CN108958027A - A kind of dynamic matrix control method of Interval System - Google Patents
A kind of dynamic matrix control method of Interval System Download PDFInfo
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Abstract
The invention belongs to process control fields, more particularly to a kind of dynamic matrix control method of Interval System, the control method is, interval analysis is introduced in the dynamic matrix control algorithm of PREDICTIVE CONTROL, the interval prediction model of system is established, and replaces point value operation to carry out rolling optimization and feedback correction with interval arithmetic.The present invention overcomes previous zone-control algorithms to control the disadvantages of precision is low, solution amount is big；Meanwhile algorithm transformation cost is low, ensure that the terseness and control precision of algorithm to greatest extent.
Description
Technical field
The invention belongs to process control fields, and in particular to a kind of dynamic matrix control method of Interval System.
Technical background
Currently, classical system design and analysis theory is often directed to deterministic model and deterministic theory,
And there is various uncertain and interference in Practical Project system.Ignore when encountering uncertain problem, or directly, or
Person uses the coarse processing method such as simplification, approximation, it tends to be difficult to scientifically design reliable product.On the one hand, if only
Analysis and design only are carried out to deterministic system, the reliability for the product designed often is made to be difficult to reach expected；Another party
Face is difficult to sufficiently estimate uncertain if be only designed uncertain problem using coarse jejune method
Problem bring influences, in the design process the increase safety coefficient of blindness, so that causing to waste.
A kind of important uncertain system is Interval System, and uncertainty can be described as system parameter in some determinations
Change in section, is often used interval model i.e. interval parameter to indicate uncertain variables.To Interval System, traditional robust control
It is generally difficult to that system is made to work in optimum state, therefore the bad steady state accuracy of system；And meet the H ∞ robust of certain performance indicator
The controller order of control is higher, and control decision is complex, cannot achieve when quickly running so as to cause real system in real time
Control.
In conclusion existing method exists, control precision is not high, solves the problems such as computationally intensive, is very difficult to apply in practice
It goes.The invention proposes a kind of dynamic matrix control method of Interval System, basic thought is the base in Classical forecast control
Interval analysis is introduced on plinth, devises the control method that an energy is quick, accurately tracks set interval for Interval System.The party
Method control precision is high, it is small to solve calculation amount, and when system exists and disturbs, if system exports still in set interval,
Control amount remains unchanged；Only when system output is beyond set interval, control amount just changes and is controlled to adjust, with this
The operating frequency of controller is reduced, executing agency's abrasion is reduced.
Summary of the invention
For the above technical problems, the present invention provides a kind of dynamic matrix control method of Interval System, described
The input variable of Interval System, i.e. control signal are to determine point value, and there are interval parameters in the Interval System, and the parameter is true
Determine to change at random in section；For by the output of Interval System control, in the output interval, the control method is to predict
Interval analysis is introduced in the dynamic matrix control algorithm of control, establishes the interval prediction model of system, and point value is replaced with interval arithmetic
Operation carries out rolling optimization and feedback correction.
The dynamic matrix control method of the Interval System, comprising the following steps:
Step 1 establishes prediction model；
Step 1.1, the controlled device are open loop asymptotically stability system, and unit is added in the input terminal of the controlled device
Phase step response signals repeatedly measure the output variable of the controlled device, i.e. unit-step response, if pendulous frequency is n, then may be used
To obtain n value of the unit-step response, take in this n value most on the ith sample period of the modeling time domain
Big value and minimum value form step response section
To obtain step response model vector section
Wherein, N is the sampling period quantity for including, T in the modeling time domainsFor the sampling period, i is in modeling time domain
Sampling period number, i.e. expression ith sample period,a(iTs) indicate in the section of the output variable in ith sample period
Lower limit,Indicate the section upper limit in the output variable in ith sample period,a 1It indicates defeated the 1st sampling period
The interval limit of variable out,Indicate the section upper limit in the 1st sampling period output variable,a NIt indicates in the n-th sampling period
The interval limit of output variable,Indicate the section upper limit in n-th sampling period output variable, T is matrix transposition symbol；
Step 1.2, take prediction time domain in include sampling period quantity be P；The sampling period number for including in control time domain
Amount is M, then the section of model prediction output is
In formula, k indicates current time,Indicate the prediction output vector lower limit at the k moment,y m(k+1 | k) is indicated at the k moment to the output predicted value lower limit at k+1 moment,y m(k+P | k) it indicates at the k moment to the k+P moment
Export predicted value lower limit；Indicate the prediction output vector upper limit of the etching system in k,It indicates at the k moment to the output predicted value upper limit at k+1 moment,It indicates at the k moment to the k+P moment
The output predicted value upper limit；
Indicate the initial vector lower limit that etching system exports in k,y 0(k+1 | k) it indicates in k
Moment exports the initial value lower limit at the k+1 moment,y 0(k+P | k) it indicates to export the initial value lower limit at the k+P moment at the k moment；Indicate the initial vector upper limit that etching system exports in k,Expression exports at the k moment
In the initial value upper limit at k+1 moment,It indicates to export the initial value upper limit at the k+P moment at the k moment；
It is the interval limit by step-response coefficientsa(iTs) composition
P × Metzler matrix, referred to as dynamic matrix interval value lower limit；It is by step
The section upper limit of response coefficientP × Metzler matrix of composition, referred to as the dynamic matrix interval value upper limit；
Indicate that the M controlling increment vector from the k moment, Δ u (k) indicate the k moment
Controlling increment, Δ u (k+M-1) indicate the k moment after m-th controlling increment；
Step 2, rolling optimization；
Step 2.1 gives the expectation section of output variable at the k moment as the dimensional vector of P × 1, it may be assumed that
With the Δ uM(k) it is optimized variable, performance indicator J (k) is made to reach minimum, it may be assumed that
Wherein,It indicates to give the expectation interval limit of output variable at the k moment,wIt (k+1) is the
The desired output lower limit at k+1 moment,wIt (k+P) is the desired output lower limit at kth+P moment；It indicates in k
Moment gives the expectation section upper limit of output variable,For the desired output upper limit at+1 moment of kth,For kth+
The desired output upper limit at P moment；
Q=diag (q1..., qP) it is output error weighting coefficient matrix, matrix, diag (q are tieed up for P × P1..., qP) table
Bright Q is with q1..., qPFor the diagonal matrix of diagonal entry, R=diag (r1..., rM) it is control variable weighting coefficient matrix,
Matrix, diag (r are tieed up for M × M1..., rM) show that R is with r1..., rMFor the diagonal matrix of diagonal entry；
Step 2.2, by the step 2.1, obtain controlling increment section when to performance indicator J (k) minimalizationI.e.
Wherein, cT=[1 0 ... 0], is 1 × M dimensional vector, and T is matrix transposition symbol；Indicate the control at the k moment
Increment interval limit processed,Indicate the controlling increment section upper limit at the k moment；
In the practical control amount at k moment are as follows:
U (k)=u (k-1)+Δ u (k)
Wherein u (k-1) is the practical control amount in the previous moment at k moment, and Δ u (k) takes sectionIt is interior
Any value；
Step 3, feedback compensation:
Step 3.1 will be implemented on object in the practical control amount u (k) at k moment, can calculate under its effect at the k moment
The section of the prediction output valve at N number of moment afterwards:
Wherein,It is N-dimensional vector, indicates the pre- of N number of moment under controlling increment Δ u (k) effect after the k moment
The interval limit of output valve is surveyed,It is N-dimensional vector, when indicating N number of after the k moment under controlling increment Δ u (k) effect
The section upper limit of the prediction output valve at quarter；It is the interval limit of prediction output initial value,It is prediction output initial value
The section upper limit；
The reality output y (k+1) of step 3.2, basis at the k+1 moment calculates prediction error:
WhereinFor interval vectorOne-component,It indicates
The interval limit that prediction under controlling increment Δ u (k) effect at the k+1 moment exports,It indicates in controlling increment Δ u (k)
In the section upper limit of the prediction output at k+1 moment under effect；
It is discussed in detail below in sectionWithThe middle control for choosing 3 kinds of representative values
Effect processed:
A, it takesThen output interval is described
It is expected that sectionMiddle position；
If b, takingThen the output interval upper limit and the expectation section upper limitIt is overlapped；
If c, takingThen output interval lower limit and the expectation interval limitw P(k) it is overlapped；
Prediction error e (k+1) is expanded the prediction error intervals equal at bound by step 3.3, i.e.,
Prediction error e (k+1) is weighted to correct the prediction to the output after the k moment, is obtained in k+1
The section of the prediction output after correcting to the k+1 moment is carved, i.e.,
Wherein,For after the k+1 moment corrects prediction output interval limit,For, to the prediction output interval lower limit after the time correction, needed at the k+1 moment by shift matrix by its
It removes；For at the k+1 moment to the prediction output interval lower limit after k+N time correction；For the section upper limit of the prediction output vector after the k+1 moment corrects,, to the prediction output interval upper limit after the time correction, to also need to pass through shift matrix at the k+1 moment
It removes it；For at the k+1 moment to the prediction output interval upper limit after k+N time correction；It is N
Updating vector is tieed up, h is taken1=...=hN=1；
It will above by shift matrixWithIt removes, i.e., is made by shift matrixMeet the setting of k+1 moment initial prediction:
Wherein,For N × N-dimensional shift matrix,As the k+1 moment
Optimize the initial prediction calculated.
The step 2.1, diag (q1..., qP) it is with q1..., qPFor the diagonal matrix of diagonal entry, q is taken1=...=
qP=1, remaining outer element of diagonal line is 0, diag (r1..., rM) it is with r1..., rMFor the diagonal matrix of diagonal entry, r is taken1
=...=rM=1, remaining outer element of diagonal line is 0.
Beneficial effects of the present invention:
The invention proposes a kind of dynamic matrix control methods of Interval System, are described using the interval model of Interval System
Mode introduces interval analysis, partial dot value operation in traditional Model Predictive Control is changed to interval arithmetic, keeps traditional algorithm suitable
Answer the control requirement of Interval System；And output interval model selection is provided, select different controlling increments that can realize respectively defeated
The upper, middle and lower limit of section tracking set interval out, to realize that the output variable of Interval System is quick, it is defeated to accurately track setting
The requirement in section out, in addition, control amount does not change when system in section there are disturbing, only when disturbance keeps system output super
Out when set interval, just changing control amount makes system return to set interval.
The present invention overcomes previous zone-control algorithms to control the disadvantages of precision is low, solution amount is big；Meanwhile generation is transformed in algorithm
Valence is low, ensure that the terseness and control precision of algorithm to greatest extent.
The present invention has rational design, it is easy to accomplish, there is good practical value.
Detailed description of the invention
Fig. 1 is middle position analogous diagram of the output interval described in the specific embodiment of the invention in desired section；
Fig. 2 is overlapped analogous diagram with the desired section upper limit for the output interval upper limit described in the specific embodiment of the invention；
Fig. 3 is overlapped analogous diagram with desired interval limit for output interval lower limit described in the specific embodiment of the invention；
Fig. 4 is to disturb output quantity analogous diagram in application section described in the specific embodiment of the invention；
Fig. 5 is to disturb control amount analogous diagram in application section described in the specific embodiment of the invention；
Fig. 6 is to disturb output quantity analogous diagram outside application section described in the specific embodiment of the invention；
Fig. 7 is to disturb control amount analogous diagram outside application section described in the specific embodiment of the invention.
Specific embodiment
In order to make the objectives, technical solutions, and advantages of the present invention clearer, below in conjunction with attached drawing and embodiment,
Further description is made to the present invention.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention,
It is not intended to limit the present invention.
The present invention proposes a kind of dynamic matrix control method of Interval System, which is characterized in that the Interval System it is defeated
Enter variable, i.e., control signal is to determine point value, and there are interval parameter in the Interval System, the parameter is random in determination section
Variation；For by the output of Interval System control, in the output interval, the control method is, in the dynamic square of PREDICTIVE CONTROL
Interval analysis is introduced in battle array algorithm, establishes the interval prediction model of system, and replace point value operation to be rolled with interval arithmetic
Optimization and feedback correction.
System is defeated during the present embodiment carries out formula calculating, optimal control effect, display emulation using Matlab software
Output and error, with Interval SystemFor controlled device；Specific step is as follows for the control method:
Step 1 establishes prediction model；
Step 1.1, the controlled device are open loop asymptotically stability system, and unit is added in the input terminal of the controlled device
Phase step response signals repeatedly measure the output variable of the controlled device, i.e. unit-step response, if pendulous frequency is n, then may be used
To obtain n value of the unit-step response, take in this n value most on the ith sample period of the modeling time domain
Big value and minimum value form step response section
To obtain step response model vector section
Wherein, N is the sampling period quantity for including in the modeling time domain, takes N=100, TsFor the sampling period, T is takens=
1, i is the sampling period number modeled in time domain, i.e. the expression ith sample period,a(iTs) indicate the ith sample period institute
The interval limit of output variable is stated,Indicate the section upper limit in the output variable in ith sample period,a 1It indicates
In the interval limit of the 1st sampling period output variable,Indicate the section upper limit in the 1st sampling period output variable,a NTable
Show the interval limit in n-th sampling period output variable,Indicate the section upper limit in n-th sampling period output variable, T
For matrix transposition symbol；
According to above content, obtained step response model vector section is as shown in table 1:
Table 1
Step 1.2 takes the sampling period quantity for including in prediction time domain to be P, in the present embodiment, takes P=10；Control time domain
In include sampling period quantity be M, in the present embodiment, take M=7, then the section of model prediction output is
In formula, k indicates current time,Indicate the prediction output vector lower limit at the k moment,y m(k+1 | k) is indicated at the k moment to the output predicted value lower limit at k+1 moment,y m(k+P | k) it indicates at the k moment to the k+P moment
Export predicted value lower limit；Indicate the prediction output vector upper limit of the etching system in k,It indicates at the k moment to the output predicted value upper limit at k+1 moment,It indicates at the k moment to the k+P moment
The output predicted value upper limit；
Indicate the initial vector lower limit that etching system exports in k,y 0(k+1 | k) it indicates in k
Moment exports the initial value lower limit at the k+1 moment,y 0(k+P | k) it indicates to export the initial value lower limit at the k+P moment at the k moment；Indicate the initial vector upper limit that etching system exports in k,Expression exports at the k moment
In the initial value upper limit at k+1 moment,It indicates to export the initial value upper limit at the k+P moment at the k moment；
It is the interval limit by step-response coefficientsa(iTs) composition
P × Metzler matrix, referred to as dynamic matrix interval value lower limit；It is by step
The section upper limit of response coefficientP × Metzler matrix of composition, referred to as the dynamic matrix interval value upper limit；
Indicate that the M controlling increment vector from the k moment, Δ u (k) indicate the k moment
Controlling increment, Δ u (k+M-1) indicate the k moment after m-th controlling increment；
Step 2, rolling optimization；
Step 2.1 gives the expectation section of output variable at the k moment as the dimensional vector of P × 1, it may be assumed that
With the Δ uM(k) it is optimized variable, performance indicator J (k) is made to reach minimum, it may be assumed that
Wherein,It indicates to give the expectation interval limit of output variable at the k moment,wIt (k+1) is the
The desired output lower limit at k+1 moment,wIt (k+P) is the desired output lower limit at kth+P moment；It indicates in k
Moment gives the expectation section upper limit of output variable,For the desired output upper limit at+1 moment of kth,For kth+
The desired output upper limit at P moment；
Q=diag (q1..., qP) it is output error weighting coefficient matrix, matrix, diag (q are tieed up for P × P1..., qP) table
Bright Q is with q1..., qPFor the diagonal matrix of diagonal entry, q is taken in the present embodiment1=...=qP=1, remaining outer member of diagonal line
Element is 0, R=diag (r1..., rM) it is control variable weighting coefficient matrix, matrix, diag (r are tieed up for M × M1..., rM) show R
It is with r1..., rMFor the diagonal matrix of diagonal entry, r is taken in the present embodiment1=...=rM=1, remaining outer element of diagonal line
It is 0；
Step 2.2, by the step 2.1, obtain controlling increment section when to performance indicator J (k) minimalizationI.e.
Wherein, cT=[1 0 ... 0], is 1 × M dimensional vector, and T is matrix transposition symbol；Indicate the control at the k moment
Increment interval limit processed,Indicate the controlling increment section upper limit at the k moment；
In the practical control amount at k moment are as follows:
U (k)=u (k-1)+Δ u (k)
Wherein u (k-1) is the practical control amount in the previous moment at k moment, and Δ u (k) takes sectionIt is interior
Any value, corresponding different control effect, will specifically discuss in step 3.2；
Step 3, feedback compensation:
Step 3.1 will be implemented on object in the practical control amount u (k) at k moment, can calculate under its effect at the k moment
The section of the prediction output valve at N number of moment afterwards:
Wherein,It is N-dimensional vector, indicates the pre- of N number of moment under controlling increment Δ u (k) effect after the k moment
The interval limit of output valve is surveyed,It is N-dimensional vector, when indicating N number of after the k moment under controlling increment Δ u (k) effect
The section upper limit of the prediction output valve at quarter；It is the interval limit of prediction output initial value,It is prediction output initial value
The section upper limit；
The reality output y (k+1) of step 3.2, basis at the k+1 moment calculates prediction error:
WhereinFor interval vectorOne-component,It indicates
The interval limit that prediction under controlling increment Δ u (k) effect at the k+1 moment exports,It indicates in controlling increment Δ u (k)
In the section upper limit of the prediction output at k+1 moment under effect；
It is discussed in detail below in sectionWithThe middle control for choosing 3 kinds of representative values
Effect processed:
A, it takesThen output interval is described
It is expected that sectionMiddle position, as shown in Figure 1；
If b, takingThen the output interval upper limit and the expectation section upper limitIt is overlapped, as shown in Figure 2；
If c, takingThen output interval lower limit and the expectation interval limitw P(k) it is overlapped, as shown in Figure 3；
Prediction error e (k+1) is expanded the prediction error intervals equal at bound by step 3.3, i.e.,
Prediction error e (k+1) is weighted to correct the prediction to the output after the k moment, is obtained in k+1
The section of the prediction output after correcting to the k+1 moment is carved, i.e.,
Wherein,For after the k+1 moment corrects prediction output interval limit,For, to the prediction output interval lower limit after the time correction, needed at the k+1 moment by shift matrix by its
It removes；For at the k+1 moment to the prediction output interval lower limit after k+N time correction；For the section upper limit of the prediction output vector after the k+1 moment corrects,, to the prediction output interval upper limit after the time correction, to also need to pass through shift matrix at the k+1 moment
It removes it；For at the k+1 moment to the prediction output interval upper limit after k+N time correction；It is N
Updating vector is tieed up, h is taken1=...=hN=1；
It will above by shift matrixWithIt removes, i.e., is made by shift matrixMeet the setting of k+1 moment initial prediction:
Wherein,For N × N-dimensional shift matrix,As the k+1 moment
Optimize the initial prediction calculated.
Using the dynamic matrix control method of above-mentioned Interval System, verified by the following method:
In the present embodiment simulation process, reality output amount y (k+1) is applied at the k=200 moment and is disturbed；
If perturbation amplitude is smaller, as shown in Fig. 4, the section of output valve is predictedRemain at the phase
Hope sectionInterior, then calculated controlling increment is 0, i.e. Δ u (k)=0, control amount remains unchanged, i.e. u (k)
=u (k-1, as shown in Fig. 5；
Weak disturbance amplitude is larger, predicts the section of output valveBeyond desired sectionWhen, as shown in Fig. 6, then calculated controlling increment is no longer 0, i.e. Δ u (k) ≠ 0, control amount variation,
That is u (k)=u (k-1)+Δ u (k) makes to predict output interval as shown in Fig. 7Return to desired sectionIt is interior.
Above-mentioned two situations have absolutely proved the method to the robustness and precise control of disturbance.
Claims (3)
1. a kind of dynamic matrix control method of Interval System, which is characterized in that the input variable of the Interval System controls
Signal is to determine point value, and there are interval parameter in the Interval System, which changes at random in determination section；For by section
The output of system controls in the output interval, and the control method is to introduce in the dynamic matrix control algorithm of PREDICTIVE CONTROL
Interval analysis establishes the interval prediction model of system, and replaces point value operation to carry out rolling optimization and feed back to rectify with interval arithmetic
Just.
2. the dynamic matrix control method of Interval System according to claim 1, which is characterized in that the control method tool
Body the following steps are included:
Step 1 establishes prediction model；
Step 1.1, the controlled device are open loop asymptotically stability system, and unit step is added in the input terminal of the controlled device
Response signal repeatedly measures the output variable of the controlled device, i.e. unit-step response, then can be if pendulous frequency is n
On the ith sample period of the modeling time domain, n value of the unit-step response is obtained, the maximum value in this n value is taken
Step response section is formed with minimum value
To obtain step response model vector section
Wherein, N is the sampling period quantity for including, T in the modeling time domainsFor the sampling period, i is the sampling modeled in time domain
Periodicity, i.e. expression ith sample period,a(iTs) indicate the ith sample period the output variable interval limit,Indicate the section upper limit in the output variable in ith sample period,a 1It indicates to become in the 1st sampling period output
The interval limit of amount,Indicate the section upper limit in the 1st sampling period output variable,a NIt indicates to export in the n-th sampling period
The interval limit of variable,Indicate the section upper limit in n-th sampling period output variable, T is matrix transposition symbol；
Step 1.2, take prediction time domain in include sampling period quantity be P；Controlling the sampling period quantity for including in time domain is
M, the then section that model prediction exports are
In formula, k indicates current time,Indicate the prediction output vector lower limit at the k moment,y m(k+
1 | it k) indicates at the k moment to the output predicted value lower limit at k+1 moment,y m(k+P | k) output of the expression at the k moment to the k+P moment
Predicted value lower limit；Indicate the prediction output vector upper limit of the etching system in k,Table
Show the output predicted value upper limit at the k moment to the k+1 moment,It indicates at the k moment to the output predicted value at k+P moment
The upper limit；
Indicate the initial vector lower limit that etching system exports in k,y 0(k+1 | k) it indicates at the k moment
The initial value lower limit at the k+1 moment is exported,y 0(k+P | k) it indicates to export the initial value lower limit at the k+P moment at the k moment；Indicate the initial vector upper limit that etching system exports in k,Expression exports at the k moment
In the initial value upper limit at k+1 moment,It indicates to export the initial value upper limit at the k+P moment at the k moment；
It is the interval limit by step-response coefficientsa(iTs) composition P
× Metzler matrix, referred to as dynamic matrix interval value lower limit；It is by step response
The section upper limit of coefficientP × Metzler matrix of composition, referred to as the dynamic matrix interval value upper limit；
Indicate that the M controlling increment vector from the k moment, Δ u (k) indicate the control at k moment
Increment processed, Δ u (k+M-1) indicate the m-th controlling increment after the k moment；
Step 2, rolling optimization；
Step 2.1 gives the expectation section of output variable at the k moment as the dimensional vector of P × 1, it may be assumed that
With the Δ uM(k) it is optimized variable, performance indicator J (k) is made to reach minimum, it may be assumed that
Wherein,It indicates to give the expectation interval limit of output variable at the k moment,wIt (k+1) is kth+1
The desired output lower limit at moment,wIt (k+P) is the desired output lower limit at kth+P moment；It indicates in k
The expectation section upper limit of given output variable is carved,For the desired output upper limit at+1 moment of kth,For kth+P
The desired output upper limit at moment；
Q=diag (q1..., qP) it is output error weighting coefficient matrix, matrix, diag (q are tieed up for P × P1..., qP) show that Q is
With q1..., qPFor the diagonal matrix of diagonal entry, R=diag (r1..., rM) be control variable weighting coefficient matrix, be M ×
M ties up matrix, diag (r1..., rM) show that R is with r1..., rMFor the diagonal matrix of diagonal entry；
Step 2.2, by the step 2.1, obtain controlling increment section when to performance indicator J (k) minimalizationI.e.
Wherein, cT=[1 0 ... 0], is 1 × M dimensional vector, and T is matrix transposition symbol；It indicates to increase in the control at k moment
Interval limit is measured,Indicate the controlling increment section upper limit at the k moment；
In the practical control amount at k moment are as follows:
U (k)=u (k-1)+Δ u (k)
Wherein u (k-1) is the practical control amount in the previous moment at k moment, and Δ u (k) takes sectionIt is interior any
Value；
Step 3, feedback compensation:
Step 3.1 will be implemented on object in the practical control amount u (k) at k moment, can calculate under its effect after the k moment
The section of the prediction output valve at N number of moment:
Wherein,It is N-dimensional vector, indicates that the prediction at N number of moment under controlling increment Δ u (k) effect after the k moment is defeated
The interval limit being worth out,It is N-dimensional vector, indicates N number of moment under controlling increment Δ u (k) effect after the k moment
Predict the section upper limit of output valve；It is the interval limit of prediction output initial value,It is the section of prediction output initial value
The upper limit；
The reality output y (k+1) of step 3.2, basis at the k+1 moment calculates prediction error:
WhereinFor interval vectorOne-component,Expression is controlling
The interval limit that prediction under increment Delta u (k) effect at the k+1 moment exports,It indicates to act in controlling increment Δ u (k)
Under the k+1 moment prediction output the section upper limit；
It is discussed in detail below in sectionWithThe middle control effect for choosing 3 kinds of representative values
Fruit:
A, it takesThen output interval is in the expectation
SectionMiddle position；
If b, takingThen the output interval upper limit and the expectation section upper limit
It is overlapped；
If c, takingThen output interval lower limit and the expectation interval limitw P(k)
It is overlapped；
Prediction error e (k+1) is expanded the prediction error intervals equal at bound by step 3.3, i.e.,
Prediction error e (k+1) is weighted to correct the prediction to the output after the k moment, is obtained at the k+1 moment pair
The k+1 moment correct after prediction output section, i.e.,
Wherein,For after the k+1 moment corrects prediction output interval limit,For, to the prediction output interval lower limit after the time correction, needed at the k+1 moment by shift matrix by its
It removes；For at the k+1 moment to the prediction output interval lower limit after k+N time correction；For the section upper limit of the prediction output vector after the k+1 moment corrects,, to the prediction output interval upper limit after the time correction, to also need to pass through shift matrix at the k+1 moment
It removes it；For at the k+1 moment to the prediction output interval upper limit after k+N time correction；It is N
Updating vector is tieed up, h is taken1=...=hN=1；
It will above by shift matrixWithIt removes, i.e., is made by shift matrixMeet the setting of k+1 moment initial prediction:
Wherein,For N × N-dimensional shift matrix,As k+1 time optimization
The initial prediction of calculating.
3. the dynamic matrix control method of Interval System according to claim 2, which is characterized in that the step 2.1,
diag(q1..., qP) it is with q1..., qPFor the diagonal matrix of diagonal entry, q is taken1=...=qP=1, remaining outer member of diagonal line
Element is 0, diag (r1..., rM) it is with r1..., rMFor the diagonal matrix of diagonal entry, r is taken1=...=rM=1, outside diagonal line
Remaining element is 0.
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