CN110442027A - A kind of gap multi-model weighting function methods of self-tuning - Google Patents
A kind of gap multi-model weighting function methods of self-tuning Download PDFInfo
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Abstract
The invention discloses a kind of gap multi-model weighting function methods of self-tuning, it is characterized in that, analyze the characteristic of nonlinear system, selection is able to reflect the scheduling variable of system operating condition, utilize the Models Sets of multi model decomposition algorithm building approximate non-linear system, sub-controller is designed based on each submodel in the Models Sets, the weighting function of sub-controller includes the inverse of the gap distance between current time nonlinear system and each submodel, there is unique setting parameter in the weighting function, the optimal value of setting parameter is obtained by optimizing the integral absolute error value between the closed loop output of nonlinear system and reference input.Advantage: it is cumbersome to avoid weighting function manual parameters adjusting bring；Reduce dependence of the parameter tuning to priori knowledge；Optimize the control performance of closed-loop system.
Description
Technical field
The present invention relates to a kind of gap multi-model weighting function methods of self-tuning, belong to nonlinear system multi-model control
Technical field processed.
Background technique
Multiple Model Control Method is in processing relatively wider, the biggish nonlinear system of jam-to-signal control with opereating specification
There is natural advantage in terms of problem processed.It can be effectively by complexity based on decomposition-synthesis principle Multiple Model Control Method
Nonlinear Control problem is a series of simple Linear Control problems by decomposition and inversion；Then by solving this array of linear
Control problem realizes the solution to nonlinear Control problem.
Multi-model process mainly contains multi model decomposition, Partial controll design and multi-model and synthesizes three key steps
Suddenly.Wherein, multi-model synthesis generallys use hard handover and soft handover two ways carries out the synthesis of sub-controller.Although hard handover
Mode can choose most suitable model controller and be cut into closed-loop system, however hard handover easilys lead to system output and trembles
It is dynamic, it is unstable to even result in closed-loop system.In contrast, soft handoff, also known as weighting function method can make system defeated
It is smooth out, avoid output jitter.Therefore weighting function method is more favourable in multi-model synthesis.
Traditional weighting function, although such as the structure such as trapezoidal weighting function, gaussian weighing function, triangular weighting function
Form is simple, however the number of setting parameter is relatively more, and increases with the increase of submodel number, thus whole to parameter
Surely huge challenge is brought.Weighting function method based on gap (gap) has been suggested in recent years and for Multiple model control device
Synthesis, however the adjusting of parameter also needs trial repeatedly, cumbersome examination to gather.
Summary of the invention
The technical problem to be solved by the present invention is to overcome the existing multi-model weighting function parameter tuning based on gap multiple
Miscellaneous cumbersome defect provides a kind of gap multi-model weighting function methods of self-tuning.
In order to solve the above technical problems, the present invention provides a kind of gap multi-model weighting function methods of self-tuning, analysis
The characteristic of nonlinear system, selection are able to reflect the scheduling variable of system operating condition, are constructed using multi model decomposition algorithm close
Like the Models Sets of nonlinear system, sub-controller, the weighting of sub-controller are designed based on each submodel in the Models Sets
Function includes the inverse of the gap distance between current time nonlinear system and each submodel, is had in the weighting function
Unique setting parameter is obtained whole by the integral absolute error value between the closed loop output of optimization nonlinear system and reference input
The optimal value of parameter is determined, to realize the Self-tuning System of parameter.
Further, the submodel in the Models Sets of the approximate non-linear system is linear submodel Pi, i=1,2,
3 ... m, m are the total number of submodel, linear submodel PiCorresponding sub-controller is Ki, the output of t moment, sub-controller is
ui(t), i=1,2,3 ... m, m are the total number of sub-controller；
The output formula of the Multiple model control device are as follows:
U (t) is input to nonlinear system, obtains closed loop output y (t) of system, whereinIndicate i-th of son control
Device K processediWeight function in t moment, θtIndicate the value of t moment scheduling variable,.
To effectively convert several Linear Control problems for complicated nonlinear control system problem, simplify.
Further, the formula of the weight function are as follows:
Wherein keIt is the setting parameter of weighting function, is nonnegative integer, l=1,2,3 ... m, when t moment, nonlinear system
Model be denoted as nPt, inearized model is denoted as P (θt), nonlinear system nPt and linear submodel PiBetween gap metric
(gap metric) distance is γi(θt)=δ (Pi, P (θt)), function δ (Pi, P (θt)) indicate linear system PiWith P (θt) between
Gap metric distance.The weight function structure is simple, calculates and is easy, and only one setting parameter, greatly reduces ginseng
The cumbersome workload of number adjusting bring.
Further, the formula of the integral absolute error value are as follows:
Wherein, error (t) indicate nonlinear system output y (t) and reference signal ref (error between (t), | |
Be that absolute value sign indicates is any symbol, and ref (t) is the reference input of t moment nonlinear system.Absolutely accidentally using integral
Poor index can effectively improve the control precision of system.
Further, objective function J is constructed:
Optimization object function J acquires optimal keCorresponding Multiple model control device is the multi-model control of optimized parameter
Device processed.By minimizing integral absolute error, the control performance of optimization system realizes the Self-tuning System of parameter, avoids cumbersome ginseng
Number tuning process.
Further, the multi model decomposition algorithm uses the multi model decomposition algorithm based on gap metric.Can be
System effectively decomposes controlled device, reduces the dependence to priori knowledge, improves the efficiency of decomposition.
Advantageous effects of the invention:
It is cumbersome to avoid weighting function manual parameters adjusting bring；Reduce dependence of the parameter tuning to priori knowledge；It is excellent
The control performance of closed-loop system is changed.
Detailed description of the invention
Fig. 1 is that output response of the CSTR system under the Multiple model control device based on Self-tuning System gap weighting of the invention is bent
Line (yg) and Multiple model control device based on trapezoidal weighting function under output response curve (yT)
Fig. 2 is the control input signal u of two kinds of Multiple model control devicesgAnd uT
Fig. 3 is the integral absolute error value of CSTR system with keVariation and the curve graph that changes.
Specific embodiment
In order to make the invention's purpose, features and advantages of the invention more obvious and easy to understand, below in conjunction with the present invention
Attached drawing in embodiment, technical scheme in the embodiment of the invention is clearly and completely described, it is clear that disclosed below
Embodiment be only a part of the embodiment of the present invention, and not all embodiment.Based on the embodiments of the present invention, this field is general
Logical technical staff all other embodiment obtained without making creative work belongs to what the present invention protected
Range.
To further illustrate the technical scheme of the present invention below with reference to the accompanying drawings and specific embodiments.
A kind of gap multi-model weighting function methods of self-tuning, specific to a continuous-stirred tank reactor
(CSTR) it is emulated and is analyzed.
Wherein CAIt (mol/l) is reaction density, input variable is u (min-1).C in equationAi(1.0mol/l) is charging
Concentration, k=0.028min-1It is rate constant, y indicates the output of system.This mission nonlinear degree is very strong, single Linear Control
Device is unable to satisfy requirement.
The present invention is controlled it using multi-model process.Using the gap multi-model weighting function Self-tuning System side
Method, steps are as follows:
S1. the output y of selecting system is scheduling variable；
S2. the linear submodel collection obtained are as follows:Wherein s indicates transmission function
Operator；
S3. it is based on submodel P1,P2Design H∞Controller, respectively And the output for calculating two sub-controller of t moment is respectively u1(t),u2(t)；
When the S4.t moment, the model of nonlinear system is denoted as nPt, and inearized model is denoted as P (θt).Then nonlinear system
NPt and linear submodel PiBetween gap metric distance definition are as follows: γi(θt)=δ (Pi,P(θt)), i=1 ..., m；S5.
Weight function when two sub-controller t moments are as follows:I=1,2；
S6. multi-model H∞Controller t moment output according to formulaIt calculates
Out, and system closed loop output y (t) is acquired；
S7. basisCalculate ke=O, the integral absolute error (IAE) when 1,2,3...20
Value.Finally obtain KeWhen=1, the IAE value of system is minimum.Therefore corresponding Multiple model control is the optimal multimode of CSTR system
Type H∞Controller.
Fig. 1 gives CSTR system in the multi-model H based on traditional trapezoidal weighting function∞Output response under controller
Curve (uses y in Fig. 1TIndicate) and Self-tuning System multi-model weighting function setting method provided by the invention under obtained multimode
Output response curve under type controller (uses y in figuregIt indicates).Obvious yTIt can not be tracked within the scope of whole operation well
The variation of reference signal, there are obvious static errors.Curve of output y in contrastgThe effect ratio y of track reference signalTIt is good
Very much: tracking accuracy is fast at high speed, and exports not only smooth but also accurate.Fig. 3 is that the IAE value of closed-loop system becomes with the variation of ke
The curve of change.It is obvious that the value of IAE obtains minimum when ke=1.Therefore ke=1 is optimal parameter, corresponding multi-model H∞
Controller is optimal.It is obvious to a person skilled in the art that invention is not limited to the details of the above exemplary embodiments,
And without departing from the spirit or essential characteristics of the present invention, the present invention can be realized in other specific forms.Cause
This, in all respects, the present embodiments are to be considered as illustrative and not restrictive, the scope of the present invention
It is indicated by the appended claims rather than the foregoing description, it is intended that the meaning and scope obtained with important document that claim will be fallen in
Interior all changes are included within the present invention.It should not treat any reference in the claims as limiting related right
It is required that.
The above, the above embodiments are merely illustrative of the technical solutions of the present invention, rather than its limitations；Although referring to before
Stating embodiment, invention is explained in detail, those skilled in the art should understand that: it still can be to preceding
Technical solution documented by each embodiment is stated to modify or equivalent replacement of some of the technical features；And these
It modifies or replaces, the spirit and scope for technical solution of various embodiments of the present invention that it does not separate the essence of the corresponding technical solution.
Claims (6)
1. a kind of gap multi-model weighting function methods of self-tuning, which is characterized in that analyze the characteristic of nonlinear system, select
The scheduling variable for being able to reflect system operating condition is selected, the model of multi model decomposition algorithm building approximate non-linear system is utilized
Collection designs sub-controller based on each submodel in the Models Sets, and the weighting function of sub-controller is non-by current time
The reciprocal of gap distance between linear system and each submodel calculates, and has unique setting parameter in the weighting function, leads to
The integral absolute error value crossed between the closed loop output of optimization nonlinear system and reference input obtains the optimal value of setting parameter.
2. gap multi-model weighting function methods of self-tuning according to claim 1, which is characterized in that the approximation
Submodel in the Models Sets of nonlinear system is linear submodel Pi, i=1,2,3 ... m, m are the total number of submodel, linearly
Submodel PiCorresponding sub-controller is Ki, t moment, the output of sub-controller is ui(t)；
The output formula of the Multiple model control device are as follows:
U (t) is input to nonlinear system, obtains closed loop output y (t) of system, whereinIndicate i-th of sub-controller
KiWeight function in t moment, θtIndicate the value of t moment scheduling variable,.
3. gap multi-model weighting function methods of self-tuning according to claim 2, which is characterized in that the weight
The formula of function are as follows:
Wherein keIt is the setting parameter of weighting function, is nonnegative integer, l=1,2,3 ... m, when t moment, the model of nonlinear system
It is denoted as nPt, inearized model is denoted as P (θt), nonlinear system nPt and linear submodel PiBetween gap metric distance be
γi(θt)=δ (Pi,P(θt)), function δ (Pi,P(θt)) indicate linear system PiWith P (θt) between gap metric distance.
4. gap multi-model weighting function methods of self-tuning according to claim 2, which is characterized in that the integral
The formula of absolute error value are as follows:
Wherein, error (t) indicates the error between the output y (t) and reference signal ref (t) of nonlinear system, | | it is exhausted
What it is to the expression of value symbol is any symbol, and ref (t) is the reference input of t moment nonlinear system.
5. gap multi-model weighting function methods of self-tuning according to claim 4, which is characterized in that building target
Function J:
Optimization object function J acquires optimal keCorresponding Multiple model control device is the Multiple model control device of optimized parameter.
6. gap multi-model weighting function methods of self-tuning according to claim 1, which is characterized in that the multimode
Type decomposition algorithm uses the multi model decomposition algorithm based on gap metric.
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| CN111256744A (en) * | 2020-02-27 | 2020-06-09 | 苏州海之博电子科技有限公司 | Calibration method of linear output position sensor |
| CN111694279A (en) * | 2020-06-30 | 2020-09-22 | 河海大学常州校区 | Multi-variable nonlinear system self-adaptive balanced multi-model decomposition and control method |
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Application publication date: 20191112 |