CN106647242A - Multivariable PID controller parameter setting method - Google Patents
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Abstract
The invention relates to a multivariable PID controller parameter setting method. The multivariable PID controller parameter setting method comprises following steps of leading in a model of a control system, and generating a reference point set in dependence on the target number of design models and a system sampling method; generating an initial population which is distributed uniformly randomly, wherein each individual in the population is a multivariable PID controller parameter; carrying out genetic algorithm operation to the population by Comprehensively considering a plurality of system performance indexes such as the steady state error, the rise time, the adjusting time and the overshoot to obtain a new population; mixing the obtained new population with the initial population, and achieving multivariable PID controller parameter setting. Under the condition that the same stability index is satisfied, the dynamic performance and the static performance of the optimization scheme provided by the invention are better.
Description
Technical field
The present invention relates to automatic control technology field, more particularly to a kind of based on the changeable of higher-dimension multi-objective genetic algorithm
Amount PID controller parameter setting method.
Background technology
The continuous development of industrial technology, production procedure becomes more complicated and compact, it means that traditional single argument control
System has been difficult to meet the demand for control of actual production flow process.And PID has been obtained for universal answering due to the advantage of its own
With, it is the demand for meeting complicated production flow process, multivariable PID of how adjusting parameter has important practical significance.
At present, domestic and international academia and engineering circles be typically the performance indications of system by its importance be converted into one plus
Power object function, then solution is optimized using traditional single object optimization algorithm.But these existing methods all generally existings are difficult
It is difficult to instruct the defects such as engineering practice accurately to set weight coefficient, allocation plan.Although existing part research staff is using biography
The Multipurpose Optimal Method of system attempts solution multivariable PID control parameter and adjusts, but traditional multi-objective optimization algorithm is usual
It is merely able to effective process 2-3 target, it is impossible to consider the over-all properties of system comprehensively, and computational efficiency is relatively low, is not easy to concrete
Engineering construction.
The content of the invention
The technical problem to be solved is to provide a kind of multivariable PID controller parameter tuning method, is meeting
The dynamic property of the prioritization scheme in the case of same stable index is more excellent with static properties.
The technical solution adopted for the present invention to solve the technical problems is：There is provided a kind of multivariable PID controller parameter whole
Determine method, comprise the following steps：
(1) model of control system is imported, is produced according to the target number and systematic sampling method that design a model and is referred to point set
Close, and determine target number M and respectively points S, the respectively points are referred to is divided equally interval [0,1] with S point；
(2) the initial population P={ P that random generation one is uniformly distributed, Population Size is NPi, i=1,2 ..., NP }, its
In each individual PiInclude the differential system of the proportionality coefficient of multiple controllers, the integral coefficient of controller and controller
Number；
(3) to each the individual P in population Pi, i=1,2 ..., NP, carry out multiple objective function assessment calculate, select,
Intersect, variation and the multiple-objection optimization of non-dominated ranking are operated, and obtain new individual population；
(4) the new individual population for obtaining and original seed group are carried out being mixed to get mixed population R, and according to the situation of domination
Mixed population R is layered, F is designated as1,F2,…；
(5) select individual as population P of future generation from mixed population Rt+1；
(6) repeat step (3)-step (5), the maximum iteration time until meeting user's setting；
(7) Pareto optimal solutions and the proportionality coefficient of corresponding controller, the integral coefficient of controller and controller are exported
Differential coefficient as multivariable PID controller parameter.
It is with reference to the generation process of point set in the step (1)：By each dimension interval [0,1] of M dimension coordinates with S
Point is divided equally, then the scale of [0,1/S, 2/S ..., 1] can be produced per dimension；Take out 1 from [0,1/S, 2/S ..., 1] scale～
The value of M dimensions, and this M being worth and for 1, this M value just may make up one group of M dimensional vector, the i.e. coordinate of reference point.
If M >=8, need to produce two-layer reference point；Target number M is determined first, and ground floor divides equally the S that counts1With second
Layer divides equally points S2；When determining ground floor reference point, each dimension interval [0,1] of M dimension coordinates is used into S1Individual point is divided equally, then often
Dimension can produce [0,1/S1,2/S1..., 1] scale；From [0,1/S1,2/S1..., 1] value of 1～M dimensions is taken out in scale,
And this M value and for 1, this M value just may make up one group of M dimensional vector, the as coordinate of ground floor reference point；Determine the second layer
During reference point, each dimension interval [0,1] of M dimension coordinates is used into S2Individual point is divided equally, then can produce [0,1/S per dimension2,2/
S2..., 1] scale；From [0,1/S2,2/S2..., 1] take out the value of 1～M dimensions in scale, and this M value and for 1, this M is individual
Value just may make up one group of M dimensional vector, the as coordinate of second layer reference point.
The step (3) specifically includes following sub-step：
(31) multiple target operation is carried out to population P, according to each individual non-dominated ranking situation, by each in population
Individuality is layered；
(32) selection operation, randomly chooses out two numberings from i={ 1,2,3 ..., NP }, by comparing two individualities
The place number of plies, selects preferably individual, repeats the step until selecting one new population NewP of NP individual composition；
(33) crossover operation, is selected in 2 individualities from new population NewP, the two individualities is carried out into arithmetic crossover, then
The two new individualities for obtaining；
(34) mutation operation, makes a variation to the individual multinomial that performs in new population NewP, obtains new individual population.
Population P is carried out in the step (31) choose steady-state error F of control system when multiple target is operatedess, rise when
Between Ftr, adjustment time FtsWith overshoot FovAs higher-dimension multiple objective function, i.e.,：Wherein, Kpm、Kim、Kdm：The respectively ratio of controller
The minimum of a value of the differential coefficient of coefficient, the integral coefficient of controller and controller；KpM、KiM、KdM：The respectively ratio of controller
The maximum of the differential coefficient of coefficient, the integral coefficient of controller and controller.
Beneficial effect
As a result of above-mentioned technical scheme, the present invention compared with prior art, has the following advantages that and actively imitates
Really：The present invention considers the stable state of system with factors such as the dynamic property of control system, static properties as this requirement of basic Jing
The multi-performance index such as error, rise time, adjustment time, overshoot, devise higher-dimension multi-objective genetic algorithm as solver,
Realize multivariable PID controller parameter tuning.Multivariable PID controller parameter tuning, phase are capable of achieving using the method for the present invention
Than traditional single object optimization method and traditional Multipurpose Optimal Method, with advantages below：For the choosing of multivariable PID controller parameter
The scheme for taking offer is more reasonable, the dynamic property and static properties of the prioritization scheme in the case of same stable index is met
More excellent, optimization method implements simple, adjusts without the need for complex cost function weight coefficient, adjusts without the need for complicated Optimal Parameters, and
Optimization efficiency is higher.
Description of the drawings
Fig. 1 is the multivariable PID controller structure chart of multivariable control system；
Fig. 2 is the multivariable PID controller parameter tuning method flow chart of higher-dimension multi-objective genetic algorithm；
Fig. 3 is M=3, reference point production method and result figure during s=5.
Specific embodiment
With reference to specific embodiment, the present invention is expanded on further.It should be understood that these embodiments are merely to illustrate the present invention
Rather than restriction the scope of the present invention.In addition, it is to be understood that after the content for having read instruction of the present invention, people in the art
Member can make various changes or modifications to the present invention, and these equivalent form of values equally fall within the application appended claims and limited
Scope.
Fig. 1 is the multivariable PID controller structure chart of multivariable control system, including multivariable PID controller D (s), many
Variable control system transmission function G (s), wherein the G (s) for choosing is terminal composition destilling tower controller：The coefficient of coup of selection
Fig. 2 is the multivariable PID controller parameter tuning method flow process of higher-dimension multi-objective genetic algorithm proposed by the present invention
Figure.By taking the control system that terminal constitutes destilling tower as an example, using the multivariable of higher-dimension multi-objective genetic algorithm proposed by the present invention
PID controller parameter setting method is designed enforcement.
The multivariable PID controller parameter tuning method of described higher-dimension multi-objective genetic algorithm, comprises the following steps：
(1) model of above-mentioned control system is imported, M object function is determined by model, according to object function number and be
System sampling method is produced and refers to point set.The process of generation is as follows：Target number M=3 and respectively points S=are determined in the present embodiment
5, so-called respectively points are referred to is divided equally interval [0,1] with S point.Because target number is M ＜ 8, it is determined that each reference point
M dimension coordinates are needed to represent.Each dimension interval [0,1] of M dimension coordinates is divided equally with S point, then can produce [0,1/ per dimension
S, 2/S ..., 1] scale.Take out the value of 1～M dimensions from [0,1/S, 2/S ..., 1] scale, and this M being worth and for 1, this M
Individual value just may make up one group of M dimensional vector, the i.e. coordinate of reference point.Shown in Fig. 3 is M=3, during s=5 reference point production method and
Result figure.
If it is noted that M >=8, if only producing one layer of reference point, the quantity of point can be very huge, to avoid producing
Many reference points, then need to produce two-layer reference point；Generation process is as follows：Target number M is determined first, and ground floor is respectively counted
S1Divide equally the S that counts with the second layer2；Determine ground floor reference point, produce situation of the process with M ＜ 8, and the reference point of generation is deposited
In being put in set A.Determine second layer reference point according still further to similar rule.
(2) initialize, random generation one is uniformly distributed the initial population P={ P that Population Size is NPi, i=1,2 ...,
NP }, wherein i-th individuality Pi=(Kpi1,Kii1,Kdi1,Kpi2,Kii2,Kdi2,…,Kpin,Kiin,Kdin), KpiFor controller
Proportionality coefficient, KiiFor the integral coefficient of controller, KdiFor the differential coefficient of controller.
(3) to each the individual P in population Pi, i=1,2 ..., NP, carry out multiple objective function assessment calculate, select,
The multiple-objection optimizations such as intersection, variation, non-dominated ranking are operated, and specifically include following sub-step：
(3.1) multiple target operation is carried out to population P, according to each individual non-dominated ranking situation, to population
In each individuality be layered；When multiple target operation is carried out, higher-dimension multiple objective function can set according to the actual requirements
It is fixed, with certain flexibility and different effect of optimization can be reached, the object function chosen in the present embodiment is as follows：Wherein, FessFor steady-state error, FtrFor rise time, Fts
For adjustment time and FovFor overshoot, Kpm、Kim、KdmThe respectively proportionality coefficient of controller, the integral coefficient of controller and control
The minimum of a value of the differential coefficient of device processed；KpM、KiM、KdMThe respectively proportionality coefficient of controller, the integral coefficient of controller and control
The maximum of the differential coefficient of device processed.
(3.2) selection operation, randomly chooses out two numberings, by comparing two individualities from i={ 1,2,3 ..., NP }
The place number of plies, select preferably individual until selecting one new population NewP of NP individual composition；
(3.3) crossover operation, selects in 2 individuality NewP1And NewP2Between carry out arithmetic crossover, then the new individual for obtaining
For：NewP1'=NewP1(1-b)+NewP2B, NewP2'=NewP2(1-b)+NewP1B, wherein, b is cross parameter, and scope is
[0,1]。
(3.4) mutation operation, to the individual multinomial that performs in NewP (Polynomial mutation, PLM) is made a variation,
Keep other constituent elements constant simultaneously, obtain new individual population.Wherein multinomial variation mode be：Wherein,
R is 0, and the number randomly generated in 1, t represents iterations；The lower limit of k-th variable is represented,Represent k-th change
The upper limit of amount；Q is Mutation parameter, and general value is [2,5].
(4) new individual population and population P are carried out into mixing and produces mixed population R, according to the situation of domination, to hybrid
Group R is layered, and is designated as F1,F2,…；
(5) select individual as population P of future generation from mixed population Rt+1；Successively from F1,F2... select individual
It is added to Pt+1, until adding a certain layer FlSo thatThen do not add.IfThen population of future generationOtherwise, need by a kind of selection mechanism from FlIn select K (K=N- | Pt+1|) individuality, then it is of future generation to plant
Group
(6) repeat step (3)-(5) are until meeting the maximum iteration time that user sets；
(7) export Pareto optimal solutions and corresponding steady-state error, rise time, adjustment time, overshoot evaluation to refer to
Scale value, and corresponding Kpi1,Kii1,Kdi1,Kpi2,Kii2,Kdi2Provide the user multivariable PID controller parameter.
Design is optimized to above-mentioned control system using the method for the present invention, is as a result shown：The present invention is capable of achieving changeable
Amount PID controller parameter is adjusted, and the dynamic performance and static properties in the case of same stable index is met is than tradition
Single object optimization method and traditional Multipurpose Optimal Method are more excellent.And the present invention is whole without the need for complex cost function weight coefficient
It is fixed, the multi-performance index such as steady-state error, rise time, adjustment time, the overshoot of control system are considered comprehensively.
It is seen that, multivariable PID controller parameter tuning is capable of achieving using the method for the present invention, compare traditional single goal
Optimization method and traditional Multipurpose Optimal Method, with advantages below：The scheme for providing is chosen for multivariable PID controller parameter
More reasonable, the dynamic property of the prioritization scheme in the case where same stable index is met is more excellent with static properties, optimization
Method implements simple, adjusts without the need for complex cost function weight coefficient, adjusts without the need for complicated Optimal Parameters, and optimization efficiency is more
It is high.
Claims (5)
1. a kind of multivariable PID controller parameter tuning method, it is characterised in that comprise the following steps：
(1) model of control system is imported, is produced according to the target number and systematic sampling method that design a model and is referred to point set, and
Determine target number M and respectively points S, the respectively points are referred to is divided equally interval [0,1] with S point；
(2) the initial population P={ P that random generation one is uniformly distributed, Population Size is NPi, i=1,2 ..., NP }, wherein often
Individual PiInclude the differential coefficient of the proportionality coefficient of multiple controllers, the integral coefficient of controller and controller；
(3) to each the individual P in population Pi, i=1,2 ..., NP, carry out multiple objective function assessment calculate, select, intersect,
Variation and the multiple-objection optimization of non-dominated ranking are operated, and obtain new individual population；
(4) the new individual population for obtaining and original seed group are carried out being mixed to get mixed population R, and according to situation about arranging to mixed
Close population R to be layered, be designated as F1,F2,…；
(5) select individual as population P of future generation from mixed population Rt+1；
(6) repeat step (3)-step (5), the maximum iteration time until meeting user's setting；
(7) the micro- of Pareto optimal solutions and the proportionality coefficient of corresponding controller, the integral coefficient of controller and controller is exported
Divide coefficient as multivariable PID controller parameter.
2. multivariable PID controller parameter tuning method according to claim 1, it is characterised in that in the step (1)
It is with reference to the generation process of point set：Each dimension interval [0,1] of M dimension coordinates is divided equally with S point, then can be produced per dimension
The scale of raw [0,1/S, 2/S ..., 1]；The value of 1～M dimensions, and the sum of this M value are taken out from [0,1/S, 2/S ..., 1] scale
For 1, this M value just may make up one group of M dimensional vector, the i.e. coordinate of reference point.
3. multivariable PID controller parameter tuning method according to claim 2, it is characterised in that if M >=8, need
Produce two-layer reference point；Target number M is determined first, and ground floor divides equally the S that counts1Divide equally the S that counts with the second layer2；Determine ground floor
During reference point, each dimension interval [0,1] of M dimension coordinates is used into S1Individual point is divided equally, then can produce [0,1/S per dimension1,2/
S1..., 1] scale；From [0,1/S1,2/S1..., 1] take out the value of 1～M dimensions in scale, and this M value and for 1, this M is individual
Value just may make up one group of M dimensional vector, the as coordinate of ground floor reference point；When determining second layer reference point, by the every of M dimension coordinates
Individual dimension interval [0,1] uses S2Individual point is divided equally, then can produce [0,1/S per dimension2,2/S2..., 1] scale；From [0,1/
S2,2/S2..., 1] take out the value of 1～M dimensions in scale, and this M being worth and for 1, this M value just may make up one group of M dimensional vector,
The as coordinate of second layer reference point.
4. multivariable PID controller parameter tuning method according to claim 1, it is characterised in that step (3) tool
Body includes following sub-step：
(31) multiple target operation is carried out to population P, it is according to each individual non-dominated ranking situation, each in population is individual
It is layered；
(32) selection operation, randomly chooses out two numberings, by the place for comparing two individualities from i={ 1,2,3 ..., NP }
The number of plies, selects preferably individual, repeats the step until selecting one new population NewP of NP individual composition；
(33) crossover operation, is selected in 2 individualities from new population NewP, and the two individualities are carried out into arithmetic crossover, then obtain
Two new individualities；
(34) mutation operation, makes a variation to the individual multinomial that performs in new population NewP, obtains new individual population.
5. multivariable PID controller parameter tuning method according to claim 1, it is characterised in that the step (31)
In population P is carried out multiple target operate when choose control system steady-state error Fess, rise time Ftr, adjustment time FtsWith it is super
Tune amount FovAs higher-dimension multiple objective function, i.e.,：Minimize(Fess1,Ftr1,Fts1,Fov1,...,Fessn,Ftrn,Ftsn,Fovn)
Wherein, Kpm、Kim、Kdm：The respectively ratio of controller
The minimum of a value of the differential coefficient of example coefficient, the integral coefficient of controller and controller；KpM、KiM、KdM：The respectively ratio of controller
The maximum of the differential coefficient of example coefficient, the integral coefficient of controller and controller.
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| CN108303872A (en) * | 2018-01-31 | 2018-07-20 | 湖北工业大学 | A kind of pid parameter setting method and system based on lightning searching algorithm |
| CN111522226A (en) * | 2020-05-20 | 2020-08-11 | 中国科学院光电技术研究所 | Multi-objective optimization high-type PID optimal controller design method for servo turntable |
| CN108197738B (en) * | 2017-12-29 | 2020-09-15 | 东华大学 | Technological parameter optimization method for polyester filament melt conveying process |
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Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108197738B (en) * | 2017-12-29 | 2020-09-15 | 东华大学 | Technological parameter optimization method for polyester filament melt conveying process |
| CN108303872A (en) * | 2018-01-31 | 2018-07-20 | 湖北工业大学 | A kind of pid parameter setting method and system based on lightning searching algorithm |
| CN108303872B (en) * | 2018-01-31 | 2020-10-02 | 湖北工业大学 | PID parameter setting method and system based on lightning search algorithm |
| CN111522226A (en) * | 2020-05-20 | 2020-08-11 | 中国科学院光电技术研究所 | Multi-objective optimization high-type PID optimal controller design method for servo turntable |
| CN111522226B (en) * | 2020-05-20 | 2022-06-28 | 中国科学院光电技术研究所 | Multi-objective optimization high-type PID optimal controller design method for servo turntable |
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