CN107422640B - Combined integral system identification method based on relay feedback - Google Patents

Combined integral system identification method based on relay feedback Download PDF

Info

Publication number
CN107422640B
CN107422640B CN201710649291.0A CN201710649291A CN107422640B CN 107422640 B CN107422640 B CN 107422640B CN 201710649291 A CN201710649291 A CN 201710649291A CN 107422640 B CN107422640 B CN 107422640B
Authority
CN
China
Prior art keywords
combined integral
relay
formula
representing
gain
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN201710649291.0A
Other languages
Chinese (zh)
Other versions
CN107422640A (en
Inventor
任正云
闫子豪
陈安钢
郭鸿宇
刘志明
张丙昌
倪潇
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Donghua University
Original Assignee
Donghua University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Donghua University filed Critical Donghua University
Priority to CN201710649291.0A priority Critical patent/CN107422640B/en
Publication of CN107422640A publication Critical patent/CN107422640A/en
Application granted granted Critical
Publication of CN107422640B publication Critical patent/CN107422640B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance

Landscapes

  • Engineering & Computer Science (AREA)
  • Health & Medical Sciences (AREA)
  • Artificial Intelligence (AREA)
  • Computer Vision & Pattern Recognition (AREA)
  • Evolutionary Computation (AREA)
  • Medical Informatics (AREA)
  • Software Systems (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Automation & Control Theory (AREA)
  • Other Investigation Or Analysis Of Materials By Electrical Means (AREA)
  • Feedback Control In General (AREA)

Abstract

The invention relates to an application method of a relay feedback identification method on a combined integral system, which is characterized by comprising the following steps: step 1, performing a relay feedback test on a combined integral system to be identified by using an ideal non-biased relay; and 2, utilizing the deviation between the actual oscillation frequency and the theoretical critical oscillation frequency compensated by the offset phase angle to establish a frequency domain information relation, and deducing to obtain system parameters. The invention adopts the parameter identification of the combined integral system based on the relay feedback, can realize single identification to obtain a plurality of parameters, and has high identification precision. Compared with an ATV method or a parameter estimation method for describing a combined integral system by an approximate model, the obtained identification effect is obviously improved.

Description

Combined integral system identification method based on relay feedback
Technical Field
The invention relates to a method for identifying system parameters and setting controller parameters of a combined integration system by using a relay technology, belonging to the field of industrial process control.
Background
In industrial processes, most objects are generally approximated as first-order and second-order plus pure hysteresis models, and a combined integral system, which is a novel process industrial system proposed in recent years, is approximated as the two process objects for a long time in the past. Although this approximate description addresses the necessity of system control, there is great room for improvement in the control effect. Industrial process devices in the process industry are in an uninterrupted operation state for a long time, and the change of the structure aging operation environment of industrial equipment enables system parameters to drift, so that the control effect of the system is deteriorated, and the situation is serious and shutdown debugging can be faced. Resulting in a reduction in industrial process productivity while reducing resource utilization. In order to solve the control limitation, the system parameter change is responded, and the control effect is improved. Parameter identification and tuning research of a controller for a combined integral system are necessary.
For the combined integral system, the model approximates the deficiencies described:
(1) the first-order and second-order plus pure hysteresis system approximately describes that the combined integral system can only track the Navier curve of the system in a partial frequency domain range of the system, and certain deviation exists;
(2) the controller obtained according to the model design of the approximate description combined integral system cannot achieve ideal effects on control effects, namely rapidity, stability and robustness;
(3) according to the approximate description model, the identification parameters obtained by using a general parameter identification method have large errors, and the accuracy of the description system is further reduced.
Disclosure of Invention
The purpose of the invention is: the accuracy of the description system is improved.
In order to achieve the above object, the present invention provides an application method of a relay feedback identification method in a combined integral system, which is characterized by comprising the following steps:
step 1, performing a relay feedback test on a combined integral system to be identified by using an ideal non-biased relay, wherein the combined integral system is an open-loop stable object, and a transfer function of the combined integral system consists of 2 or more time-lag objects and is expressed in the following form:
Figure BDA0001367076030000011
in the formula, kiRepresenting system gain, s-table complex frequency domain operator, Gi(s) represents a stable polynomial without integral element, τ1iRepresenting a system time-lag parameter, τ2iRepresenting a system time lag parameter.
Step 2, utilizing deviation between the actual oscillation frequency and the theoretical critical oscillation frequency compensated by the offset phase angle to establish a frequency domain information relation, and deducing to obtain system parameters:
(a) the ideal non-biased relay receives the feedback signal to realize the switch switching, and the output of the system presents the frequency omega near the working point under the condition of satisfying the establishment limit switchingoscIs oscillated with a period of ToscAnd y (t) is a controlled object output signal, comprising:
Figure BDA0001367076030000021
Figure BDA0001367076030000022
in the formula, Fsn、FcnIf all the values are non-zero constants, phase angle shift exists between the oscillation point and the critical point on the open-loop Nyquist curve of the system, and:
Figure BDA0001367076030000023
in the formula (I), the compound is shown in the specification,pna phase angle representing the nth harmonic;
(b) for the second-order combined integral object, a new system frequency domain relation is established through offset angle compensation, and the relation is expressed as follows:
Figure BDA0001367076030000024
in the formula (1), k represents a system gain, ωsDenotes a frequency parameter, T denotes a time constant, k1The gain of the system is represented by,
Figure BDA0001367076030000025
τ2representing a system time lag;
Figure BDA0001367076030000031
in the formula (2), k3The gain of the system is represented by,
Figure BDA0001367076030000032
Figure BDA0001367076030000033
in the formula (3), k5The gain of the system is represented by,
Figure BDA0001367076030000034
from the amplitude relationships of equations (1), (2), and (3), we can obtain:
Figure BDA0001367076030000035
Figure BDA0001367076030000036
Figure BDA0001367076030000037
from the phase angle relationship:
Figure BDA0001367076030000038
k1、k3、k5derived from the frequency response of the object being estimated by numerical calculation, i.e.
Figure BDA0001367076030000039
In equation (8), K is 1,2,3, h denotes a relay output level, and y (i) denotes a system output signal;
the joint type (4) - (8) is calculated by using a 1stopst optimization tool box to obtain system parameters, namely k, tau1，τ2，T。
Due to the adoption of the technical scheme, compared with the prior art, the invention has the following advantages and positive effects:
the invention adopts the system input signal level as the selection principle for determining the switching level of an ideal relay, the relay switch level is set to be five to ten percent of the input level, and the switch is switched in the identification process, so that the system has a limit ring. And establishing a new frequency domain relation, and deducing to obtain the parameters of the combined integral system. Based on the reasons, the system performance analysis method specially aiming at the combined integration process and the application of the combined integration link in other fields have important theoretical and practical significance.
The invention adopts the parameter identification of the combined integral system based on the relay feedback, can realize single identification to obtain a plurality of parameters, and has high identification precision. Compared with an ATV method or a parameter estimation method for describing a combined integral system by an approximate model, the obtained identification effect is obviously improved.
Drawings
FIG. 1 is a basic schematic diagram of a relay feedback;
FIG. 2 is a diagram illustrating function analysis;
FIG. 3 is a waveform of an oscillation output of the combined integration system;
FIGS. 4(a) and 4(b) are comparisons of estimated model Nyquist curves;
FIGS. 5(a) and 5(b) are comparisons of pad approximation, estimated model Nyquist curves;
FIG. 6 is a step response curve for a second order combined integral system;
fig. 7 is a nominal system response curve.
Detailed Description
The invention will be further illustrated with reference to the following specific examples. It is to be understood that these examples are for illustrative purposes only and are not intended to limit the scope of the present invention, and that various changes and modifications may be suggested to one skilled in the art upon reading the teachings herein, and that such equivalents are within the scope of the appended claims.
The invention provides an application method of a relay feedback identification method on a combined integral system, which is characterized by comprising the following steps:
step 1, performing a relay feedback test on a combined integral system to be identified by using an ideal non-biased relay, wherein the combined integral system is an open-loop stable object, and a transfer function of the combined integral system consists of 2 or more time-lag objects and is expressed in the following form:
Figure BDA0001367076030000041
in the formula, kiRepresenting system gain, s represents complex frequency domain operator, Gi(s) represents a stable polynomial without integral element, τ1iRepresenting a system time-lag parameter, τ2iA parameter representing the time lag of the system,
without loss of generality, there are typically one to five combined integral objects, the transfer functions i.e. (i) one (v)
Figure BDA0001367076030000053
Figure BDA0001367076030000054
Figure BDA0001367076030000055
Figure BDA0001367076030000056
Figure BDA0001367076030000057
Where k denotes the system gain, k1Denotes the system gain, k2Denotes the system gain, T denotes the time constant, τ denotes the system time lag parameter, τ1Representing a system time-lag parameter, τ2Representing a system time-lag parameter, τ3Representing a system time-lag parameter, τ4Representing a system time-lag parameter, τ4＝τ1+τ2And s denotes a complex frequency domain operator.
Step 2, utilizing deviation between the actual oscillation frequency and the theoretical critical oscillation frequency compensated by the offset phase angle to establish a frequency domain information relation, and deducing to obtain system parameters:
(a) the ideal non-biased relay receives the feedback signal to realize the switch switching, and the output of the system presents the frequency omega near the working point under the condition of satisfying the establishment limit switchingoscIs oscillated with a period of ToscAnd y (t) is a controlled object output signal, comprising:
Figure BDA0001367076030000058
Figure BDA0001367076030000059
in the formula, Fsn、FcnIf all the values are non-zero constants, phase angle shift exists between the oscillation point and the critical point on the open-loop Nyquist curve of the system, and:
Figure BDA0001367076030000061
in the formula (I), the compound is shown in the specification,pna phase angle representing the nth harmonic;
the characteristics of the combined integral system are different from the characteristics of a first-order or second-order plus pure hysteresis system, and the oscillation waveform output shows the characteristic difference of the first-order or second-order plus pure hysteresis system under the condition that a limit loop is established, as shown in figure 3. The second combined integration system, i.e. (ii), exhibits a typical combined integration characteristic, with an oscillatory output of a trapezoidal wave. The situation that when the combined integral system is approximately described by a first-order or second-order plus lag model, estimated parameters are difficult to solve by using a phase angle shift identification method is explained.
(b) A second order combined integral object (iv) having a frequency characteristic of:
Figure BDA0001367076030000062
in the formula (I), the compound is shown in the specification,
Figure BDA0001367076030000063
for the second-order combined integral object, a new system frequency domain relation is established through offset angle compensation, and the relation is expressed as follows:
Figure BDA0001367076030000064
in the formula (1), k represents a system gain, ωsDenotes a frequency parameter, T denotes a time constant, k1The gain of the system is represented by,
Figure BDA0001367076030000065
τ2representing a system time lag parameter;
Figure BDA0001367076030000066
in the formula (2), k3The gain of the system is represented by,
Figure BDA0001367076030000071
Figure BDA0001367076030000072
in the formula (3), k5The gain of the system is represented by,
Figure BDA0001367076030000073
from the amplitude relationships of equations (1), (2), and (3), we can obtain:
Figure BDA0001367076030000074
Figure BDA0001367076030000075
Figure BDA0001367076030000076
from the phase angle relationship:
Figure BDA0001367076030000077
k1、k3、k5derived from the frequency response of the object being estimated by numerical calculation, i.e.
Figure BDA0001367076030000078
In equation (8), K is 1,2,3, h denotes a relay output level, and y (t) denotes a system output signal;
the joint type (4) - (8) is calculated by using a 1stopst optimization tool box to obtain system parameters, namely k, tau1，τ2，T。
In order to verify the effectiveness of the algorithm, a plurality of groups of different combined integral object model tests are selected for comparison. Assuming that the ATV prior information is known, the parameter identification result for the second combined integral object is shown in table 1, and is known from the Nyquist curve comparison of fig. 4(a) and fig. 4 (b): the phase angle shift method is used for identifying that the obtained system model is almost coincident with the actual system, and the identification result of the ATV method has certain deviation.
For the fourth combined integral object, the pad approximation model is directly used to compare with the actual object, and the parameter identification result is shown in table 2. From a comparison of the Nyquist curves of fig. 5(a) and 5(b), it can be seen that: the model obtained by phase angle shift method identification almost coincides with the actual system, and the effect is better than that of a Pade approximate model.
TABLE 1 comparison of identification results for a second combined integration object
Figure BDA0001367076030000081
TABLE 2 comparison of recognition results for fourth combined integration objects
Figure BDA0001367076030000082
Since the combined integral object has good open-loop characteristics, the system can respond quickly to reach a given value when a step is given. The step response curve of the second order combined integral system is shown in fig. 6. In order to make the whole closed loop system have good characteristics as shown in fig. 6, the desired closed loop transfer function is selected to have the following structural form:
Figure BDA0001367076030000083
in the formula, τ10Representing a system time-lag parameter, τ20Representing a system time lag parameter. When lambda is 1, the response time of the open loop is the same as that of the closed loop; when lambda is larger than 1, the response time of the open loop is faster than that of the closed loop; when λ < 1, the response time of the open loop is slower than that of the closed loop. This may reverse the controller transfer function:
Figure BDA0001367076030000084
let λ be 1, τ10＝τ1，τ20＝τ2，k0K, there are:
Figure BDA0001367076030000091
the input and output relations of the controller in the time domain are as follows:
Figure BDA0001367076030000092
where u(s) represents the controller output. Part of the equation is a proportional term, and the second term can be interpreted as the controller being at [ t- (τ)10+τ20)，i-τ20]The output of the time is obtained by predicting the output of the controller at the past time.
And (4) considering 1 second-order combined integral object, and performing simulation comparison by utilizing IMC-PID, predicted PI, PID and a combined integral controller.
Figure BDA0001367076030000093
According to the identified parameters, the transfer function of the system is known as follows:
Figure BDA0001367076030000094
compared with a step response curve under the condition of step interference, the control algorithm obtains the step response curve, and as can be seen from fig. 7, the combined integral controller is excellent in rapidity and almost free of overshoot, while IMC-PID and PID have certain overshoot more or less, and the adjusting time is longer. The predicted PI, although not overshooting, is somewhat slower. Overall, the control effect of the combined integral controller is fast and smooth.
The invention applies the concept of phase angle deviation to the relay feedback identification of the combined integral system, and avoids the problem that the estimated parameters cannot be obtained by describing the combined integral system by a first-order or second-order plus pure hysteresis model to carry out parameter identification. And the phase angle deviation is utilized to compensate the deviation between the experimental oscillation point of the relay and the theoretical critical value, so that the approximate error is eliminated. Under the condition of not needing prior information, a plurality of parameters of the combined integral system can be identified and obtained, and a combined integral generator is designed and obtained on the basis, and the control effect is fast and stable.

Claims (1)

1. A combined integral system identification method based on relay feedback is characterized by comprising the following steps:
step 1, performing a relay feedback test on a combined integral system to be identified by using an ideal non-biased relay, wherein the combined integral system is an open-loop stable object, and a transfer function of the combined integral system consists of 2 or more time-lag objects and is expressed in the following form:
Figure FDA0002383821580000011
in the formula, kiRepresenting system gain, s represents complex frequency domain operator, Gi(s) represents a stable polynomial without integral element, τ1iRepresenting a system time-lag parameter, τ2iRepresenting a system time lag parameter, i represents an ith harmonic, and n represents a harmonic order;
step 2, utilizing deviation between the actual oscillation frequency and the theoretical critical oscillation frequency compensated by the offset phase angle to establish a frequency domain information relation, and deducing to obtain system parameters:
(a) the ideal non-biased relay receives the feedback signal to realize the switch switching, and the output of the system presents the frequency omega near the working point under the condition of meeting the establishment of limit switchingoscIs oscillated with a period of ToscAnd y (t) is a controlled object output signal, comprising:
Figure FDA0002383821580000012
Figure FDA0002383821580000013
in the formula, Fsn、FcnIf all the values are non-zero constants, phase angle shift exists between the oscillation point and the critical point on the open-loop Nyquist curve of the system, and:
Figure FDA0002383821580000014
in the formula (I), the compound is shown in the specification,pna phase angle representing the nth harmonic;
(b) for the second-order combined integral object, a new system frequency domain relation is established through offset angle compensation, and the relation is expressed as follows:
Figure FDA0002383821580000021
in the formula (1), k represents a system gain, ωsDenotes a frequency parameter, T denotes a time constant, k1The gain of the system is represented by,
Figure FDA0002383821580000022
τ2representing a system time lag parameter;
Figure FDA0002383821580000023
in the formula (2), k3The gain of the system is represented by,
Figure FDA0002383821580000024
Figure FDA0002383821580000025
in the formula (3), k5The gain of the system is represented by,
Figure FDA0002383821580000026
from the amplitude relationships of equations (1), (2), and (3), we can obtain:
Figure FDA0002383821580000027
Figure FDA0002383821580000028
Figure FDA0002383821580000029
from the phase angle relationship:
Figure FDA00023838215800000210
k1、k3、k5derived from the frequency response of the object being estimated by numerical calculation, i.e.
Figure FDA0002383821580000031
In equation (8), K is 1,2,3, h denotes a relay output level, and y (t) denotes a system output;
the joint type (4) - (8) is calculated by using a 1stopst optimization tool box to obtain system parameters, namely k, tau1,τ2,T。
CN201710649291.0A 2017-08-01 2017-08-01 Combined integral system identification method based on relay feedback Active CN107422640B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201710649291.0A CN107422640B (en) 2017-08-01 2017-08-01 Combined integral system identification method based on relay feedback

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201710649291.0A CN107422640B (en) 2017-08-01 2017-08-01 Combined integral system identification method based on relay feedback

Publications (2)

Publication Number Publication Date
CN107422640A CN107422640A (en) 2017-12-01
CN107422640B true CN107422640B (en) 2020-08-11

Family

ID=60437129

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201710649291.0A Active CN107422640B (en) 2017-08-01 2017-08-01 Combined integral system identification method based on relay feedback

Country Status (1)

Country Link
CN (1) CN107422640B (en)

Families Citing this family (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111522224A (en) * 2020-05-09 2020-08-11 东华大学 Parameter self-tuning PLC control method based on prediction PI and bias relay feedback
CN111897204A (en) * 2020-06-29 2020-11-06 华东理工大学 PID parameter setting method of cascade control system based on single relay feedback

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2004274623A (en) * 2003-03-11 2004-09-30 Sharp Corp Data rounding correction circuit and video equipment
EP2161853A3 (en) * 2008-09-09 2013-06-05 NTT DoCoMo, Inc. Radio relay apparatus and method

Family Cites Families (10)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US7599752B2 (en) * 2005-05-17 2009-10-06 Utah State University Tuning methods for fractional-order controllers
KR100846554B1 (en) * 2006-11-15 2008-07-15 경북대학교 산학협력단 Integrals of relay feedback responses for extracting process information
US8255066B2 (en) * 2009-05-18 2012-08-28 Imb Controls Inc. Method and apparatus for tuning a PID controller
CN101807878B (en) * 2010-03-25 2011-07-27 上海交通大学 Servo system control method based on relay feedback
CN103269110A (en) * 2013-06-09 2013-08-28 哈尔滨工业大学 Control parameter self-tuning lithium battery charging control method based on relay feedback
CN103699010B (en) * 2013-12-04 2016-03-09 上海交通大学 A kind of servo system identification method based on relay position feedback temporal signatures
CN103941580A (en) * 2014-04-08 2014-07-23 上海理工大学 Closed loop frequency domain identification method of generator set based on bias relay feedback
CN104950679A (en) * 2015-06-17 2015-09-30 上海建坤信息技术有限责任公司 Air conditioning system model identification method based on bias relay feedback
CN105674935A (en) * 2016-02-25 2016-06-15 上海交通大学 Relay-feedback-based servo system gap identification method
CN105759607B (en) * 2016-02-26 2018-08-14 北京工业大学 The design method of PAC controllers based on intelligent control algorithm

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2004274623A (en) * 2003-03-11 2004-09-30 Sharp Corp Data rounding correction circuit and video equipment
EP2161853A3 (en) * 2008-09-09 2013-06-05 NTT DoCoMo, Inc. Radio relay apparatus and method

Also Published As

Publication number Publication date
CN107422640A (en) 2017-12-01

Similar Documents

Publication Publication Date Title
Zhang et al. Low-complexity tracking control of strict-feedback systems with unknown control directions
Gao Scaling and bandwidth-parameterization based controller tuning
CN108303885B (en) Self-adaptive control method of motor position servo system based on disturbance observer
Huang et al. Adaptive sliding control for single-link flexible-joint robot with mismatched uncertainties
Joseph et al. Cohen-coon PID tuning method; A better option to Ziegler Nichols-PID tuning method
Deng et al. Adaptive integral robust control and application to electromechanical servo systems
CN107422640B (en) Combined integral system identification method based on relay feedback
Ryu et al. Auto-tuning of sliding mode control parameters using fuzzy logic
CN109361333B (en) Online inertia identification method and system, motor controller and readable memory
Berger et al. Time optimal trajectory planning with feedforward and friction compensation
Raza et al. Feedback linearization using high gain observer for nonlinear electromechanical actuator
Patelski et al. Tracking control for a cascade perturbed control system using the active disturbance rejection paradigm
Su et al. On performance limitation in tracking a sinusoid
Chen et al. Motion control with deadzone estimation and compensation using GRNN for TWUSM drive system
Liu et al. Hybrid reference governor-based adaptive robust control of a linear motor driven system
Kim et al. Ga-based practical auto-tuning technique for industrial robot controller with system identification
CN110048600B (en) Method for carrying out second-order sliding mode synchronous optimization on time lag value delta and switching frequency in DC-DC buck converter
Al Janaideh et al. Adaptive control of uncertain Hammerstein systems with hysteretic nonlinearities
Davoodi et al. Design and implementation of a feedforward feedback controller for a piezoelectric actuator
Herrera et al. Identification and adaptive control of delayed unstable systems
Nguyen et al. Robust precision positioning control on linear ultrasonic motor
Zheng et al. Modified Smith predictor for frequency identification and disturbance rejection of single sinusoidal signal
Antritter et al. Nonlinear tracking control of a dc motor via a boost-converter using linear dynamic output feedback
Osypiuk Simple robust control structures based on the model‐following concept–A theoretical analysis
Zhao et al. Self-optimizing Control of an Air Source Heat Pump

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant