CN107168072A - A kind of non-matching interference system Auto-disturbance-rejection Control based on interference observer - Google Patents
A kind of non-matching interference system Auto-disturbance-rejection Control based on interference observer Download PDFInfo
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Abstract
The present invention relates to a kind of non-matching interference system Auto-disturbance-rejection Control based on interference observer, matching is subjected to mathematical character with the interference of non-matching two rahmonic and unknown nonlinear function；Interference observer is separately designed to the interference of two rahmonics, the real-time estimation to harmonic wave interference is completed；Output design extended state observer based on interference observer, completes the estimation to unknown nonlinear function and system mode；Next, with reference to the estimate of non-matching interference, the state variable new by introducing completes coordinate transform；Automatic disturbance rejection controller is designed according to the output of interference observer and extended state observer on the basis of above-mentioned Coordinate Conversion；Theoretical based on separation theorem and POLE PLACEMENT USING, the gain for completing observer and controller is solved, so as to complete the design of controller；The present invention has the advantages that strong antijamming capability, control accuracy are high, available for the high-precision control containing matching with non-matching harmonic wave interference and Unknown Nonlinear Systems.
Description
Technical field
The present invention relates to a kind of non-matching interference system Auto-disturbance-rejection Control based on interference observer, it is possible to achieve
Estimation is with offsetting while with non-matching harmonic wave interference and unknown nonlinear function, available for containing harmonic wave interference and unknown non-thread
Property function system control in.
Background technology
Due to controlled device and the complexity of task, a variety of sources such as modeling error, Parameters variation and unbalanced input
Unknown nonlinear factor the performance of control system produced had a strong impact on, or even dissipate system.In addition, from external rings
The disturbing factors such as border, internal sensor and actuator have been further exacerbated by the deterioration of control performance.For unknown nonlinear factor
With disturbing simultaneous situation, scholars propose many advanced control methods, for example, LQG controls, PID control and
H∞Control etc..However, the LQG theories of optimal control are the modellings based on system, the degree of dependence to model is higher, and
And the system that is influenceed by white Gaussian noise is only limitted to, when system has unknown nonlinear or other types of interference, performance can not be protected
Barrier.And result from the advantages of PID control of last century the '20s is because its is simple in construction, independent of system model so that
It is top dog in Industry Control always so far.However, PID control also has its limitation：First, PID control
The information of system model is have ignored completely；Secondly, the differential signal in PID control is often difficult to preferable acquisition, easily produces
High-frequency noise；Again, integral element brings the consequences such as delayed phase and vibration；Finally, the tune reference of PID control is cumbersome；
In addition, PID control can only compensate constant value interference, poor to the rejection ability of harmonic wave and unknown nonlinear factor.H∞Deng Shandong
Rod control mode also can only carry out AF panel to harmonic wave and unknown nonlinear function, it is impossible to compensate, cause control accuracy limited,
Conservative is larger.
In order to lift control performance, a variety of disturbance factors that compensation system is subject to, Han Jing Puritanisms are awarded to be carried from PID control
Gone out to possess Active Disturbance Rejection Control (ADRC) method of disturbance compensation ability, comprising Nonlinear Tracking Differentiator, extended state observer with it is non-
The part of linear feedback controller three is constituted, and complicated nonlinear system can be converted into the form of series connection integral form, realized
To the real-time estimation of unknown nonlinear function and a variety of disturbance factors and compensation, overcome modern control theory and be too dependent on and be
The limitation of system model.But, the model of traditional ADRC due to have ignored interference, by all disturbances and unknown nonlinear as
Total disturbance of derivative bounded is estimated and compensated, and causes its estimation effect to harmonic wave interference often unsatisfactory, for example, patent
Grant number be ZL200410070983.2, the patent of Application No. 201510359468.4 in employ Active Disturbance Rejection Control side
Method, by all disturbances and it is non-linear handled as total disturbance, but be a lack of the modeling to harmonic wave interference and accurate Estimation Study.
Control (DOBC) based on interference observer takes full advantage of the model information of interference, it is possible to achieve to harmonic wave, often
The accurate estimation of the interference such as value and compensation, and easily can be combined with other controls, realized by complex controll multiple
Suppress while interference with compensating, for example, patent authorization number is ZL200910086897.3, ZL201310081167.0 patent
In employ while complex controll mode realizes a variety of disturbances such as harmonic wave compensation with suppressing.However, current complex controll
There is also 2 limitations：First, while harmonic wave interference is considered, unknown nonlinear is dynamically considered not enough；Secondly, it is considered to
Interference be mostly matching type interference, disturb simultaneous situation deficiency state to feed back etc. simply to have with match for non-matching
The compensation way research of effect.And many real systems usually contain non-matching harmonic wave interference, such as airborne vehicle, permanent magnet synchronous electric
Machine, magnetic suspension control system etc..Because not in control passage, the cancellation problem of non-matching harmonic wave interference is always that research is difficult
One of point.
To sum up analyze, at present for being done containing matching with the multi-source such as non-matching harmonic wave interference and unknown nonlinear dynamic simultaneously
Wretched insufficiency is gone back in the interference compensation research for disturbing system.Because interference is dynamically mutually mixed with coupling with unknown nonlinear, interference is estimated
Meter error influences each other with Nonlinear Dynamic evaluated error, interference from different control passages, not yet find at present on
DOBC is with the ADRC researchs effectively combined, it is necessary to fully combine DOBC and ADRC respective advantage, and realization is disturbed and non-a variety of
Offset while linear dynamic, so that strengthening system accuracy and robustness.
The content of the invention
The technology of the present invention solves problem：It is difficult to compensate interference for existing control method, it is especially difficult
To possess non-matching with matching there is provided one kind the problem of being compensated to non-matching harmonic wave interference and unknown nonlinear function simultaneously
Auto-disturbance-rejection Control based on interference observer of harmonic wave interference and unknown nonlinear the function estimation in real time with offsetting ability,
Have the advantages that strong antijamming capability, control accuracy are high, available for containing matching and non-matching harmonic wave interference and unknown nonlinear system
The high-precision control of system.
The present invention technical solution be：A kind of non-matching interference system Active Disturbance Rejection Control side based on interference observer
Method, for containing the non-matching nonlinear system with matching harmonic wave interference and unknown nonlinear function, first, will matching with it is non-
Match the interference of two rahmonics and unknown nonlinear function carries out mathematical character；Secondly, the interference of two rahmonics is separately designed dry
Observer is disturbed, the real-time estimation to harmonic wave interference is completed；Again, the output design expansion state observation based on interference observer
Device, completes the estimation to unknown nonlinear function and system mode；Next, with reference to the estimate of non-matching interference, by drawing
Enter new state variable and complete coordinate transform；Further, on the basis of above-mentioned Coordinate Conversion according to interference observer and
The output design automatic disturbance rejection controller of extended state observer；Finally, it is theoretical based on separation theorem and POLE PLACEMENT USING, complete observation
The gain of device and controller is solved, so as to complete the design of controller；Specific implementation step is as follows：
(1) matching is subjected to mathematical character with the interference of non-matching two rahmonic and unknown nonlinear function：
Consider following containing matching and non-matching harmonic wave interference and the second-order system of unknown nonlinear function：
Wherein, x1With x2For system mode,WithFor the time-derivative of system mode, y exports to measure, x=[x1 x2
]T, u is control input, and b is the constant more than zero, f (x1,x2) it is the unknown nonlinear function that single order can be led；d0With d1Difference table
Show that non-matching harmonic wave interference is with matching harmonic wave interference known to frequency information, can be characterized as Wherein, D0With D1Unknown amplitude is represented,WithRepresent unknown phase, ω0With ω1Represent
Know frequency, t represents the moment；
Non-matching harmonic wave interference d0With matching harmonic wave interference d1It can be described respectively by following external model：
Wherein, w and ξ is the state of external model, coefficient matrixV0=
V1=[1 0]；
Unknown nonlinear function f (x1,x2) meet single order can sliver part, i.e.,Wherein, h is unknown bounded
Function；
(2) interference observer is separately designed to the interference of two rahmonics, completes the real-time estimation to harmonic wave interference：
To non-matching harmonic wave interference d0Designing interference observer is：
Wherein,Represent d0Estimate,Expression state w estimate, v0For the state variable of auxiliary, L1For observation
Device gain matrix；
To matching harmonic wave interference d1Designing interference observer is：
Wherein,Represent d1Estimate,Represent ξ estimate, writ state x3=f (x1,x2), andFor state x3's
Estimate, v1For the state variable of auxiliary, L2For observer gain matrix；
(3) the output design extended state observer based on interference observer, is completed to unknown nonlinear function and system
The estimation of state：
By x3It is used as the state of augmentation, second-order system Σ0It can be written as the form of augmented system：
Based on interference observer Σ3With Σ4Output, to augmented system Σ5Designing extended state observer is：
Wherein,State x is represented respectively1,x2,x3Estimate,Y estimate is represented,Represent x estimation
Value, l1,l2,l3Represent the gain of extended state observer；
With reference to external model Σ1With interference observer Σ3, non-matching harmonic wave interference d can be obtained0Evaluated errorDynamical equation：
With reference to external model Σ2With interference observer Σ4, may be matched harmonic wave interference d1Evaluated error's
Dynamical equation：
Wherein,Expression state x3Evaluated error；
Similarly, with reference to augmented system Σ5With extended state observer Σ6, obtain state estimation errorI=
1,2,3 dynamical equation：
Above-mentioned three classes dynamical equation simultaneous is got up and converted accordingly, can be obtained：
Wherein,The expression of coefficient matrix is as follows：
C1=[0 0 1],
(4) estimate of non-matching interference is combined, the state variable new by introducing completes coordinate transform：
Based on non-matching harmonic wave interference d0With matching harmonic wave interference d1Estimate, second-order system Σ0It can be converted into：
Wherein,
Ignore the evaluated error of interference and state and introduce new state variable z1=x1,z3=x3, can be with
Obtain such as the control system after down conversion：
(5) designed certainly according to the output of interference observer and extended state observer on the basis of above-mentioned Coordinate Conversion
Disturbance rejection control device：
For system Σ9, designing the automatic disturbance rejection controller based on interference observer is：
Wherein, p1,p2For controller gain,
(6) theoretical with POLE PLACEMENT USING based on separation theorem, the gain for completing observer and controller is solved, so as to complete control
The design of device processed：
Based on linear system separation theorem, interference observer gain matrix L1With L2, extended state observer gain matrix L
And controller gain p1,p2It can be solved respectively by POLE PLACEMENT USING：
Wherein, s represents complex variable, and I represents the unit matrix of appropriate dimension, symbol | | represent to solve the ranks of square formation
Formula, ω0>0、ω1>0 is given constant, represents the bandwidth of system.
The advantage of the present invention compared with prior art is：The present invention completes the interference of two rahmonics by interference observer
Estimation and compensation problem, solve the estimation of non-matching harmonic wave interference and compensation problem especially by coordinate transform, and
It is combined, estimates while completing matching with non-matching harmonic wave interference and dynamic unknown nonlinear with extended state observer
With compensation problem, the limitation that single automatic disturbance rejection controller is difficult to compensate for harmonic wave interference is overcome, available for containing matching and non-
High-precision control with harmonic wave interference and Unknown Nonlinear Systems.
Brief description of the drawings
Fig. 1 is a kind of non-matching interference system Auto-disturbance-rejection Control FB(flow block) based on interference observer.
Embodiment
Below in conjunction with the accompanying drawings and embodiment the present invention is described in more detail.
As shown in figure 1, to implement step as follows by the present invention：
The first step, mathematical character is carried out by matching with the interference of non-matching two rahmonic and unknown nonlinear function：
Consider following containing matching and non-matching harmonic wave interference and the second-order system of unknown nonlinear function：
Wherein, x1With x2For system mode,WithFor the time-derivative of system mode, y exports to measure, x=[x1 x2]T,
U is control input, and b is the constant more than zero, f (x1,x2) it is the unknown nonlinear function that single order can be led；d0With d1Frequency is represented respectively
Non-matching harmonic wave interference known to rate information can be characterized as with matching harmonic wave interference
Wherein, D0With D1Unknown amplitude is represented,WithRepresent unknown phase, ω0With ω1Given frequency is represented, t represents the moment；
In embodiments of the present invention, the unknown nonlinear function is taken to beTake b=1, D0=D1=0.05,ω0=10, ω1=15；
Non-matching harmonic wave interference d0With matching harmonic wave interference d1It can be described respectively by following external model：
Wherein, w and ξ is the state of external model, coefficient matrixV0=
V1=[1 0]；
Unknown nonlinear function f (x1,x2) meet single order can sliver part, i.e.,Wherein, h is unknown bounded
Function；
Second step, separately designs interference observer to the interference of two rahmonics, completes the real-time estimation to harmonic wave interference：
To non-matching harmonic wave interference d0Designing interference observer is：
Wherein,Represent d0Estimate,Expression state w estimate, v0For the state variable of auxiliary, L1For observer
Gain matrix；
To matching harmonic wave interference d1Designing interference observer is：
Wherein,Represent d1Estimate,Represent ξ estimate, writ state x3=f (x1,x2), andFor state x3's
Estimate, v1For the state variable of auxiliary, L2For observer gain matrix；
3rd step, based on interference observer output design extended state observer, complete to unknown nonlinear function with
The estimation of system mode：
By x3It is used as the state of augmentation, second-order system Σ0It can be written as the form of augmented system：
Based on interference observer Σ3With Σ4Output, to augmented system Σ5Designing extended state observer is：
Wherein,State x is represented respectively1,x2,x3Estimate,Y estimate is represented,Represent x estimation
Value, l1,l2,l3Represent the gain of extended state observer；
With reference to external model Σ1With interference observer Σ3, non-matching harmonic wave interference d can be obtained0Evaluated errorDynamical equation：
With reference to external model Σ2With interference observer Σ4, may be matched harmonic wave interference d1Evaluated error's
Dynamical equation：
Wherein,Expression state x3Evaluated error；
Similarly, with reference to augmented system Σ5With extended state observer Σ6, obtain state estimation errorI=1,
2,3 dynamical equation：
Above-mentioned three classes dynamical equation simultaneous is got up and converted accordingly, can be obtained：
Wherein,The expression of coefficient matrix is as follows：
C1=[0 0 1],
4th step, with reference to the estimate of non-matching interference, the state variable new by introducing completes coordinate transform：
Based on non-matching harmonic wave interference d0With matching harmonic wave interference d1Estimate, second-order system Σ0It can be converted into：
Wherein,
Ignore the evaluated error of interference and state and introduce new state variable z1=x1,z3=x3, can be with
Obtain such as the control system after down conversion：
5th step, sets on the basis of above-mentioned Coordinate Conversion according to the output of interference observer and extended state observer
Count automatic disturbance rejection controller：
For system Σ9, designing the automatic disturbance rejection controller based on interference observer is：
Wherein, p1,p2For controller gain,
6th step, theoretical based on separation theorem and POLE PLACEMENT USING, the gain for completing observer and controller is solved, so that complete
Into the design of controller：
Based on linear system separation theorem, interference observer gain matrix L1With L2, extended state observer gain matrix L
And controller gain p1,p2It can be solved respectively by POLE PLACEMENT USING：
Wherein, s represents complex variable, and I represents the unit matrix of appropriate dimension, symbol | | represent to solve the ranks of square formation
Formula, ω0>0、ω1>0 is given constant, represents the bandwidth of system.In the implementation case, the value of each element in L, K is tried to achieve
Between -5 to 5, parameter p1,p2Value between -20 to 20.
The content not being described in detail in description of the invention belongs to prior art known to professional and technical personnel in the field.
Claims (7)
1. a kind of non-matching interference system Auto-disturbance-rejection Control based on interference observer, it is characterised in that：Including following step
Suddenly：
The first step, mathematical character is carried out by matching with the interference of non-matching two rahmonic and unknown nonlinear function；
Second step, separately designs interference observer with the interference of non-matching two rahmonic to matching, completes to the real-time of harmonic wave interference
Estimation；
3rd step, the output design extended state observer based on interference observer, is completed to unknown nonlinear function and system
The estimation of state；
4th step, with reference to the estimate of non-matching interference, the state variable new by introducing completes coordinate transform；
5th step, is designed on the basis of the 4th step Coordinate Conversion according to the output of interference observer and extended state observer
Automatic disturbance rejection controller；
6th step, finally, theoretical based on separation theorem and POLE PLACEMENT USING, the gain for completing observer and controller is solved, so that
Complete the design of controller.
2. the non-matching interference system Auto-disturbance-rejection Control according to claim 1 based on interference observer, its feature
It is：The first step is implemented as follows：
Consider following containing matching and non-matching harmonic wave interference and the second-order system of unknown nonlinear function：
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Control input, b is the constant more than zero, f (x1,x2) it is the unknown nonlinear function that single order can be led；d0With d1Frequency is represented respectively
Non-matching harmonic wave interference is characterized as with matching harmonic wave interference known to information
D0With D1Unknown amplitude is represented,WithRepresent unknown phase, ω0With ω1Given frequency is represented, t represents the moment；
Non-matching harmonic wave interference d0With matching harmonic wave interference d1Described respectively by following external model：
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Wherein, w and ξ is the state of external model, coefficient matrixV0=V1=[1
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Unknown nonlinear function f (x1,x2) meet single order can sliver part, i.e.,Wherein, h is unknown bounded letter
Number.
3. the non-matching interference system Auto-disturbance-rejection Control according to claim 1 based on interference observer, its feature
It is：The second step is implemented as follows：
To non-matching harmonic wave interference d0Designing interference observer is：
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Wherein,Represent d0Estimate,Expression state w estimate, v0For the state variable of auxiliary, L1For observer gain
Matrix；
To matching harmonic wave interference d1Designing interference observer is：
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</mrow>
Wherein,Represent d1Estimate,Represent ξ estimate；Writ state x3=f (x1,x2), andFor state x3Estimation
Value, v1For the state variable of auxiliary, L2For observer gain matrix.
4. the non-matching interference system Auto-disturbance-rejection Control according to claim 1 based on interference observer, its feature
It is：3rd step is implemented as follows：
By x3It is used as the state of augmentation, second-order system Σ0It is written as the form of augmented system：
<mrow>
<msub>
<mi>&Sigma;</mi>
<mn>5</mn>
</msub>
<mo>:</mo>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<msub>
<mover>
<mi>x</mi>
<mo>&CenterDot;</mo>
</mover>
<mn>1</mn>
</msub>
<mo>=</mo>
<msub>
<mi>x</mi>
<mn>2</mn>
</msub>
<mo>+</mo>
<msub>
<mi>d</mi>
<mn>0</mn>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mover>
<mi>x</mi>
<mo>&CenterDot;</mo>
</mover>
<mn>2</mn>
</msub>
<mo>=</mo>
<msub>
<mi>x</mi>
<mn>3</mn>
</msub>
<mo>+</mo>
<mi>b</mi>
<mrow>
<mo>(</mo>
<mi>u</mi>
<mo>+</mo>
<msub>
<mi>d</mi>
<mn>1</mn>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mover>
<mi>x</mi>
<mo>&CenterDot;</mo>
</mover>
<mn>3</mn>
</msub>
<mo>=</mo>
<mi>h</mi>
</mtd>
</mtr>
<mtr>
<mtd>
<mi>y</mi>
<mo>=</mo>
<mi>x</mi>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
Based on interference observer Σ3With Σ4Output, to augmented system Σ5Designing extended state observer is：
<mrow>
<msub>
<mi>&Sigma;</mi>
<mn>6</mn>
</msub>
<mo>:</mo>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<msub>
<mover>
<mover>
<mi>x</mi>
<mo>^</mo>
</mover>
<mo>&CenterDot;</mo>
</mover>
<mn>1</mn>
</msub>
<mo>=</mo>
<msub>
<mover>
<mi>x</mi>
<mo>^</mo>
</mover>
<mn>2</mn>
</msub>
<mo>+</mo>
<msub>
<mover>
<mi>d</mi>
<mo>^</mo>
</mover>
<mn>0</mn>
</msub>
<mo>+</mo>
<msub>
<mi>l</mi>
<mn>1</mn>
</msub>
<mo>(</mo>
<mi>y</mi>
<mo>-</mo>
<mover>
<mi>y</mi>
<mo>^</mo>
</mover>
<mo>)</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mover>
<mover>
<mi>x</mi>
<mo>^</mo>
</mover>
<mo>&CenterDot;</mo>
</mover>
<mn>2</mn>
</msub>
<mo>=</mo>
<msub>
<mover>
<mi>x</mi>
<mo>^</mo>
</mover>
<mn>3</mn>
</msub>
<mo>+</mo>
<mi>b</mi>
<mo>(</mo>
<mi>u</mi>
<mo>+</mo>
<msub>
<mover>
<mi>d</mi>
<mo>^</mo>
</mover>
<mn>1</mn>
</msub>
<mo>)</mo>
<mo>+</mo>
<msub>
<mi>l</mi>
<mn>2</mn>
</msub>
<mo>(</mo>
<mi>y</mi>
<mo>-</mo>
<mover>
<mi>y</mi>
<mo>^</mo>
</mover>
<mo>)</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mover>
<mover>
<mi>x</mi>
<mo>^</mo>
</mover>
<mo>&CenterDot;</mo>
</mover>
<mn>3</mn>
</msub>
<mo>=</mo>
<msub>
<mi>l</mi>
<mn>3</mn>
</msub>
<mo>(</mo>
<mi>y</mi>
<mo>-</mo>
<mover>
<mi>y</mi>
<mo>^</mo>
</mover>
<mo>)</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mover>
<mi>y</mi>
<mo>^</mo>
</mover>
<mo>=</mo>
<mover>
<mi>x</mi>
<mo>^</mo>
</mover>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
Wherein,State x is represented respectively1,x2,x3Estimate,Y estimate is represented,Represent x estimate, l1,
l2,l3Represent the gain of extended state observer；
With reference to external model Σ1With interference observer Σ3, obtain non-matching harmonic wave interference d0Evaluated errorDynamic
Equation；With reference to external model Σ2With interference observer Σ4, obtain matching harmonic wave interference d1Evaluated errorDynamic side
Journey；With reference to augmented system Σ5With extended state observer Σ6Obtain state estimation errorDynamical equation, i=1,
2,3；Above-mentioned dynamical equation simultaneous is got up, obtained：
<mrow>
<msub>
<mi>&Sigma;</mi>
<mn>7</mn>
</msub>
<mo>:</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mover>
<mover>
<mi>x</mi>
<mo>~</mo>
</mover>
<mo>&CenterDot;</mo>
</mover>
</mtd>
</mtr>
<mtr>
<mtd>
<mover>
<mover>
<mi>w</mi>
<mo>~</mo>
</mover>
<mo>&CenterDot;</mo>
</mover>
</mtd>
</mtr>
<mtr>
<mtd>
<mover>
<mover>
<mi>&xi;</mi>
<mo>~</mo>
</mover>
<mo>&CenterDot;</mo>
</mover>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mrow>
<mi>A</mi>
<mo>-</mo>
<mi>L</mi>
<mi>C</mi>
</mrow>
</mtd>
<mtd>
<mi>M</mi>
</mtd>
<mtd>
<mi>N</mi>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mrow>
<msub>
<mi>W</mi>
<mn>0</mn>
</msub>
<mo>-</mo>
<msub>
<mi>L</mi>
<mn>1</mn>
</msub>
<msub>
<mi>V</mi>
<mn>0</mn>
</msub>
</mrow>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>-</mo>
<msub>
<mi>L</mi>
<mn>2</mn>
</msub>
<msub>
<mi>C</mi>
<mn>1</mn>
</msub>
</mrow>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mrow>
<msub>
<mi>W</mi>
<mn>1</mn>
</msub>
<mo>-</mo>
<msub>
<mi>L</mi>
<mn>2</mn>
</msub>
<msub>
<mi>bV</mi>
<mn>1</mn>
</msub>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mover>
<mi>x</mi>
<mo>~</mo>
</mover>
</mtd>
</mtr>
<mtr>
<mtd>
<mover>
<mi>w</mi>
<mo>~</mo>
</mover>
</mtd>
</mtr>
<mtr>
<mtd>
<mover>
<mi>&xi;</mi>
<mo>~</mo>
</mover>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>+</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mover>
<mi>h</mi>
<mo>&OverBar;</mo>
</mover>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
Wherein,The expression of coefficient matrix is as follows：
C1=[0 0 1],
5. the non-matching interference system Auto-disturbance-rejection Control according to claim 1 based on interference observer, its feature
It is：4th step is implemented as follows：
Based on non-matching harmonic wave interference d0With matching harmonic wave interference d1Estimate, second-order system Σ0It is converted into：
<mrow>
<msub>
<mi>&Sigma;</mi>
<mn>8</mn>
</msub>
<mo>:</mo>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mover>
<mi>x</mi>
<mo>&CenterDot;</mo>
</mover>
<mn>1</mn>
</msub>
<mo>=</mo>
<msub>
<mi>x</mi>
<mn>2</mn>
</msub>
<mo>+</mo>
<msub>
<mover>
<mi>d</mi>
<mo>^</mo>
</mover>
<mn>0</mn>
</msub>
<mo>+</mo>
<msub>
<mover>
<mi>d</mi>
<mo>~</mo>
</mover>
<mn>0</mn>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mover>
<mi>x</mi>
<mo>&CenterDot;</mo>
</mover>
<mn>2</mn>
</msub>
<mo>=</mo>
<mi>f</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>x</mi>
<mn>1</mn>
</msub>
<mo>,</mo>
<msub>
<mi>x</mi>
<mn>2</mn>
</msub>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>b</mi>
<mrow>
<mo>(</mo>
<mi>u</mi>
<mo>+</mo>
<msub>
<mover>
<mi>d</mi>
<mo>^</mo>
</mover>
<mn>1</mn>
</msub>
<mo>+</mo>
<msub>
<mover>
<mi>d</mi>
<mo>~</mo>
</mover>
<mn>1</mn>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mi>y</mi>
<mo>=</mo>
<mi>x</mi>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
Wherein,
Ignore the evaluated error of interference and state, with reference to the estimate of non-matching interferenceAnd introduce new state variable z1=
x1,z3=x3, obtain such as the control system after down conversion：
<mrow>
<msub>
<mi>&Sigma;</mi>
<mn>9</mn>
</msub>
<mo>:</mo>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mover>
<mi>z</mi>
<mo>&CenterDot;</mo>
</mover>
<mn>1</mn>
</msub>
<mo>=</mo>
<msub>
<mi>z</mi>
<mn>2</mn>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mover>
<mi>z</mi>
<mo>&CenterDot;</mo>
</mover>
<mn>2</mn>
</msub>
<mo>=</mo>
<msub>
<mi>z</mi>
<mn>3</mn>
</msub>
<mo>+</mo>
<mi>b</mi>
<mrow>
<mo>(</mo>
<mi>u</mi>
<mo>+</mo>
<msub>
<mover>
<mi>d</mi>
<mo>^</mo>
</mover>
<mn>1</mn>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<msub>
<mi>V</mi>
<mn>0</mn>
</msub>
<msub>
<mi>W</mi>
<mn>0</mn>
</msub>
<mover>
<mi>w</mi>
<mo>^</mo>
</mover>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mover>
<mi>z</mi>
<mo>&CenterDot;</mo>
</mover>
<mn>3</mn>
</msub>
<mo>=</mo>
<mi>h</mi>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>.</mo>
</mrow>
6. the non-matching interference system Auto-disturbance-rejection Control according to claim 1 based on interference observer, its feature
It is：5th step is implemented as follows：
According to control system Σ9Designing the automatic disturbance rejection controller based on interference observer is：
<mrow>
<mi>u</mi>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mi>b</mi>
</mfrac>
<mrow>
<mo>(</mo>
<msub>
<mi>p</mi>
<mn>1</mn>
</msub>
<msub>
<mover>
<mi>z</mi>
<mo>^</mo>
</mover>
<mn>1</mn>
</msub>
<mo>+</mo>
<msub>
<mi>p</mi>
<mn>2</mn>
</msub>
<msub>
<mover>
<mi>z</mi>
<mo>^</mo>
</mover>
<mn>2</mn>
</msub>
<mo>-</mo>
<msub>
<mover>
<mi>z</mi>
<mo>^</mo>
</mover>
<mn>3</mn>
</msub>
<mo>+</mo>
<msub>
<mi>V</mi>
<mn>0</mn>
</msub>
<msub>
<mi>W</mi>
<mn>0</mn>
</msub>
<mover>
<mi>w</mi>
<mo>^</mo>
</mover>
<mo>)</mo>
</mrow>
<mo>-</mo>
<msub>
<mover>
<mi>d</mi>
<mo>^</mo>
</mover>
<mn>1</mn>
</msub>
</mrow>
Wherein, p1,p2For controller gain,
7. the non-matching interference system Auto-disturbance-rejection Control according to claim 1 based on interference observer, its feature
It is：6th step is implemented as follows：
Based on linear system separation theorem, the gain matrix L of interference observer1With L2, extended state observer gain matrix L
And controller gain p1,p2Solved respectively by POLE PLACEMENT USING：
<mrow>
<mrow>
<mo>|</mo>
<mrow>
<mi>s</mi>
<mi>I</mi>
<mo>-</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mrow>
<mi>A</mi>
<mo>-</mo>
<mi>L</mi>
<mi>C</mi>
</mrow>
</mtd>
<mtd>
<mi>M</mi>
</mtd>
<mtd>
<mi>N</mi>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mrow>
<msub>
<mi>W</mi>
<mn>0</mn>
</msub>
<mo>-</mo>
<msub>
<mi>L</mi>
<mn>1</mn>
</msub>
<msub>
<mi>V</mi>
<mn>0</mn>
</msub>
</mrow>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>-</mo>
<msub>
<mi>L</mi>
<mn>2</mn>
</msub>
<msub>
<mi>C</mi>
<mn>1</mn>
</msub>
</mrow>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mrow>
<msub>
<mi>W</mi>
<mn>1</mn>
</msub>
<mo>-</mo>
<msub>
<mi>L</mi>
<mn>2</mn>
</msub>
<msub>
<mi>bV</mi>
<mn>1</mn>
</msub>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
<mo>|</mo>
</mrow>
<mo>=</mo>
<msup>
<mrow>
<mo>(</mo>
<mi>s</mi>
<mo>+</mo>
<msub>
<mi>&omega;</mi>
<mn>0</mn>
</msub>
<mo>)</mo>
</mrow>
<mn>10</mn>
</msup>
</mrow>
<mrow>
<mrow>
<mo>|</mo>
<mrow>
<mi>s</mi>
<mi>I</mi>
<mo>-</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>p</mi>
<mn>1</mn>
</msub>
</mtd>
<mtd>
<msub>
<mi>p</mi>
<mn>2</mn>
</msub>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
<mo>|</mo>
</mrow>
<mo>=</mo>
<msup>
<mrow>
<mo>(</mo>
<mi>s</mi>
<mo>+</mo>
<msub>
<mi>&omega;</mi>
<mn>1</mn>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
Wherein, s represents complex variable, and I represents the unit matrix of appropriate dimension, symbol | | represent to solve the determinant of square formation, ω0>
0、ω1>0 is given constant, represents the bandwidth of system.
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Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107994815A (en) * | 2017-12-08 | 2018-05-04 | 重庆邮电大学 | The mismatch time-varying disturbance restraining method of permanent-magnet brushless DC electric machine governing system |
| CN110687800A (en) * | 2019-11-19 | 2020-01-14 | 大连海事大学 | Data-driven adaptive anti-interference controller structure and estimation method thereof |
| CN110908279A (en) * | 2018-09-18 | 2020-03-24 | 通用汽车环球科技运作有限责任公司 | System and method for using nonlinear Model Predictive Control (MPC) for autonomous systems |
| CN111158343A (en) * | 2020-01-10 | 2020-05-15 | 淮阴工学院 | Asynchronous fault-tolerant control method for switching system with actuator and sensor faults |
| CN112077847A (en) * | 2020-09-08 | 2020-12-15 | 西华大学 | Position tracking control method of robot interfered by non-matching |
| CN114265311A (en) * | 2021-12-21 | 2022-04-01 | 杭州电子科技大学 | Control method of nonlinear liquid level control resonant circuit system based on dynamic feedback |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20030199997A1 (en) * | 2002-04-18 | 2003-10-23 | Zhiqiang Gao | Scaling and parameterizing a controller |
| CN101969210A (en) * | 2010-10-22 | 2011-02-09 | 天津理工大学 | Active disturbance rejection control technology-based method for controlling synchronization of photovoltaic power generation system |
-
2017
- 2017-07-17 CN CN201710579482.4A patent/CN107168072B/en active Active
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20030199997A1 (en) * | 2002-04-18 | 2003-10-23 | Zhiqiang Gao | Scaling and parameterizing a controller |
| CN101969210A (en) * | 2010-10-22 | 2011-02-09 | 天津理工大学 | Active disturbance rejection control technology-based method for controlling synchronization of photovoltaic power generation system |
Non-Patent Citations (2)
| Title |
|---|
| GUO B Z, ZHAO Z L: "On convergence of non-linear extended state observer for multi-input multi-output system with uncertainty", 《IET CONTROL THEORY AND APPLICATIONS》 * |
| 吴忠，等: "航天器姿态自抗扰控制", 《控制理论与应用》 * |
Cited By (10)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107994815A (en) * | 2017-12-08 | 2018-05-04 | 重庆邮电大学 | The mismatch time-varying disturbance restraining method of permanent-magnet brushless DC electric machine governing system |
| CN110908279A (en) * | 2018-09-18 | 2020-03-24 | 通用汽车环球科技运作有限责任公司 | System and method for using nonlinear Model Predictive Control (MPC) for autonomous systems |
| CN110687800A (en) * | 2019-11-19 | 2020-01-14 | 大连海事大学 | Data-driven adaptive anti-interference controller structure and estimation method thereof |
| CN110687800B (en) * | 2019-11-19 | 2022-05-13 | 大连海事大学 | Data-driven self-adaptive anti-interference controller and estimation method thereof |
| CN111158343A (en) * | 2020-01-10 | 2020-05-15 | 淮阴工学院 | Asynchronous fault-tolerant control method for switching system with actuator and sensor faults |
| CN111158343B (en) * | 2020-01-10 | 2023-03-21 | 淮阴工学院 | Asynchronous fault-tolerant control method for switching system with actuator and sensor faults |
| CN112077847A (en) * | 2020-09-08 | 2020-12-15 | 西华大学 | Position tracking control method of robot interfered by non-matching |
| CN112077847B (en) * | 2020-09-08 | 2022-02-22 | 西华大学 | Position tracking control method of robot interfered by non-matching |
| CN114265311A (en) * | 2021-12-21 | 2022-04-01 | 杭州电子科技大学 | Control method of nonlinear liquid level control resonant circuit system based on dynamic feedback |
| CN114265311B (en) * | 2021-12-21 | 2024-03-29 | 杭州电子科技大学 | Control method of nonlinear liquid level control resonant circuit system based on dynamic feedback |
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