CN106527120A - Stability margin configuration method for specified-accuracy PID control system - Google Patents

Stability margin configuration method for specified-accuracy PID control system Download PDF

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Publication number
CN106527120A
CN106527120A CN201611144175.5A CN201611144175A CN106527120A CN 106527120 A CN106527120 A CN 106527120A CN 201611144175 A CN201611144175 A CN 201611144175A CN 106527120 A CN106527120 A CN 106527120A
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omega
frequency
margin
pid
frequency characteristic
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杨启文
刘赏还
薛云灿
韩胜
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Changzhou Campus of Hohai University
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Changzhou Campus of Hohai University
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    • GPHYSICS
    • G05CONTROLLING; REGULATING
    • G05BCONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B11/00Automatic controllers
    • G05B11/01Automatic controllers electric
    • G05B11/36Automatic controllers electric with provision for obtaining particular characteristics, e.g. proportional, integral, differential
    • G05B11/42Automatic controllers electric with provision for obtaining particular characteristics, e.g. proportional, integral, differential for obtaining a characteristic which is both proportional and time-dependent, e.g. P. I., P. I. D.

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  • General Physics & Mathematics (AREA)
  • Engineering & Computer Science (AREA)
  • Automation & Control Theory (AREA)
  • Feedback Control In General (AREA)

Abstract

The present invention discloses a stability margin configuration method for a specified-accuracy PID control system. The method comprises the steps of firstly, establishing a frequency characteristics model of a controlled object; secondly, according to a specified open-loop crossover frequency and a desired amplitude margin, calculating a proportional gain required by a PID controller; thirdly, according to the definition formula of a phase angle margin, searching an open-loop cut-off frequency that meets the desired amplitude margin through the optimizing control algorithm; finally, according to a given formula, calculating the integral gain and the differential gain of the PID controller. Based on above three parameter values of the PID, the specified stability margin of the system is realized. According to the technical scheme of the invention, the difficulty of solving non-linear equations is avoided through the analytic method. Therefore, the PID parameter setting is realized at the specified stability margin.

Description

PID control system stability margin collocation method with designated precision
Technical field
The invention belongs to control method technical field, more particularly to a kind of PID control system with designated precision is stably Nargin collocation method.
Background technology
As control algolithm is simple, adjustable parameter is few and can meet the performance requirement of most of control systems, so far The control loop for still having 95% adopts PID controller.Due to PID controller parameter configuration it is whether suitable, it will usually have influence on The performance of control system, therefore, the parameter tuning problem of PID controller is always the focus of academia and industrial quarters concern. In numerous setting methods of PID controller, it is broadly divided into that time domain is adjusted and frequency domain is adjusted two classes.Wherein, system stablizes abundant Degree (including magnitude margin and Phase margin) is an important indicator must being fulfilled in frequency domain setting method.However, due to nothing Method solves trigonometric function equation, thus system design index is difficult to done with high accuracy.
The content of the invention
In order to meet the design exact requirements of stability margin, the present invention provides one kind and solves cutoff frequency by optimization method The method for designing of rate:By the solving precision for arranging cut-off frequency, the cutoff frequency of designated precision is obtained using linear search algorithm Rate, so as to finally calculate three parameters of PID controller.
The technical scheme that the present invention takes is as follows:
A kind of collocation method of the PID control system stability margin with designated precision, comprises the following steps:
S1, sets up the frequency characteristic model of the frequency characteristic model and PID controller of controlled device;
S2, according to specified cross-over frequency ωxWith magnitude margin AmRequire, calculate the proportional gain of PID controller;
S3, based on optimizing algorithm, search meets specifies Phase margin ΦmCut-off frequency ωc
S4, based on the cut-off frequency ω that the optimizing of step S3 is obtainedc, calculate the storage gain K of PIDiWith differential gain Kd
Step S1, frequency characteristic G of controlled devicep(j ω) is:
Gp(j ω)=u (ω)+jv (ω) (1)
In formula (1), j is imaginary symbols, and ω is frequency, real parts of the u (ω) for the frequency characteristic of controlled device, and v (ω) is The imaginary part of the frequency characteristic of controlled device;
The frequency characteristic model of PID controller is:
Gc(j ω)=Kp+X(ω)j (2)
Wherein,For the imaginary part of the frequency characteristic of PID controller, Kp、Ki、KdIt is expressed as PID controls The proportional gain of device processed, storage gain and the differential gain.
Step S2, it is intended that cross-over frequency be ωx, then meet and specify magnitude margin AmProportional gain by formula (3) count Calculate:
Wherein u (ωx) for ω=ωxWhen controlled device frequency characteristic real part, v (ωx) for ω=ωxWhen controlled device The imaginary part of frequency characteristic.
In step S3, it is intended that Phase margin be ΦmMeet nonlinear equation (4):
u(ωc) for ω=ωcWhen controlled device frequency characteristic real part, v (ωc) for ω=ωcWhen controlled device frequency The imaginary part of characteristic;Wherein X (ωc) computing formula be formula (5):
Solving precision ε is set, and by optimizing algorithm, search meets the cut-off frequency ω of solving precision εc.More preferably, pass through Two way classification is searching for ωc
More preferably, the cut-off frequency ω of solving precision ε is met using dichotomizing searchc, comprise the following steps:
S001:The region of search [ω is setL ωR] (ω during initializationLx, ωR=0), interval midpoint is taken for ωc= 0.5(ωLR);
S002:By ωcNonlinear equation (4) is updated to, the value on the right of nonlinear equation (4) is calculated;
S003:Judge the absolute value of difference of the value on nonlinear equation (4) left side and the value on the right whether less than default precision ε;If less than default precision ε, based on gained ωc, turn to step S4;S004 is performed otherwise;
S004:If value is worth less than the left side on the right of nonlinear equation (4), ω is takenLc;Conversely, ωRc;Return S001。
The storage gain K of PID controller described in step S4iWith differential gain KdCalculated based on formula (6):
Wherein,Compared with prior art, the present invention's has Beneficial effect includes:The solution of nonlinear equation is searched for by optimized algorithm, it is to avoid the difficulty of direct solution nonlinear equation, can Obtain the balance between solving precision and solving complexity, meet the needs of engineering design, can under the conditions of designated precision, PID control system stability margin configuration is carried out, the configuration required precision of PID control system stability margin is met.
Specific embodiment
PID control system stability margin collocation method with designated precision, takes following steps to calculate pid parameter, can To obtain desired stability margin (magnitude margin Am and Phase margin Φm):
A kind of collocation method of the PID control system stability margin with designated precision, comprises the following steps:
S1, sets up the frequency characteristic model of the frequency characteristic model and PID controller of controlled device;
S2, according to specified cross-over frequency ωxWith magnitude margin AmRequire, calculate the proportional gain of PID controller;
S3, based on optimizing algorithm, search meets specifies Phase margin ΦmCut-off frequency ωc
S4, based on the cut-off frequency ω that the optimizing of step S3 is obtainedc, calculate the storage gain K of PIDiWith differential gain Kd
Step S1, frequency characteristic G of controlled devicep(j ω) is:
Gp(j ω)=u (ω)+jv (ω) (1)
In formula (1), j is imaginary symbols, and ω is frequency, real parts of the u (ω) for the frequency characteristic of controlled device, and v (ω) is The imaginary part of the frequency characteristic of controlled device;
The frequency characteristic model of PID controller is:
Gc(j ω)=Kp+X(ω)j (2)
Wherein,For the imaginary part of the frequency characteristic of PID controller, Kp、Ki、KdIt is expressed as PID controls The proportional gain of device processed, storage gain and the differential gain.
Step S2, it is intended that cross-over frequency be ωx, then meet and specify magnitude margin AmProportional gain by formula (3) count Calculate:
u(ωx) for ω=ωxWhen controlled device frequency characteristic real part, v (ωx) for ω=ωxWhen controlled device frequency The imaginary part of characteristic.
In step S3, it is intended that Phase margin be ΦmMeet nonlinear equation (4):
u(ωc) for ω=ωcWhen controlled device frequency characteristic real part, v (ωc) for ω=ωcWhen controlled device frequency The imaginary part of characteristic;Wherein X (ωc) computing formula be formula (5):
Solving precision ε is set, and by optimizing algorithm, search meets the cut-off frequency ω of solving precision εc
The present embodiment, searches for ω using two way classificationc
S001:The region of search [ω is setL ωR] (ω during initializationLx, ωR=0), interval midpoint is taken for ωc= 0.5(ωLR);
S002:By ωcIt is updated to nonlinear equation (4), the value on the right of accounting equation (4);
S003:Whether the absolute value of the difference of decisive equation (4) left and right value is less than default precision ε;Turn if condition is met To S005;S004 is performed otherwise;
S004:If value takes ω less than the left side on the right of equation (4)Lc;Conversely, ωRc;Return S001;
S005:Using gained ωc, based on equation below, calculate the storage gain K of the PID controlleriAnd the differential gain Kd
In formula,
So, when three parameters of PID controller are arranged according to above-mentioned requirements, the stability margin required by design objective Required precision can just be met.
Those skilled in the art the present invention can be modified or modification design but without departing from the present invention think of Think and scope.Therefore, if these modifications of the present invention and modification belong to the technical scope of the claims in the present invention and its equivalent Within, then the present invention is also intended to comprising these changes and modification.

Claims (6)

1. a kind of collocation method of the PID control system stability margin with designated precision, its feature are comprised the following steps:
S1, sets up the frequency characteristic model of the frequency characteristic model and PID controller of controlled device;
S2, according to specified cross-over frequency ωxWith magnitude margin AmRequire, calculate the proportional gain of PID controller;
S3, based on optimizing algorithm, search meets specifies Phase margin ΦmCut-off frequency ωc
S4, calculates the storage gain K of PIDiWith differential gain Kd
2. the PID control system stability margin degree collocation method with designated precision according to claim 1, its feature exist In:Frequency characteristic G of controlled devicep(j ω) is:
Gp(j ω)=u (ω)+jv (ω) (1)
In formula (1), j is imaginary symbols, and ω is frequency, real parts of the u (ω) for the frequency characteristic of controlled device, and v (ω) is controlled The imaginary part of the frequency characteristic of object;
The frequency characteristic model of PID controller is:
Gc(j ω)=Kp+X(ω)j (2)
Wherein,For the imaginary part of the frequency characteristic of PID controller, Kp、KiAnd KdIt is expressed as PID controller Proportional gain, storage gain and the differential gain.
3. the PID control system stability margin collocation method with designated precision according to claim 1, its feature exist In:
The cross-over frequency specified is ωx, then meet and specify magnitude margin AmProportional gain by formula (3) calculate:
K p = - u ( ω x ) A m [ u 2 ( ω x ) + v 2 ( ω x ) ] - - - ( 3 )
u(ωx) for ω=ωxWhen controlled device frequency characteristic real part, v (ωx) for ω=ωxWhen controlled device frequency characteristic Imaginary part.
4. the PID control system stability margin collocation method with designated precision according to claim 1, its feature exist In:
In step S3, it is intended that Phase margin be ΦmMeet nonlinear equation (4):
Wherein X (ωc) computing formula be formula (5):
X ( ω c ) = - 1 u 2 ( ω c ) + v 2 ( ω c ) - K p 2 - - - ( 5 )
Solving precision ε is set, and by optimizing algorithm, search meets the cut-off frequency ω of solving precision εc
5. the PID control system stability margin collocation method with designated precision according to claim 4, its feature exist In:
The cut-off frequency ω of solving precision ε is met using dichotomizing searchc, comprise the following steps:
S001:The region of search [ω is setL ωR], interval midpoint is taken for ωc=0.5 (ωLR);
S002:By ωcNonlinear equation (4) is updated to, the value on the right of nonlinear equation (4) is calculated;
S003:Judge the absolute value of difference of the value on nonlinear equation (4) left side and the value on the right whether less than default precision ε;Such as Fruit is less than default precision ε, based on gained ωc, then turn to step S4;S004 is performed otherwise;
S004:If value is worth less than the left side on the right of nonlinear equation (4), ω is takenLc;Conversely, ωRc;Return S001.
6. the PID control system stability margin collocation method with designated precision according to claim 1, its feature exist In:The storage gain K of PID controller described in step S4iWith differential gain KdCalculated based on formula (6):
K i = λ [ X ( ω x ) ω c - X ( ω c ) ω x ] K d = λ [ X ( ω x ) ω c - X ( ω c ) ω x ] - - - ( 6 )
Wherein,
CN201611144175.5A 2016-12-13 2016-12-13 Stability margin configuration method for specified-accuracy PID control system Pending CN106527120A (en)

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Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110032171A (en) * 2019-04-23 2019-07-19 北京航天飞腾装备技术有限责任公司 One kind being based on cutoff frequency control loop design method
CN111812967A (en) * 2020-05-27 2020-10-23 浙江中控技术股份有限公司 PID control parameter setting method based on stability margin and dynamic response index
CN113157503A (en) * 2021-03-19 2021-07-23 山东英信计算机技术有限公司 Heat dissipation debugging method and related device

Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108594676A (en) * 2018-04-04 2018-09-28 河海大学常州校区 A kind of industry controlled process characteristic parameter Fast Identification Method

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108594676A (en) * 2018-04-04 2018-09-28 河海大学常州校区 A kind of industry controlled process characteristic parameter Fast Identification Method

Non-Patent Citations (4)

* Cited by examiner, † Cited by third party
Title
任丰原 等: "ATM网络拥塞控制中PID控制器的设计", 《计算机学报》 *
张富强 等: "满足幅值裕度和相角裕度的PID 参数域", 《天津科技大学学报》 *
王亚刚 等: "基于频域辨识的自整定PID 控制器", 《自动化仪表》 *
黄静静 等: "《MATLAB与数学实验》", 31 July 2015 *

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110032171A (en) * 2019-04-23 2019-07-19 北京航天飞腾装备技术有限责任公司 One kind being based on cutoff frequency control loop design method
CN110032171B (en) * 2019-04-23 2020-06-12 北京航天飞腾装备技术有限责任公司 Control loop design method based on cut-off frequency
CN111812967A (en) * 2020-05-27 2020-10-23 浙江中控技术股份有限公司 PID control parameter setting method based on stability margin and dynamic response index
CN113157503A (en) * 2021-03-19 2021-07-23 山东英信计算机技术有限公司 Heat dissipation debugging method and related device

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