+ki1kd2+kd1ki2)r21(i)+(kp1ki2+ki1kp2)r31(i)+ki1ki2r41(i)-kd1kd2y01(i)-(kp1kd2+kd1kp2)y11(i)-(kp1kp2+ki1kd2+kd1ki2)y21(i)-(kp1ki2+ki1kp2)y31(i)-ki1ki2y41(i)
θ2(i)＝-y10(i)；
wherein ,θ1(i) and θ2(i) Are respectively a sequence set theta1 and θ2The ith data in (1); sequence set theta1 and θ2In the form of:
θ1＝[θ1(1),…,θ1(i),…,θ1(n)]
θ2＝[θ2(1),…,θ2(i),…,θ2(n)]；
7) the sequence set theta obtained in the step 6) is added1 and θ2Transforming to obtain a sequence set theta; the mathematical calculation of the sequence set θ is as follows:
Figure FDA0003287093360000051
wherein ,
Figure FDA0003287093360000052
and
Figure FDA0003287093360000053
respectively a sequence set theta1Transposed and sequence set θ of2Transposing;
8) parameter a to be identified of object to be identified1 and a2Composed parameter vector
Figure FDA0003287093360000054
Outputting the first-level sequence set Y obtained by the step 3)1And calculating the sequence set theta obtained in the step 7);
coefficient a to be identified of object to be identified1 and a2Composed parameter vector
Figure FDA0003287093360000055
Parameter vector
Figure FDA0003287093360000056
The form of (A) is as follows:
Figure FDA0003287093360000057
parameter vector
Figure FDA0003287093360000058
The calculation formula of (a) is as follows:
Figure FDA0003287093360000059
wherein ,
Figure FDA00032870933600000510
θTand
Figure FDA00032870933600000511
are respectively parameter vectors
Figure FDA00032870933600000512
Transpose of (2), transpose of sequence set θ, and output first level sequence set Y1Transpose of (θ)Tθ)-1Is thetaTMatrix inversion of theta;
thereby identifying the parameter a to be identified of the object to be identified1 and a2And obtaining a transfer function of the object to be identified and optimizing a control strategy of the object to be identified.
2. A dual-controller closed-loop system identification method based on slope response is characterized in that the method aims at a second-order inertia plus pure delay object to be identified, and comprises the following steps:
1) describing an object to be identified by adopting a transfer function of second-order inertia plus pure delay, wherein the mathematical expression of the object to be identified is as follows:
Figure FDA00032870933600000513
wherein G(s) is a transfer function of the object, s and tau are respectively a differential operator and a delay time constant known by the object to be identified, a1、a2 and a3The parameter to be identified is the object to be identified;
2) the extraction is composed of an object to be identified, two feedback controllers and a feedforward controllerThe closed loop system composed of the devices has a set value sequence set R in the same time period before and after the set value is changed in a slope mode0And output sequence set Y0The data length is n, and the sampling period is delta T; set value sequence set R0And output sequence set Y0The form of (A) is as follows:
R0＝[r0(1),…,r0(i),…,r0(n)]
Y0＝[y0(1),…,y0(i),…,y0(n)]；
wherein i represents the position of the data in the sequence set, and i is more than or equal to 1 and less than or equal to n; r is0(1)、r0(i) and r0(n) the first data, the ith data and the nth data of the set value sequence set respectively; y is0(1)、y0(i) and y0(n) the first data, the ith data and the nth data of the output sequence set respectively;
3) the steady state value of the closed loop system before the set value is changed in a slope is rssSetting value sequence set R extracted in step 2)0And output sequence set Y0Subtracting a steady state value r from each of the datassRespectively obtaining a first-level sequence set R of a set value1And outputting the first level sequence set Y1；
Set value first order sequence set R1And outputting the first level sequence set Y1Each calculated by the following formula:
r1(1)＝r0(1)-rss
r1(i)＝r0(i)-rss
r1(n)＝r0(n)-rss
y1(1)＝y0(1)-rss
y1(i)＝y0(i)-rss
y1(n)＝y0(n)-rss
wherein ,r1(1)、r1(i) and r1(n) first-level sequence sets R respectively being set values1The first data, the ith data and the nth data of (a);y1(1)、y1(i) and y1(n) respectively output first level sequence set Y1The first data, the ith data and the nth data of (a);
set value first order sequence set R1And outputting the first level sequence set Y1In the form of:
R1＝[r1(1),…,r1(i),…,r1(n)]
Y1＝[y1(1),…,y1(i),…,y1(n)]；
4) the amplitude value of the slope response of the set value of the closed loop system is l, the slope is gamma, and the maximum integer not exceeding tau/delta T is defined as
Figure FDA0003287093360000075
The maximum integer not exceeding (tau + l/gamma)/delta T is xi; for the set value obtained in the step 3), a first-level sequence set R is obtained1The data in the sequence table is subjected to algebraic transformation to obtain a set value second-level sequence set R11、R21、R31、R41 and R51The data of (1); set value second level sequence set R11、R21、R31、R41 and R51The data length of the medium data is n;
set value second level sequence set R11、R21、R31、R41 and R51The mathematical calculation of the data in (1) is as follows:
Figure FDA0003287093360000071
Figure FDA0003287093360000072
Figure FDA0003287093360000073
Figure FDA0003287093360000074
Figure FDA0003287093360000081
wherein ,r11(i)、r21(i)、r31(i)、r41(i) and r51(i) Set value second level sequence set R11、R21、R31、R41 and R51The ith data in (1); set value second level sequence set R11、R21、R31、R41 and R51In the form of:
R11＝[r11(1),…,r11(i),…,r11(n)]
R21＝[r21(1),…,r21(i),…,r21(n)]
R31＝[r31(1),…,r31(i),…,r31(n)]
R41＝[r41(1),…,r41(i),…,r41(n)]
R51＝[r51(1),…,r51(i),…,r51(n)]；
5) for the output primary sequence set Y obtained in the step 3)1The data in (2) is calculated to obtain an output second-level sequence set Y10、Y20、Y11、Y21、Y31、Y41 and Y51The data of (1); second level sequence set Y10、Y20、Y11、Y21、Y31、Y41 and Y51The data length of the medium data is n;
outputting a second level sequence set Y10、Y20、Y11、Y21、Y31、Y41 and Y51The data in (1) are obtained by the following formula:
Figure FDA0003287093360000082
Figure FDA0003287093360000083
Figure FDA0003287093360000084
Figure FDA0003287093360000085
Figure FDA0003287093360000086
Figure FDA0003287093360000087
Figure FDA0003287093360000091
wherein j is the position of the data in the sequence set which exceeds i, and j is more than or equal to 1 and less than or equal to i; y is10(i)、y20(i)、y11(i)、y21(i)、y31(i)、y41(i) and y51(i) Respectively, outputting a second level sequence set Y10、Y20、Y11、Y21、Y31、Y41 and Y51The ith data in (1); outputting a second level sequence set Y10、Y20、Y11、Y21、Y31、Y41 and Y51In the form of:
Y10＝[y10(1),…,y10(i),…,y10(n)]
Y20＝[y20(1),…,y20(i),…,y20(n)]
Y11＝[y11(1),…,y11(i),…,y11(n)]
Y21＝[y21(1),…,y21(i),…,y21(n)]
Y31＝[y31(1),…,y31(i),…,y31(n)]
Y41＝[y41(1),…,y41(i),…,y41(n)]
Y51＝[y51(1),…,y51(i),…,y51(n)]；
6) two series feedback controllers in the closed loop system are respectively Gc1(s) and Gc2(s), feedback controller Gc1(s) and Gc2The mathematical expressions of(s) are respectively as follows:
Figure FDA0003287093360000092
Figure FDA0003287093360000093
wherein ,kp1、ki1 and kd1Is a feedback controller Gc1(s) known parameters, respectively Gc1(s) a proportional gain coefficient, an integral gain coefficient, and a differential gain coefficient; k is a radical ofp2、ki2 and kd2Is a feedback controller Gc2(s) known parameters, respectively Gc2(s) a proportional gain coefficient, an integral gain coefficient, and a differential gain coefficient;
for the set value obtained in the step 4), a second-level sequence set R is obtained11、R21、R31、R41 and R51The data in (5) and the output second level sequence set Y obtained in step 5)10、Y20、Y11、Y21、Y31、Y41 and Y51In combination with a feedback controller Gc1(s) and Gc2Parameters in(s) are subjected to algebraic transformation to obtain a sequence set theta1、θ2 and θ3The data of (1);
sequence set theta1、θ2 and θ3The mathematical calculation of the data in (1) is as follows:
θ1(i)＝kd1kd2r11(i)+(kp1kd2+kd1kp2)r21(i)+(kp1kp2+ki1kd2+kd1ki2)r31(i)+(kp1ki2+ki1kp2)r41(i)+ki1ki2r51(i)-kd1kd2y11(i)-(kp1kd2+kd1kp2)y21(i)-(kp1kp2+ki1kd2+kd1ki2)y31(i)-(kp1ki2+ki1kp2)y41(i)-ki1ki2y51(i)
θ2(i)＝-y10(i)
θ3(i)＝-y20(i)；
wherein ,θ1(i)、θ2(i) and θ3(i) Are respectively a sequence set theta1、θ2 and θ3The ith data in (1); sequence set theta1、θ2 and θ3In the form of:
θ1＝[θ1(1),…,θ1(i),…,θ1(n)]
θ2＝[θ2(1),…,θ2(i),…,θ2(n)]
θ3＝[θ3(1),…,θ3(i),…,θ3(n)]；
7) the sequence set theta obtained in the step 6) is added1、θ2 and θ3Transforming to obtain a sequence set theta; the mathematical calculation of the sequence set θ is as follows:
Figure FDA0003287093360000101
wherein ,
Figure FDA0003287093360000102
and
Figure FDA0003287093360000103
respectively a sequence set theta1Transposed, sequence set θ of2Transposed and sequence set θ of3Transposing;
8) parameter a to be identified of object to be identified1、a2 and a3Composed parameter vector
Figure FDA0003287093360000104
Outputting the first-level sequence set Y obtained by the step 3)1And calculating the sequence set theta obtained in the step 7);
coefficient a to be identified of object to be identified1、a2 and a3Composed parameter vector
Figure FDA0003287093360000105
Parameter vector
Figure FDA0003287093360000106
The form of (A) is as follows:
Figure FDA0003287093360000107
parameter vector
Figure FDA0003287093360000108
The calculation formula of (a) is as follows:
Figure FDA0003287093360000109
wherein ,
Figure FDA00032870933600001010
θT and Y1 TAre respectively parameter vectors
Figure FDA00032870933600001011
Transpose of (2), transpose of sequence set θ, and output first level sequence set Y1Transpose of (θ)Tθ)-1Is thetaTMatrix inversion of theta;
thereby identifying the parameter a to be identified of the object to be identified1、a2 and a3And obtaining a transfer function of the object to be identified and optimizing a control strategy of the object to be identified.
3. The utility model provides a dual controller closed loop system, includes two feedback controller and the object of waiting to discern that series connection in proper order which characterized in that: the identification method of the object to be identified of the dual-controller closed-loop system adopts the identification method of the dual-controller closed-loop system based on the slope response as claimed in claim 1 or 2.
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