CN112099359B - Closed loop system identification method based on slope response and known time lag - Google Patents

Closed loop system identification method based on slope response and known time lag Download PDF

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CN112099359B
CN112099359B CN202011015885.4A CN202011015885A CN112099359B CN 112099359 B CN112099359 B CN 112099359B CN 202011015885 A CN202011015885 A CN 202011015885A CN 112099359 B CN112099359 B CN 112099359B
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荆立坤
马春雷
宋宝玉
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Huadian Weifang Power Generation Co Ltd
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Abstract

The invention provides a closed loop system identification method based on slope response and known time lag, and belongs to the technical field of automatic control. In the invention, a controlled object is described by adopting a transfer function of second-order inertia plus pure delay; calculating an input data set and an output data set acquired in a ramp response process to obtain an available input data set and an available output data set; obtaining a processing input data set and a processing output data set through algebraic operation based on the available input data set and the available output data set; based on the feedback controller coefficient, the processing input data set and the processing output data set, calculating to obtain a final data set, and obtaining a final big data set through algebraic transformation; and obtaining the coefficient to be identified of the controlled object through matrix calculation based on the obtained final big data set and the available output data set. The method can identify the controlled object as a continuous system, lays a foundation for dynamic characteristic analysis and controller design optimization of the controlled object, and has good industrial application potential.

Description

Closed loop system identification method based on slope response and known time lag
Technical Field
The invention belongs to the technical field of automatic control, and particularly relates to a closed loop system identification method based on slope response and known time lag.
Background
In the fields of chemical industry and energy, in order to ensure the stability and safety of production equipment and production process, the open-loop excitation system-based identification is difficult to apply. In order to realize system identification based on closed-loop excitation, closed-loop excitation is generally required to be performed on a system to be identified in the chemical and energy fields, step signal excitation is a closed-loop excitation mode which is relatively easy to realize in the chemical and energy fields, and the step signal excitation is difficult to be allowed to be applied in practice because irreversible damage is easily brought to an actuator due to sudden change of a signal, for example, load change in a thermal power generating unit is generally realized through ramp signal response rather than step signal response. Therefore, the closed-loop identification based on the ramp signal excitation can realize the identification of the system in the chemical and energy fields, lays a foundation for the dynamic characteristic analysis of the subsequent controlled object and the design optimization of the controller, and has good industrial application potential.
However, the currently researched closed-loop excitation-based closed-loop identification generally obtains a discrete system, and since the discrete system is obviously affected by the sampling period, the irrational sampling period brings a pathological operation basis, which is difficult to be found in the obtained model, and thus, the optimization improvement of the control strategy and the implementation failure of the advanced control method are caused. Therefore, the closed-loop identification method based on the slope response has important significance for practical industrial application. Since the second order inertia plus pure delay system can describe almost all system dynamics in the chemical and energy fields, the delay system of the system can be easily obtained by analyzing input and output data based on closed loops, can be known artificially, and therefore does not need to be identified.
In summary, it is necessary to provide a closed-loop identification method for input and output data based on slope response in an industrial process, which can provide a basis for dynamic characteristic analysis and controller design optimization of a controlled object, and has a good industrial application potential.
Disclosure of Invention
In order to solve the technical problems, the invention provides a closed loop system identification method based on ramp response and known time lag. The method can identify the controlled object as a continuous system of second-order inertia plus pure delay based on the slope response data of the closed-loop system and the delay constant of the system, avoids the system from carrying out open-loop step identification to obtain a discrete system, can provide a foundation for the dynamic characteristic analysis and the design optimization of the controller of the controlled object, and has good industrial application potential.
The invention provides a closed loop system identification method based on slope response and known time lag, which is characterized by comprising the following steps of:
1) describing a controlled object to be identified by adopting a transfer function of second-order inertia plus pure delay, wherein the mathematical expression of the controlled object is as follows:
Figure BDA0002701181750000021
where G(s) is the transfer function of the controlled object, s and tau are the known delay constants of the differential operator and the controlled object, k, a1And a2Parameters which need to be identified for a controlled object;
2) acquiring the input data set R in the time period when the closed loop system starts to experience the slope response from the steady state and reaches the new steady state value0And output data set Y0The length of the data is n, and the sampling period is delta T; input data set R0And output data set Y0In the form of:
R0＝[r0(1),…,r0(i),…,r0(n)]
Y0＝[y0(1),…,y0(i),…,y0(n)]
wherein i represents the position of data in the data set, i is more than or equal to 1 and less than or equal to n; r is0(1)、r0(i) And r0(n) the 1 st data, the ith data, and the nth data of the input data set, respectively; y is0(1)、y0(i) And y0(n) the 1 st data, the ith data, and the nth data of the output data set, respectively;
3) the steady state value of the closed loop system in the steady state at the beginning of the acquisition is rσInputting the data set R in the step 2)0And output data set Y0All data in (1) minus the steady state value rσCorresponding data in the available input data set R and the available output data set Y can be obtained;
the mathematical calculations for the data in the available input data set R and the available output data set Y are as follows:
r(1)＝r0(1)-rσ
r(i)＝r0(i)-rσ
r(n)＝r0(n)-rσ
y(1)＝y0(1)-rσ
y(i)＝y0(i)-rσ
y(n)＝y0(n)-rσ
wherein R (1), R (i) and R (n) are respectively the 1 st data, the ith data and the nth data of the available input data set R; y (1), Y (i) and Y (n) are respectively the 1 st, ith and nth data of the available output data set Y;
the available input data set R and the available output data set Y are in the form of:
R＝[r(1),…,r(i),…,r(n)]
Y＝[y(1),…,y(i),…,y(n)]；
4) the amplitude of the closed loop system slope response is l, and the slope is k; the maximum integer not exceeding tau/delta T is m, and the maximum integer not exceeding (tau + l kappa)/delta T is xi; performing algebraic operation on all data in the available input data set R in the step 3) to obtain a processed input data set R11、R21And R31The data of (1);
processing an input data set R11、R21And R31The mathematical calculation of the data in (1) is as follows:
Figure BDA0002701181750000031
Figure BDA0002701181750000032
Figure BDA0002701181750000033
wherein r is11(i)、r21(i) And r31(i) Respectively, processing an input data set R11、R21And R31The ith data in (1); processing an input data set R11、R21And R31In the form of:
R11＝[r11(1),…,r11(i),…,r11(n)]
R21＝[r21(1),…,r21(i),…,r21(n)]
R31＝[r31(1),…,r31(i),…,r31(n)]；
5) performing algebraic operation transformation on all data in the available output data set Y obtained in the step 3) to obtain processed outputData set Y10、Y20、Y11、Y21And Y31The data of (1);
processing the output data set Y10、Y20、Y11、Y21And Y31The mathematical calculation of the data in (1) is as follows:
Figure BDA0002701181750000041
Figure BDA0002701181750000042
Figure BDA0002701181750000043
Figure BDA0002701181750000044
Figure BDA0002701181750000045
j is the position where the data in the data set 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) And y31(i) Respectively processing the output data set Y10、Y20、Y11、Y21And Y31The ith data in (1); processing the output data set Y10、Y20、Y11、Y21And Y31In 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)]；
6) the feedback controller in the closed-loop system is C(s), and the mathematical expressions of the feedback controller C(s) are respectively as follows:
Figure BDA0002701181750000046
wherein k isp、kiAnd kdProportional gain coefficient, integral gain coefficient and differential gain coefficient of feedback controller C(s);
for processing the input data set R in step 4)11、R21And R31The data and the processing output data set Y in step 5)10、Y20、Y11、Y21And Y31The data in (1) is subjected to data transformation to obtain a final data set theta1、θ2And theta3The data of (1);
last data set θ1、θ2And theta3The mathematical calculation of the data in (1) is as follows:
θ1(i)＝kdr11(i)+kpr21(i)+kir31(i)-kdy11(i)-kpy21(i)-kiy31(i)
θ2(i)＝-y10(i)
θ3(i)＝-y20(i)
θ1(i)、θ2(i) and theta3(i) Respectively, the last data set theta1、θ2And theta3The ith data in (1); last data set θ1、θ2And theta3In 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) setting the final data set theta in the step 6)1、θ2And theta3Algebraic transformation is carried out to obtain a final big data set theta; the final mathematical calculation for the large data set θ is as follows:
Figure BDA0002701181750000051
wherein
Figure BDA0002701181750000052
And
Figure BDA0002701181750000053
respectively, the last data set theta1Transposed, final data set theta2Transposed and final data set θ of3Transposing;
8) coefficient k, a to be identified of controlled object1And a2Composed parameter vector
Figure BDA0002701181750000054
Calculating the available output data set Y obtained in the step 3) and the final large data set theta obtained in the step 7);
parameter vector
Figure BDA0002701181750000055
The form of (A) is as follows:
Figure BDA0002701181750000056
parameter vector
Figure BDA0002701181750000057
The mathematical calculation of (a) is as follows:
Figure BDA0002701181750000058
wherein
Figure BDA0002701181750000059
θTAnd YTAre respectively a parameter vector
Figure BDA00027011817500000510
Transpose of the last large data set theta and transpose of the available output data set Y, (theta)Tθ)-1Is thetaTMatrix inversion of θ.
Drawings
Fig. 1 is a closed loop control system including a controlled object and a feedback controller.
Fig. 2 is a trend graph of the output of the input data set, the output data set and the recognition model (i.e., controlled object) in the embodiment.
Detailed Description
An embodiment of a method for identifying a closed loop system based on a ramp response and a known skew is described in detail below with reference to fig. 1:
1) describing a controlled object to be identified by adopting a transfer function of second-order inertia plus pure delay, wherein the mathematical expression of the controlled object is as follows:
Figure BDA0002701181750000061
where G(s) is the transfer function of the controlled object, s and tau are the known delay constants of the differential operator and the controlled object, k, a1And a2Parameters which need to be identified for a controlled object; the delay constant of the controlled object is generally more than or equal to 0 and less than or equal to 100;
2) acquiring the input data set R in the time period when the closed loop system starts to experience the slope response from the steady state and reaches the new steady state value0And output data set Y0The length of the data is n, and the sampling period is delta T; input data set R0And output data set Y0In the form of:
R0＝[r0(1),…,r0(i),…,r0(n)]
Y0＝[y0(1),…,y0(i),…,y0(n)]
wherein i represents the position of data in the data 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 1 st data, the ith data, and the nth data of the input data set, respectively; y is0(1)、y0(i) And y0(n) the 1 st data, the ith data, and the nth data of the output data set, respectively; the length of the collected data is generally more than or equal to 1000 and less than or equal to 10000, and the sampling period of a typical industrial process is generally more than or equal to 0.1s and less than or equal to 1 s;
3) the steady state value of the closed loop system in the steady state at the beginning of the acquisition is rσInputting the data set R in the step 2)0And output data set Y0All data in (1) minus the steady state value rσCorresponding data in the available input data set R and the available output data set Y can be obtained;
the mathematical calculations for the data in the available input data set R and the available output data set Y are as follows:
r(1)＝r0(1)-rσ
r(i)＝r0(i)-rσ
r(n)＝r0(n)-rσ
y(1)＝y0(1)-rσ
y(i)＝y0(i)-rσ
y(n)＝y0(n)-rσ
wherein R (1), R (i) and R (n) are respectively the 1 st data, the ith data and the nth data of the available input data set R; y (1), Y (i) and Y (n) are respectively the 1 st, ith and nth data of the available output data set Y; the steady state value of the closed loop system at the beginning stage of data acquisition is determined according to the physical quantity, and is generally equal to or more than 0.05 and less than or equal to rσ≤1000；
The available input data set R and the available output data set Y are in the form of:
R＝[r(1),…,r(i),…,r(n)]
Y＝[y(1),…,y(i),…,y(n)]；
4) the amplitude of the closed loop system slope response is l, and the slope is k; the maximum integer not exceeding tau/delta T is m, and the maximum integer not exceeding (tau + l/kappa)/delta T is xi; performing algebraic operation on all data in the available input data set R in the step 3) to obtain a processed input data set R11、R21And R31The data of (1);
processing an input data set R11、R21And R31The mathematical calculation of the data in (1) is as follows:
Figure BDA0002701181750000071
Figure BDA0002701181750000072
Figure BDA0002701181750000081
wherein r is11(i)、r21(i) And r31(i) Respectively, processing an input data set R11、R21And R31The ith data in (1); the amplitude of the slope response of the closed-loop system is generally more than or equal to 0.1 and less than or equal to l and less than or equal to 100, and the slope is generally more than or equal to 0.01 and less than or equal to k and less than or equal to 100; processing an input data set R11、R21And R31In the form of:
R11＝[r11(1),…,r11(i),…,r11(n)]
R21＝[r21(1),…,r21(i),…,r21(n)]
R31＝[r31(1),…,r31(i),…,r31(n)]；
5) for available output data set Y obtained in step 3)All data are subjected to algebraic operation transformation to obtain a processed output data set Y10、Y20、Y11、Y21And Y31The data of (1);
processing the output data set Y10、Y20、Y11、Y21And Y31The mathematical formula of the data in (1) is as follows:
Figure BDA0002701181750000082
Figure BDA0002701181750000083
Figure BDA0002701181750000084
Figure BDA0002701181750000085
Figure BDA0002701181750000086
j is the position where the data in the data set 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) And y31(i) Respectively processing the output data set Y10、Y20、Y11、Y21And Y31The ith data in (1); processing the output data set Y10、Y20、Y11、Y21And Y31In 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)]；
6) the feedback controller in the closed-loop system is C(s), and the mathematical expressions of the feedback controller C(s) are respectively as follows:
Figure BDA0002701181750000091
wherein k isp、kiAnd kdProportional gain coefficient, integral gain coefficient and differential gain coefficient of feedback controller C(s);
for processing the input data set R in step 4)11、R21And R31The data and the processing output data set Y in step 5)10、Y20、Y11、Y21And Y31The data in (1) is subjected to data transformation to obtain a final data set theta1、θ2And theta3The data of (1);
last data set θ1、θ2And theta3The mathematical calculation of the data in (1) is as follows:
θ1(i)＝kdr11(i)+kpr21(i)+kir31(i)-kdy11(i)-kpy21(i)-kiy31(i)
θ2(i)＝-y10(i)
θ3(i)＝-y20(i)
θ1(i)、θ2(i) and theta3(i) Respectively, the last data set theta1、θ2And theta3The ith data in (1); last data set θ1、θ2And theta3In 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) setting the final data set theta in the step 6)1、θ2And theta3Algebraic transformation is carried out to obtain a final big data set theta; the final mathematical calculation for the large data set θ is as follows:
Figure BDA0002701181750000092
wherein
Figure BDA0002701181750000101
And
Figure BDA0002701181750000102
respectively, the last data set theta1Transposed, final data set theta2Transposed and final data set theta3Transposing;
8) coefficient k, a to be identified of controlled object1And a2Composed parameter vector
Figure BDA0002701181750000103
Calculating the available output data set Y obtained in the step 3) and the final large data set theta obtained in the step 7);
parameter vector
Figure BDA0002701181750000104
The form of (A) is as follows:
Figure BDA0002701181750000105
parameter vector
Figure BDA0002701181750000106
Is calculated by the mathematical formulaThe following:
Figure BDA0002701181750000107
wherein
Figure BDA0002701181750000108
θTAnd YTAre respectively parameter vectors
Figure BDA0002701181750000109
Transpose of the last large data set theta and transpose of the available output data set Y, (theta)Tθ)-1Is thetaTMatrix inversion of θ.
According to the steps, the implementation of the closed-loop system identification method based on the slope response and the known time lag can be completed.
The technical advantages of the invention will be illustrated by the following example of an embodiment in which the actual system is used
Figure BDA00027011817500001010
The description is made on input and output data with a slope of 0.02, an amplitude of 2, and the presence of output white noise:
1) describing a controlled object to be identified by adopting a transfer function of second-order inertia plus pure delay, wherein the mathematical expression of the controlled object is as follows:
Figure BDA00027011817500001011
where G(s) is the transfer function of the controlled object, s and tau are the known delay constants of the differential operator and the controlled object, k, a1And a2Parameters which need to be identified for a controlled object; in this embodiment, the delay constant of the controlled object is τ 45;
2) acquiring the input data set R in the time period when the closed loop system starts to experience the slope response from the steady state and reaches the new steady state value0And output data set Y0The length of the data is n,the sampling period is delta T; input data set R0And output data set Y0In the form of:
R0＝[r0(1),…,r0(i),…,r0(n)]
Y0＝[y0(1),…,y0(i),…,y0(n)]
wherein i represents the position of data in the data set, i is more than or equal to 1 and less than or equal to n; r is0(1)、r0(i) And r0(n) the 1 st data, the ith data, and the nth data of the input data set, respectively; y is0(1)、y0(i) And y0(n) the 1 st data, the ith data, and the nth data of the output data set, respectively; the length of the data acquired in this embodiment is n ═ 4000, and the sampling period in this embodiment is Δ T ═ 0.2 s;
3) the steady state value of the closed loop system in the steady state at the beginning of the acquisition is rσInputting the data set R in the step 2)0And output data set Y0All data in (1) minus the steady state value rσCorresponding data in the available input data set R and the available output data set Y can be obtained;
the mathematical calculations for the data in the available input data set R and the available output data set Y are as follows:
r(1)＝r0(1)-rσ
r(i)＝r0(i)-rσ
r(n)＝r0(n)-rσ
y(1)＝y0(1)-rσ
y(i)＝y0(i)-rσ
y(n)＝y0(n)-rσ
wherein R (1), R (i) and R (n) are respectively the 1 st data, the ith data and the nth data of the available input data set R; y (1), Y (i) and Y (n) are respectively the 1 st, ith and nth data of the available output data set Y; in this embodiment, the steady state value of the closed loop system at the beginning stage of data acquisition is rσ＝0；
The available input data set R and the available output data set Y are in the form of:
R＝[r(1),…,r(i),…,r(n)]
Y＝[y(1),…,y(i),…,y(n)]；
4) the amplitude of the closed loop system slope response is l, and the slope is k; the maximum integer not exceeding tau/delta T is m, and the maximum integer not exceeding (tau + l kappa)/delta T is xi; performing algebraic operation on all data in the available input data set R in the step 3) to obtain a processed input data set R11、R21And R31The data of (1);
processing an input data set R11、R21And R31The mathematical calculation of the data in (1) is as follows:
Figure BDA0002701181750000121
Figure BDA0002701181750000122
Figure BDA0002701181750000123
wherein r is11(i)、r21(i) And r31(i) Respectively, processing an input data set R11、R21And R31The ith data of (2); in this embodiment, the amplitude of the step input of the closed-loop system is l ═ 2, the maximum positive integer not exceeding τ/Δ T in this embodiment is m ═ 225, and the maximum integer not exceeding (τ + l/κ)/Δ T in this embodiment is ξ ═ 725; processing an input data set R11、R21And R31In the form of:
R11＝[r11(1),…,r11(i),…,r11(n)]
R21＝[r21(1),…,r21(i),…,r21(n)]
R31＝[r31(1),…,r31(i),…,r31(n)]；
5) performing algebraic operation transformation on all data in the available output data set Y obtained in the step 3) to obtain a processed output data set Y10、Y20、Y11、Y21And Y31The data of (1);
processing the output data set Y10、Y20、Y11、Y21And Y31The mathematical calculation of the data in (1) is as follows:
Figure BDA0002701181750000124
Figure BDA0002701181750000131
Figure BDA0002701181750000132
Figure BDA0002701181750000133
Figure BDA0002701181750000134
j is the position where the data in the data set 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) And y31(i) Respectively processing the output data set Y10、Y20、Y11、Y21And Y31The ith data in (1); processing the output data set Y10、Y20、Y11、Y21And Y31In 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)]；
6) the feedback controller in the closed-loop system is C(s), and the mathematical expressions of the feedback controller C(s) are respectively as follows:
Figure BDA0002701181750000135
wherein k isp、kiAnd kdProportional gain coefficient, integral gain coefficient and differential gain coefficient of feedback controller C(s); in this example kp＝3.2、ki1/230 and kd＝0；
For processing the input data set R in step 4)11、R21And R31The data and the processing output data set Y in step 5)10、Y20、Y11、Y21And Y31The data in (1) is subjected to data transformation to obtain a final data set theta1、θ2And theta3The data of (1);
last data set θ1、θ2And theta3The mathematical calculation of the data in (1) is as follows:
θ1(i)＝kdr11(i)+kpr21(i)+kir31(i)-kdy11(i)-kpy21(i)-kiy31(i)
θ2(i)＝-y10(i)
θ3(i)＝-y20(i)
θ1(i)、θ2(i) and theta3(i) Respectively, the last data set theta1、θ2And theta3The ith data of (1)(ii) a Last data set θ1、θ2And theta3In 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) setting the final data set theta in the step 6)1、θ2And theta3Algebraic transformation is carried out to obtain a final big data set theta; the final mathematical calculation for the large data set θ is as follows:
Figure BDA0002701181750000141
wherein
Figure BDA0002701181750000142
And
Figure BDA0002701181750000143
respectively, the last data set theta1Transposed, final data set theta2Transposed and final data set theta3Transposing;
8) coefficient k, a to be identified of controlled object1And a2Composed parameter vector
Figure BDA0002701181750000144
Calculating the available output data set Y obtained in the step 3) and the final large data set theta obtained in the step 7);
parameter vector
Figure BDA0002701181750000145
The form of (A) is as follows:
Figure BDA0002701181750000146
parameter vector
Figure BDA0002701181750000147
The mathematical calculation of (a) is as follows:
Figure BDA0002701181750000148
wherein
Figure BDA0002701181750000149
θTAnd YTAre respectively parameter vectors
Figure BDA00027011817500001410
Transpose of the last large data set theta and transpose of the available output data set Y, (theta)Tθ)-1Is thetaTMatrix inversion of theta; in this embodiment, k is 0.00495, a10.09993 and a2＝0.003977。
Fig. 2 is a trend graph of the output of the recognition model (i.e., controlled object) and the available input data set and the available output data set in the embodiment. The dashed line is the trend of the available input data set, the dashed line is the trend of the available output data set, and the solid line is the output trend of the recognition model in the embodiment under excitation of the available input data set in the closed-loop structure of fig. 1. From fig. 2, it can be known that although a delay constant of the system has a certain deviation, the identification model can still be well matched with the available output data set, and can more accurately reflect the dynamic characteristics of the closed-loop system, which illustrates the effectiveness of the method provided by the present invention.

Claims (1)

1. A method for identifying a closed loop system based on a ramp response and a known skew, the method comprising the steps of:
1) describing a controlled object to be identified by adopting a transfer function of second-order inertia plus pure delay, wherein the mathematical expression of the controlled object is as follows:
Figure FDA0002701181740000011
where G(s) is the transfer function of the controlled object, s and tau are the known delay constants of the differential operator and the controlled object, k, a1And a2Is a parameter that needs to be identified for the controlled object,
2) acquiring the input data set R in the time period when the closed loop system starts to experience the slope response from the steady state and reaches the new steady state value0And output data set Y0The length of the data is n, the sampling period is delta T, and a data set R is input0And output data set Y0In the form of:
R0＝[r0(1),…,r0(i),…,r0(n)]
Y0＝[y0(1),…,y0(i),…,y0(n)]
wherein i represents the position of data in the data set, i is more than or equal to 1 and less than or equal to n; r is0(1)、r0(i) And r0(n) the 1 st data, the ith data, and the nth data of the input data set, respectively; y is0(1)、y0(i) And y0(n) the 1 st data, the ith data and the nth data of the output data set, respectively,
3) the steady state value of the closed loop system in the steady state at the beginning of the acquisition is rσInputting the data set R in the step 2)0And output data set Y0All data in (1) minus the steady state value rσCorresponding data in the available input data set R and the available output data set Y are available,
the mathematical calculations for the data in the available input data set R and the available output data set Y are as follows:
r(1)＝r0(1)-rσ
r(i)＝r0(i)-rσ
r(n)＝r0(n)-rσ
y(1)＝y0(1)-rσ
y(i)＝y0(i)-rσ
y(n)＝y0(n)-rσ
wherein R (1), R (i) and R (n) are respectively the 1 st data, the ith data and the nth data of the available input data set R, Y (1), Y (i) and Y (n) are respectively the 1 st data, the ith data and the nth data of the available output data set Y,
the available input data set R and the available output data set Y are in the form of:
R＝[r(1),…,r(i),…,r(n)]
Y＝[y(1),…,y(i),…,y(n)]，
4) the amplitude of the slope response of the closed-loop system is l, the slope is k, the maximum integer not exceeding tau/delta T is m, the maximum integer not exceeding (tau + l/k)/delta T is xi, all the data in the available input data set R in the step 3) are subjected to algebraic operation to obtain a processed input data set R11、R21And R31The data of (2) is stored in the storage unit,
processing an input data set R11、R21And R31The mathematical formula of (1) is as follows:
Figure FDA0002701181740000021
Figure FDA0002701181740000022
Figure FDA0002701181740000023
wherein r is11(i)、r21(i) And r31(i) Respectively, processing an input data set R11、R21And R31Processing the input data set R11、R21And R31In the form of:
R11＝[r11(1),…,r11(i),…,r11(n)]
R21＝[r21(1),…,r21(i),…,r21(n)]
R31＝[r31(1),…,r31(i),…,r31(n)]，
5) performing algebraic operation transformation on all data in the available output data set Y obtained in the step 3) to obtain a processed output data set Y10、Y20、Y11、Y21And Y31The data of (1) is stored in a memory,
processing the output data set Y10、Y20、Y11、Y21And Y31The mathematical calculation of the data in (1) is as follows:
Figure FDA0002701181740000031
Figure FDA0002701181740000032
Figure FDA0002701181740000033
Figure FDA0002701181740000034
Figure FDA0002701181740000035
j is the position where the data in the data set 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) And y31(i) Respectively processing the output data set Y10、Y20、Y11、Y21And Y31The ith data in (1); processing the output data set Y10、Y20、Y11、Y21And Y31In 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)]，
6) the feedback controller in the closed-loop system is C(s), and the mathematical expressions of the feedback controller C(s) are respectively as follows:
Figure FDA0002701181740000036
wherein k isp、kiAnd kdThe proportional gain coefficient, the integral gain coefficient and the differential gain coefficient of the feedback controller C(s),
for processing the input data set R in step 4)11、R21And R31The data and the processing output data set Y in step 5)10、Y20、Y11、Y21And Y31The data in (1) is subjected to data transformation to obtain a final data set theta1、θ2And theta3The data of (1) is stored in a memory,
last data set θ1、θ2And theta3The mathematical calculation of the data in (1) is as follows:
θ1(i)＝kdr11(i)+kpr21(i)+kir31(i)-kdy11(i)-kpy21(i)-kiy31(i)
θ2(i)＝-y10(i)
θ3(i)＝-y20(i)
θ1(i)、θ2(i) and theta3(i) Respectively, the last data set theta1、θ2And theta3The ith data in (1); last data set θ1、θ2And theta3In 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) setting the final data set theta in the step 6)1、θ2And theta3Algebraic transformation is carried out to obtain a final big data set theta, and the mathematical calculation formula of the final big data set theta is as follows:
Figure FDA0002701181740000041
wherein
Figure FDA0002701181740000042
And
Figure FDA0002701181740000043
respectively, the last data set theta1Transposed, final data set theta2Transposed and final data set theta3Transposing;
8) coefficient k, a to be identified of controlled object1And a2Composed parameter vector
Figure FDA0002701181740000044
Calculated from the available output data set Y obtained in step 3) and the final large data set theta obtained in step 7),
parameter vector
Figure FDA0002701181740000045
The form of (A) is as follows:
Figure FDA0002701181740000046
parameter vector
Figure FDA0002701181740000047
The mathematical calculation of (a) is as follows:
Figure FDA0002701181740000048
wherein
Figure FDA0002701181740000049
θTAnd YTAre respectively parameter vectors
Figure FDA00027011817400000410
Transpose of the last large data set theta and transpose of the available output data set Y, (theta)Tθ)-1Is thetaTMatrix inversion of θ.
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