CN108762097A - A kind of tracking disturbance rejection control method based on dummy model - Google Patents
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Abstract
The tracking disturbance rejection control method based on dummy model that the invention discloses a kind of, it is characterized in that：System Discrimination is carried out to linear practical controlled device first and obtained dynamic model will be recognized as dummy model, for dummy model design tracing control rule；Then tracing control rule is respectively applied on dummy model and linear practical controlled device, is restrained using dummy model output and the tolerance design disturbance rejection control of linear practical controlled device output；Tracing control rule is added with disturbance rejection control rule, the tracking disturbance rejection control as linear practical controlled device is restrained, and realizes the tracking disturbance rejection control to linear practical controlled device.The present invention solves the problems, such as contradiction between tracking and anti-interference present in traditional closed-loop control system, still with preferable tracking performance while system is with good Immunity Performance.
Description
Technical field
The present invention relates to automation field, more specifically a kind of tracking disturbance rejection control side based on dummy model
Method.
Background technology
There are two kinds of basic control modes, i.e. opened loop control and closed-loop control in the controls.Compared to open loop control
System, closed-loop control have the advantages that it is many, one is negative-feedback can reduce influence of the forward path Parameters variation to system；Two
Influence of the external disturbance signal to system can be reduced by being negative-feedback so that control system is adapted to severe external environment；
Third, negative-feedback can improve the transient state and steady-state behaviour of control system.These advantages make closed-loop control be widely used in work
In industry control, and achieve preferable control effect.Well known PID control system is namely based on this negative feedback control.But
There is also some problems for closed-loop control system：There is low frequency strong disturbance, frequency and given input signal in the controls
Frequency is identical or close, poor to the rejection ability of disturbance if system is to giving the fast of input signal tracking；If system is anti-
Immunity can be good, then system is poor to the ability of tracking for giving input signal.That is, in closed-loop control system, there is tracking
Contradiction between interference rejection ability.In order to solve this problem, some outstanding control strategies are suggested.
In " Automatic Control Theory " (Wang Xiaowu, Fang Min, Ge Suoliang write) book that China Machine Press in 2009 publishes
In, it is referred to the Compound Control Strategy by disturbance compensation.The strategy can be in the feelings for ensureing closed-loop system transient state and steady-state behaviour
Influence of the compensating disturbance to system under condition, but it is that measurable and disturbance compensation mechanism can physics realization that it, which requires disturbing signal,.
But in Industry Control, interference signal cannot be measured under normal circumstances.
In 2011, Wang Guoqiang et al. is published an article on Proceedings of the CSEE, and " population existed with PIDNN controllers
PID is combined with neural network and proposes PIDNN controllers by the application in VSC-HVDC ", this article, which passes through reality
When adjustment controller parameter come solve tracking anti-interference between contradiction sex chromosome mosaicism；But the controller based on neural network exists
Following disadvantage：It is computationally intensive, be not easy to realize in embedded device；It easily is absorbed in local minimum, influences control effect.
Invention content
The present invention is to provide a kind of tracking anti-interference based on dummy model to avoid the problems of above-mentioned prior art
Control method, to solve the problems, such as that closed-loop system is contradicted with amiable interference rejection ability, and control program is easy to Project Realization.
The present invention is to solve technical problem to adopt the following technical scheme that：
The present invention is based on the characteristics of tracking disturbance rejection control method of dummy model to be：First to linear practical controlled device into
Row System Discrimination simultaneously will recognize obtained dynamic model as dummy model, for dummy model design tracing control rule；
Then tracing control rule is respectively applied on dummy model and linear practical controlled device, using dummy model output and
The tolerance design disturbance rejection control rule of linear practical controlled device output；Tracing control rule is added with disturbance rejection control rule, as line
Property practical controlled device tracking disturbance rejection control rule, realize the tracking disturbance rejection control to linear practical controlled device.
It is to carry out as follows the present invention is based on the characteristics of tracking disturbance rejection control method of dummy model：
Step 1 characterizes linear practical controlled device by formula (1)：
Wherein：
K is sampling instant；naAnd nbFor the order of known linear practical controlled device；
Y (k+1), y (k) and y (k-na) it is followed successively by k+1, k and k-naThe linear practical controlled device output at moment；
U (k), u (k-1) and u (k-nb) it is followed successively by k, k-1 and k-nbThe linear practical controlled device input at moment；
aiAnd bjFor linear practical object parameters, i=0,1,2 ..., na, j=0,1,2 ..., nb；
Step 2 carries out System Discrimination to the linear practical controlled device, obtains the first expression side shown in formula (2)
The System identification model of formula：
Wherein：
WithIt is followed successively by k+1, k and k-naThe identification system at moment exports；
WithFor identification system parameter, wherein i=0,1,2 ..., na, j=0,1,2 ..., nb；
Step 3, by formula (2) it is collated obtain the second expression way shown in formula (3) System identification model：
Wherein：
z-1、WithFor hysteresis factors, and have：
Using the System identification model expressed by formula (3) as dummy model；
Step 4 is directed to Setting signal r (k), dummy model and the first PID controller PID designed by tracking performance1Structure
At the first closed loop L1, the first closed loop L1Structure type be：It is subtracted using r (k)Obtain tracking error ε
(k), it regard ε (k) as the first PID controller PID1Input signal, in the first PID controller PID1Middle generation first is defeated
Go out signal u1(k), by the first output signal u1(k) as the input signal of dummy model；First PID controller
PID1Input/output relation such as formula (4)：
u1(k)=u1(k-1)+kp1(ε(k)-ε(k-1))+kI1ε(k)+kd1(ε (k) -2 ε (k-1)+ε (k-2)) (4),
Wherein：u1(k-1) it is the PID at k-1 moment1Output signal；ε (k-1) is the tracking error signal at k-1 moment；ε(k-
2) it is the tracking error signal at k-2 moment；kp1、kI1And kd1It is followed successively by the first PID controller PID1Scale parameter, integral ginseng
Number and differential parameter；
Step 5, using gather examination method estimate kp1、kI1And kd1Value, the kp1、kI1And kd1Value meet by formula (5) institute table
The discriminant equation of sign：
Wherein：
H(z-1)=1-z-1；G(z-1)=g0+g1z-1+g2z-2；g0=kp1+kI1+kd1；g1=-kp1-2kd1；g2=kd1；
Step 6, by the first output signal u1(k) while as the input signal of linear practical controlled device, due to virtual
The undisturbed influence of model, and the influence of the linear practical perturbed d of controlled device, therefore, dummy model output with
There are difference es (k) between linear practical controlled device output, and have：
Step 7, by difference e (k), linear practical controlled device and the second PID controller according to Immunity Performance design
PID2Constitute the second closed loop L2, the second closed loop L2Structure type be：Difference e (k) is controlled as the 2nd PID
Device PID processed2Input signal, in the second PID controller PID2The second output signal u of middle generation2(k), defeated by described second
Go out signal u2(k) input signal as linear practical controlled device；The second PID controller PID2Input/output relation
It is characterized by formula (6)：
u2(k)=u2(k-1)+kp2(e(k)-e(k-1))+kI2e(k)+kd2(e (k) -2e (k-1)+e (k-2)) (6),
Wherein, u2(k-1) it is the PID at k-1 moment2Output signal；E (k-1) and e (k-2) is respectively k-1 the and k-2 moment
Dummy model exports the difference between linear practical controlled device output；kp2、kI2And kd2It is followed successively by the second PID controller
PID2Scale parameter, integral parameter and differential parameter, kp2、kI2And kd2Value by gather examination method obtain；
Step 8, the tracking disturbance rejection control rule by u (k) as linear practical controlled device, and have：U (k)=u1(k)+u2
(k), the tracking disturbance rejection control to linear practical controlled device is realized.
The present invention is based on the tracking disturbance rejection control methods of dummy model, are applied to the level with low frequency sinusoidal disturbance
System is using the first-order system as linear practical controlled device, according to the method for claim 1 to the first-order system
Design tracking disturbance rejection control rule, realizes the tracking disturbance rejection control to first-order system.
Compared with the prior art, the present invention has the beneficial effect that：
The present invention is by using Setting signal r (k), dummy model, the first PID controller PID1, the second PID controller
PID2There are two the tracking disturbance rejection control control framework of closed loop, the control framework knots with linear practical controlled device structure tool
The advantage that tracking control unit tracking performance is good and disturbance rejection control device Disturbance Rejection ability is strong has been closed, has preferably been realized to linear real
The tracking disturbance rejection control of border controlled device, the control framework stability prove simple and are easy to Project Realization.
Description of the drawings
Fig. 1 is the tracking disturbance rejection control frame based on dummy model；
Fig. 2 is the response curve that the method for the present invention is applied to first-order system.
Specific implementation mode
The tracking disturbance rejection control method based on dummy model is in the present embodiment：Linear practical controlled device is carried out first
System Discrimination simultaneously will recognize obtained dynamic model as dummy model, for dummy model design tracing control rule；Then will
Tracing control rule is respectively applied on dummy model and linear practical controlled device, utilizes dummy model output and linear practical quilt
Control the tolerance design disturbance rejection control rule of object output；Tracing control rule is added with disturbance rejection control rule, it is controlled as linear reality
The tracking disturbance rejection control of object is restrained, and realizes the tracking disturbance rejection control to linear practical controlled device.
Referring to Fig. 1, the tracking disturbance rejection control method based on dummy model is to carry out as follows in the present embodiment：
Step 1 characterizes linear practical controlled device by formula (1)：
Wherein：
K is sampling instant；naAnd nbFor the order of known linear practical controlled device；
Y (k+1), y (k) and y (k-na) it is followed successively by k+1, k and k-naThe linear practical controlled device output at moment；
U (k), u (k-1) and u (k-nb) it is followed successively by k, k-1 and k-nbThe linear practical controlled device input at moment；
aiAnd bjFor linear practical object parameters, i=0,1,2 ..., na, j=0,1,2 ..., nb；
Step 2 carries out System Discrimination to linear practical controlled device, obtains the first expression way shown in formula (2)
System identification model：
Wherein：
WithIt is followed successively by k+1, k and k-naThe identification system at moment exports；
WithFor identification system parameter, wherein i=0,1,2 ..., na, j=0,1,2 ..., nb。
Step 3, by formula (2) it is collated obtain the second expression way shown in formula (3) System identification model：
First formula (2) right-hand component is expanded into：
Again willMove on to the equation left side；Finally both members merging similar terms are obtained by formula (3)：
Wherein：
z-1、WithFor hysteresis factors, and have：
Using the System identification model expressed by formula (3) as dummy model.
Step 4 is directed to Setting signal r (k), dummy model and the first PID controller PID designed by tracking performance1Structure
At the first closed loop L1, the first closed loop L1Structure type be：It is subtracted using r (k)Tracking error ε (k) is obtained,
It regard ε (k) as the first PID controller PID1Input signal, in the first PID controller PID1The first output signal u of middle generation1
(k), by the first output signal u1(k) as the input signal of dummy model；First PID controller PID1Input/output relation
Such as formula (4)：
u1(k)=u1(k-1)+kp1(ε(k)-ε(k-1))+kI1ε(k)+kd1(ε (k) -2 ε (k-1)+ε (k-2)) (4),
Wherein：u1(k-1) it is the PID at k-1 moment1Output signal；ε (k-1) is the tracking error signal at k-1 moment；ε(k-
2) it is the tracking error signal at k-2 moment；kp1、kI1And kd1It is followed successively by the first PID controller PID1Scale parameter, integral ginseng
Number and differential parameter.
Step 5, using gather examination method estimate kp1、kI1And kd1Value, kp1、kI1And kd1Value meet and characterized by formula (5)
Discriminant equation：
Wherein, H (z-1)=1-z-1；G(z-1)=g0+g1z-1+g2z-2；g0=kp1+kI1+kd1；g1=-kp1-2kd1；g2=
kd1。
Step 6, by the first output signal u1(k) while as the input signal of linear practical controlled device, due to virtual
The undisturbed influence of model, and the influence of the linear practical perturbed d of controlled device, therefore, dummy model output with
There are difference es (k) between linear practical controlled device output, and have：
Step 7, by difference e (k), linear practical controlled device and the second PID controller according to Immunity Performance design
PID2Constitute the second closed loop L2, the second closed loop L2Structure type be：It regard difference e (k) as the second PID controller
PID2Input signal, in the second PID controller PID2The second output signal u of middle generation2(k), by the second output signal u2(k)
Input signal as linear practical controlled device；Second PID controller PID2Input/output relation characterized by formula (6)：
u2(k)=u2(k-1)+kp2(e(k)-e(k-1))+kI2e(k)+kd2(e (k) -2e (k-1)+e (k-2)) (6),
Wherein, u2(k-1) it is the PID at k-1 moment2Output signal；E (k-1) and e (k-2) is respectively k-1 the and k-2 moment
Dummy model exports the difference between linear practical controlled device output；kp2、kI2And kd2It is followed successively by the second PID controller
PID2Scale parameter, integral parameter and differential parameter, kp2、kI2And kd2Value by gather examination method obtain.
Step 8, the tracking disturbance rejection control rule by u (k) as linear practical controlled device, and have：U (k)=u1(k)+u2
(k), the tracking disturbance rejection control to linear practical controlled device is realized.
The tracking disturbance rejection control method based on dummy model is applied to the single order with low frequency sinusoidal disturbance in the present embodiment
System is resisted to first-order system design tracking according to method of claim 1 using first-order system as linear practical controlled device
Control law is disturbed, realizes the tracking disturbance rejection control to first-order system.
Fig. 2 show the response curve that the method for the present invention is applied to single order control system, is illustrated in first-order system in Fig. 2
As linear practical controlled device, Setting signal r (k)=0.4 is set, and under the perturbed d=sin of first-order system (4 π t),
Using in the present embodiment based on dummy model tracking disturbance rejection control method when single order control system response curve.
Control method of the present invention is applied to the simulation process of the first-order system with low frequency sinusoidal disturbance：
1, using first-order system as linear practical controlled device, then linear practical controlled device is expressed by formula (11)：
Y (k+1)=0.999y (k)+0.000995u (k)=θTW (k) (11),
W (k)=[y (k), u (k)]T, θ=[0.999,0.000995]T；
2, System Discrimination is carried out to linear practical controlled device, obtain the first expression way characterized by formula (2) is
It unites identification model, in formula (2)：
3, by the collated System identification model for obtaining the second expression way shown in formula (3) of formula (2)：First by formula
(2) right-hand component expands into：Again willMove on to the equation left side；Finally by equation
Both sides merge the System identification model that similar terms obtain being characterized the second expression way by formula (3), by the system expressed by formula (3)
Identification model is as dummy model；And have：
4, it is for Setting signal r (k)：R (k)=0.4, the first PID controller PID1Input/output relation such as formula
(4)；
5, using gather examination method estimate kp1, kI1, kd1Value, determine kp1=10, kI1=10, kd1=0；
6, by the first output signal u1(k) while as the input signal of linear practical controlled device；Dummy model not by
The influence of disturbance, the influence of the linear practical perturbed d of controlled device, d=sin (4 π t), therefore there are dummy model outputs
Difference e (k) between linear practical controlled device output,
7, the second PID controller PID is obtained2Input/output relation characterized by formula (6), by gather examination method obtain：
kp2=100, kI2=1000, kd2=0；
8, by u1(k) and u2(k) it is added and obtains tracking anti-interference control rule u (k), by u (k) as linear practical controlled device
Disturbance rejection control rule is tracked, realizes the tracking disturbance rejection control to linear practical controlled device.
Claims (3)
1. a kind of tracking disturbance rejection control method based on dummy model, it is characterized in that：Linear practical controlled device is carried out first
System Discrimination simultaneously will recognize obtained dynamic model as dummy model, for dummy model design tracing control rule；So
Tracing control rule is respectively applied on dummy model and linear practical controlled device afterwards, utilizes dummy model output and line
Property the output of practical controlled device tolerance design disturbance rejection control rule；Tracing control rule is added with disturbance rejection control rule, as linear
The tracking disturbance rejection control of practical controlled device is restrained, and realizes the tracking disturbance rejection control to linear practical controlled device.
2. the tracking disturbance rejection control method according to claim 1 based on dummy model, it is characterized in that as follows into
Row：
Step 1 characterizes linear practical controlled device by formula (1)：
Wherein：
K is sampling instant；naAnd nbFor the order of known linear practical controlled device；
Y (k+1), y (k) and y (k-na) it is followed successively by k+1, k and k-naThe linear practical controlled device output at moment；
U (k), u (k-1) and u (k-nb) it is followed successively by k, k-1 and k-nbThe linear practical controlled device input at moment；
aiAnd bjFor linear practical object parameters, i=0,1,2 ..., na, j=0,1,2 ..., nb；
W (k)=[y (k) ... y (k-na),u(k),...u(k-nb)]T；
Step 2 carries out System Discrimination to the linear practical controlled device, obtains the first expression way shown in formula (2)
System identification model：
Wherein：
WithIt is followed successively by k+1, k and k-naThe identification system at moment exports；
WithFor identification system parameter, wherein i=0,1,2 ..., na, j=0,1,2 ..., nb；
Step 3, by formula (2) it is collated obtain the second expression way shown in formula (3) System identification model：
Wherein：
z-1、WithFor hysteresis factors, and have：
z-1Y (k+1)=y (k)；
Using the System identification model expressed by formula (3) as dummy model；
Step 4 is directed to Setting signal r (k), dummy model and the first PID controller PID designed by tracking performance1Constitute first
Closed loop L1, the first closed loop L1Structure type be：It is subtracted using r (k)Tracking error ε (k) is obtained, by ε
(k) it is used as the first PID controller PID1Input signal, in the first PID controller PID1The first output signal u of middle generation1
(k), by the first output signal u1(k) as the input signal of dummy model；The first PID controller PID1Input
Output relation such as formula (4)：
u1(k)=u1(k-1)+kp1(ε(k)-ε(k-1))+kI1ε(k)+kd1(ε (k) -2 ε (k-1)+ε (k-2)) (4),
Wherein：u1(k-1) it is the PID at k-1 moment1Output signal；ε (k-1) is the tracking error signal at k-1 moment；ε (k-2) is
The tracking error signal at k-2 moment；kp1、kI1And kd1It is followed successively by the first PID controller PID1Scale parameter, integral parameter and
Differential parameter；
Step 5, using gather examination method estimate kp1、kI1And kd1Value, the kp1、kI1And kd1Value meet and characterized by formula (5)
Discriminant equation：
Wherein:
H(z-1)=1-z-1；G(z-1)=g0+g1z-1+g2z-2；g0=kp1+kI1+kd1；g1=-kp1-2kd1；g2=kd1；
Step 6, by the first output signal u1(k) while as the input signal of linear practical controlled device, not due to dummy model
It is influenced by disturbing, and therefore the influence of the linear practical perturbed d of controlled device exports and linearly real in dummy model
There are difference es (k) between the controlled device output of border, and have：
Step 7, by difference e (k), linear practical controlled device and the second PID controller PID according to Immunity Performance design2It constitutes
Second closed loop L2, the second closed loop L2Structure type be：It regard difference e (k) as the second PID controller PID2
Input signal, in the second PID controller PID2The second output signal u of middle generation2(k), by the second output signal u2
(k) input signal as linear practical controlled device；The second PID controller PID2Input/output relation by formula (6)
It is characterized：
u2(k)=u2(k-1)+kp2(e(k)-e(k-1))+kI2e(k)+kd2(e (k) -2e (k-1)+e (k-2)) (6),
Wherein, u2(k-1) it is the PID at k-1 moment2Output signal；E (k-1) and e (k-2) is respectively the virtual of k-1 and k-2 moment
Model exports the difference between linear practical controlled device output；kp2、kI2And kd2It is followed successively by the second PID controller PID2's
Scale parameter, integral parameter and differential parameter, kp2、kI2And kd2Value by gather examination method obtain；
Step 8, the tracking disturbance rejection control rule by u (k) as linear practical controlled device, and have：U (k)=u1(k)+u2(k), real
Now to the tracking disturbance rejection control of linear practical controlled device.
3. a kind of tracking disturbance rejection control method described in claim 1 based on dummy model is applied to have low frequency sinusoidal
The first-order system of disturbance, be using the first-order system as linear practical controlled device, it is right according to the method for claim 1
The first-order system design tracking disturbance rejection control rule, realizes the tracking disturbance rejection control to first-order system.
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