CN109324512A - A method of depression of order automatic disturbance rejection controller parameter is adjusted using known models information - Google Patents
A method of depression of order automatic disturbance rejection controller parameter is adjusted using known models information Download PDFInfo
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Abstract
The method with bandwidth-version adjusting depression of order automatic disturbance rejection controller parameter based on known models information that the present invention provides a kind of.The method uses tradition RADRC control structure, for GADRC controller, GADRC feedback controller is approached using the feedback controller transmission function of RADRC, consider the two zero point having the same, ensure that the two has similar Immunity Performance, to obtain the traditional RADRC parameter adjusted with bandwidth-version, the present invention is set out with the equivalent composite construction of second order RADRC, analysis design, simple, intuitive are carried out in frequency domain, so that more project planner is received；The present invention can obtain preferable control performance, and Robust degree is high, and anti-interference is good, and convenient for being adjusted according to the requirement of object actual motion state and control performance, model it is adaptable, operability is good.
Description
Technical field
The invention belongs to control theories and applied technical field, and in particular to a kind of to adjust depression of order using known models information
The method of automatic disturbance rejection controller parameter.
Background technique
Active Disturbance Rejection Control (Active Disturbance Rejection Control, abbreviation ADRC) is Chinese Academy of Sciences's system
Institute Han Jingqing researcher deep anatomy classical PID control working principle on the basis of, absorb and developed classical PID control by
The marrow that error is adjusted, acts on Special Nonlinear, a kind of new control technology of proposition.ADRC technology is a kind of non-
Linear control method, by Nonlinear Tracking Differentiator (tracking differentiator, TD), extended state observer (extended
State observer, ESO) and the parts group such as nonlinear feedback (nonlinear state error feedback, NLSEF)
At core concept is that the uncertainty (permanent or time-varying, linearly or nonlinearly) of internal system and outside is uncertain (outer
Portion's disturbance) together as " always disturbance ", estimate simultaneously real-time compensation to " total disturbance " by construction extended state observer, from
And obtain stronger Ability of Resisting Disturbance.This method does not need to disturb outside directly measurement, does not need to know perturbation action rule in advance yet,
It is easily obtained in opposite order, I/O channel number, signal delay time for having understood controlled device etc. and physical quantity is clear
Characteristic quantity on the basis of, it will be able to carry out relevant controller design.ADRC small, fast response time, essence with control overshoot
The features such as degree height, strong antijamming capability.But program structure also seems complex, and the parameter for needing to adjust is more, reason
It proves bright also more difficult, therefore is restricted in practical applications.
To solve the above-mentioned problems, professor Gao Zhiqiang etc. propose ADRC " linear " version (linear active disturbance rejection control,
LADRC), Linear State Feedback is carried out using estimated error and its all-order derivative, and design and state feedback ESO
Design be converted into the selections of two parameters of observer bandwidth and controller bandwidth, structure and the parameter for enormously simplifying ADRC are whole
It is fixed, make it possible the practical application of ADRC.Thus the method for some adjusting LADRC parameters has also been derived.Such as: Lee Tung Hai
Et al. propose it is a kind of using closed-loop system time domain response adjustment time carry out parameter tuning method；Yuan Dong et al. is from frequency-domain analysis
Method is started with, and closed loop transfer function, and frequency bandwidth characteristics curve based on linear active disturbance rejection controller systematically analyze expansion shape
The stability of the tracking estimated capacity of state observer and automatic disturbance rejection controller is inputted to the rejection ability of external disturbance, to control
The robustness and its noise transmission characteristic of gain uncertainty and model parameter uncertainty have inquired into system dynamic characteristic and control
The relationship of parameter processed；The engineering configuration method of control parameter is proposed on this basis；The superfine people of Xue Wen proposes with adaptive
Answer the ADRC method of adjustment of ESO；Tan Wen et al. analysis has obtained equivalence relation between LADRC and IMC, while proposing addition mould
The parameter tuning method GADRC of type Given information.GADRC is a kind of general control structure, it can be the dynamic of controlled device
State information (including pole, zero point and/or delay) is added in the design of LADRC.Model information, which is added, in GADRC can reduce ESO
Burden, therefore it can be desirable to obtain than traditional LADRC better performance.Moreover, the design of GADRC controller need to only adjust two
A parameter (With), therefore easily understood by Practical Project controllers.But how to obtain the initial parameter of LADRC still
It is a problem, sweet smell et al. of laying on colors proposes a kind of to obtain the adjusting side of LADRC parameter by frequency domain approximation using higher order controller
Method；Zhao Chun wise man et al. proposes a kind of method for converting LADRC parameter for existing pid parameter.Since both the above method is given
LADRC parameter out is provided in the form of state observer and feedback control gain, if necessary to on-line tuning
When the parameter of LADRC, unlike conventional bandwidth setting method is so intuitive easy.Davi G in 1964 is put forward for the first time depression of order observation
Device, the principle of reduced order observer are that some outputs of object are known not need to estimate, it is only necessary to be estimated to other information
Meter.Tian G has studied the frequency domain characteristic of the automatic disturbance rejection controller with depression of order.It is mentioned for the biggish deficiency of ESO delayed phase
The LADRC for using depression of order extended state observer (Reduced Extend State Observer, RESO) out, is denoted as
RADRC.RADRC also lacks a kind of parameter tuning method using known models information of bandwidth-version at present.
Summary of the invention
To solve the above-mentioned problems, the present invention provides a kind of utilization known models information adjusting depression of order automatic disturbance rejection controller ginseng
Several methods, the method approaches GADRC feedback controller using the feedback controller transmission function of RADRC, according to RADRC
Feedback controller and GADRC feedback controller zero point having the same, guarantee two kinds of feedback controllers have similar anti-interference
Performance, to obtain two bandwidth parameters of traditional RADRC adjusted with bandwidth-version；
Further, which comprises
S1: traditional LADRC controller architecture and bandwidth setting method are provided；
S2: providing the GADRC controller architecture and bandwidth setting method that model information is added, and provides its tradition two freely
Degree form；
S3: by being analyzed to obtain the controller architecture of RADRC to the LADRC structure in S1；
S4: equivalent traditional feedback control structure of RADRC is obtained by being analyzed the RADRC structure in S3, and is given
RADRC feedback controller transmission function C out2(s) feedback control gain and observer gain of molecule denominator and RADRC it
Between relationship；
S5: the feedback controller by the way that the feedback controller transmission function of RADRC in S3 to be approached to GADRC transmits letter
Number, both considerations zero point having the same guarantee that the two has similar Immunity Performance, to obtain with bandwidth-version adjusting
Two bandwidth parameters of traditional RADRC；To make traditional RADRC identical as the feedback control integral gain of GADRC, tradition is obtained
The parameter b of RADRC0；
Further, the S1 is specifically included:
S11: assuming that object is
Conventional linear Active Disturbance Rejection Control is using series connection integrator model, it is assumed that the model of controlled device (1) is as follows
In formula,For the estimation of object model high-frequency gain, y (t) is system output, and u (t) is system input, and f (t) is
System always disturbs；
S12: the state of controlled device and unknown is estimated in linear active disturbance rejection control using linear extended state observer
General disturbance；
Wherein
According to the state-space model of (4), whereinAnd
Wherein
For selected state andFor observer gain:
Under the hypothesis of general disturbance f (t) bounded, whenWhen asymptotically stability, z1(t),z2(t) it levels off to and exports y
(t) andAnd z3(t) f (t) is leveled off to；
S13: z is utilized3(t) it is controlled, inhibits f (t) quickly, the shape based on controlled device achieved above
State and the general disturbance of estimation are controlled using following linear state feedback control rate
Wherein r (t) is the reference signal to be tracked,To combine reference signal r (t) and its derivativeBroad sense ginseng
Examine signal
And state feedback oscillatorIt is defined as
S14: linear active disturbance rejection controller is according to following state space realization
By the above design process it is found that a linear active disturbance rejection control needs to design following three groups of parameters:ESO's
Observer gainAnd 2 rank Integrating control gainWhereinValue should as far as possible approximation system practical high frequency increase
Beneficial b, usuallySmaller, control action is stronger, but stability margin is smaller, aboutAndIt, will using bandwidth TuningAndAdjusting be converted into the adjusting of two parameters: observer bandwidthAnd controller bandwidthWherein
Further, the S2 is specifically included:
S21: for object (1), if it is known that by the model of u (t) to y (t), it is assumed that the transmission function of controlled device P (s)
Model is
Assuming thatState beIts corresponding controllable state space is embodied as Cm
(sI-Am)-1Bm, wherein
Unknown broad sense interference f (t) will be estimated using extended state observer (ESO) below, is defined as follows broad sense pair
As:
Wherein
And
Wherein 0 indicate the zero vector being adapted with dimension；
GADRC has following state space realization form:
WhereinFor broad sense reference signal, feedback control gain is defined as
For ESO,Characteristic equation are as follows:
Wherein coefficient l1,l2,l3By a0,a1, b0,b1AndIt determines, it is assumed that all poles of observer are respectively positioned on
Characteristic equation (20) write as again forWhereinFor optimum wideband, according to Ackerman theorem, observer increases
Beneficial vector are as follows:
If general disturbance f (t) is adequately compensated for, original controlled device is reduced to 2 rank linear objectsIf stateAccurately estimated, then final feedback control system is
Similarly, if all closed-loop poles are placed inExcept origin, i.e.,
ThereforeFor the parameter for uniquely needing to adjust in STATE FEEDBACK CONTROL,
S22: Laplace transformation is carried out to the state space realization of 2 rank GADRC, is had
WhereinIt isLaplace transformation,It isLaplace transformation, can be obtained by (25)
Wherein
Preferably closed-loop system is
WhenReach " optimal " tracking, takesFor filter, to make control system obtain no error following
One adequate condition is
Not needing additional dynamic to set point filter can enable
Further, the S3 is specifically included:
S31: the state-space model (4) of object (1) is as follows:
Wherein, x1=y can measure,Accordingly
Estimated using following RESO controlled device state and unknown general disturbance；
Observer gain L at this timeoAre as follows:
Lo=[β1 β2]T(35)；
S32: the general disturbance of state and estimation based on controlled device achieved above, it is anti-using following linear condition
Present control rate control
Wherein
S33: the following state space realization of linear active disturbance rejection controller:
Further, the S4 is specifically included:
S41: Laplace transformation is carried out to formula (38):
Wherein, the Laplace that Z (s) is z (t) is converted,ForLaplace transformation；
The Laplace that wherein R (s) is reference signal r (t) is converted, and removes intermediate variable:
It is equivalent compound that RADRC is become into two degrees of freedom；
S42: to feedback controller C2(s) (41) carry out analysis and solution:
Wherein numerator coefficients are calculate by the following formula
Denominator coefficients can be calculate by the following formula
C2It (s) is the 2 rank canonical transmission functions with integral；
Further, the S5 is specifically included:
S51:RADRC parameter KoAnd LoBy controller bandwidth omegacWith observer bandwidth omegaoIt determines
Controller gain KoA parameter ζ is increased, for eliminating the oscillation of response；
The feedback transfer function (46) of second order RADRC is equal to
S52: the feedback controller of GADRC is approached with feedback transfer function (46)(28), consider the two with identical
Zero point, to have
Wherein α is an adjustable constant, is obtained by the first two equation of (47)
(48) are brought into the third equation of (47), are obtained
Work as LoBy observer bandwidth omegaoWhen determining, β1,β2It is provided by (45), so that above-mentioned equation becomes
Equation (50) has 4 solutions, guarantees that the solution real solution that is positive takes most when there are multiple positive real solutions by choosing sufficiently large α
Big is used as observer bandwidth；
S53: observer bandwidth omega has been determinedo, obtained by (47,45)
Above-mentioned steps ensure that the feedback controller of second order RADRC and GADRCWith same zero point, second order RADRC
Also include three poles in addition to origin, guarantees the feedback controller of RADRC (46) integral gain and original GADRCIntegral gain
It is identical, adjustment parameter b0, enable
To b0It is set as
The gain ensures the integral gain of RADRC (46) and the feedback controller of GADRCIntegral gain is identical；
Further, the method is directed to general industry process control objects, according to the GADRC feedback control of known object
Device parameter obtains the parameter ω of second order RADRC using the methodo, ωc, ζ, bo, the second order RADRC that is obtained by above step
Anti-interference similar with GADRC and robust performance are obtained, is controlled using obtained RADRC controller parameter, when needed may be used
To carry out necessary on-line tuning to obtain ideal control performance；
Beneficial effects of the present invention are as follows:
1, to the present invention in the case where meeting control requirement, control system is simple and reliable；
2, the present invention is set out with the equivalent composite construction of second order RADRC, analysis design is carried out in frequency domain, thus more work
Journey designer is received；
3, The present invention gives the parameter tuning method of the second order RADRC based on bandwidth, simple, intuitives；
4, preferable control performance can be obtained using the RADRC controller that the present invention adjusts, Robust degree is high, anti-interference
It is good, and convenient for being adjusted according to the requirement of object actual motion state and control performance, model it is adaptable, can grasp
The property made is good.
Detailed description of the invention
Fig. 1 is heretofore described second order RADRC controller structure diagram；
Fig. 2 is the tracking of system described in the embodiment of the present invention and anti-interference result figure.
Specific embodiment
In order to make the objectives, technical solutions, and advantages of the present invention clearer, with reference to the accompanying drawings and embodiments, right
The present invention is explained in further detail.It should be appreciated that specific embodiment described herein is used only for explaining the present invention, and
It is not used in the restriction present invention.On the contrary, the present invention cover it is any be defined by the claims do on the essence and scope of the present invention
Substitution, modification, equivalent method and scheme.Further, in order to make the public have a better understanding the present invention, below to this
It is detailed to describe some specific detail sections in the datail description of invention.It is thin without these for a person skilled in the art
The present invention can also be understood completely in the description of section part.
The present invention will be further explained below with reference to the attached drawings and specific examples, but not as a limitation of the invention.
Most preferred embodiment is enumerated below for of the invention:
As Figure 1-Figure 2, the present invention provides a kind of certainly anti-with bandwidth-version adjusting depression of order based on known models information
The method for disturbing controller parameter.The method uses tradition RADRC control structure, for GADRC controller, using RADRC's
Feedback controller transmission function approaches GADRC feedback controller, both considers zero point having the same, and both ensure that has
Similar Immunity Performance, to obtain the conventional RADRC parameter adjusted with bandwidth-version.
The design procedure of the linear active disturbance rejection controller are as follows:
S1: traditional LADRC controller architecture and bandwidth setting method are provided；
S2: providing the GADRC controller architecture and bandwidth setting method that model information is added, and provides its tradition two freely
Degree form；
S3: by being analyzed to obtain the controller architecture of RADRC to the LADRC structure in S1；
S4: equivalent traditional feedback control structure of RADRC is obtained by being analyzed the RADRC structure in S3, and is given
RADRC feedback controller transmission function C out2(s) feedback control gain and observer gain of molecule denominator and RADRC it
Between relationship；
S5: the feedback controller by the way that the feedback controller transmission function of RADRC in S3 to be approached to GADRC transmits letter
Number, both considerations zero point having the same guarantee that the two has similar Immunity Performance, to obtain with bandwidth-version adjusting
Two bandwidth parameters of traditional RADRC；To make traditional RADRC identical as the feedback control integral gain of GADRC, tradition is obtained
The parameter b of RADRC0；
The step S1 is specifically included:
Assuming that object are as follows:
For conventional linear Active Disturbance Rejection Control using series connection integrator model, i.e. the model of hypothesis controlled device (1) is as follows
In formula,For the estimation of object model high-frequency gain, y (t) is system output, and u (t) is system input, and f (t) is
System always disturbs.
The state of controlled device and unknown wide is estimated in linear active disturbance rejection control using linear extended state observer
Justice disturbance.
Wherein
It is the state-space model of (4), whereinAnd
Wherein
For selected state andFor observer gain:
Under the hypothesis of general disturbance f (t) bounded, whenWhen asymptotically stability, z1(t),z2(t) it levels off to and exports y
(t) andAnd z3(t) f (t) is leveled off to.Therefore it can use z3(t) it is controlled, inhibits f (t) quickly.
The general disturbance of state and estimation based on controlled device achieved above, using following Linear State Feedback control
Rate control processed
Wherein r (t) is the reference signal to be tracked,To combine reference signal r (t) and its derivativeBroad sense ginseng
Examine signal
And state feedback oscillatorIt is defined as
In summary, linear active disturbance rejection controller has following state space realization
By the above design process it is found that a linear active disturbance rejection control needs to design following three groups of parameters:ESO's
Observer gainAnd 2 rank Integrating control gainWhereinValue should as far as possible approximation system practical high frequency increase
Beneficial b.UsuallySmaller, control action is stronger, but stability margin is smaller.AboutAndUsing bandwidth Tuning, i.e., willAndAdjusting be converted into the adjusting of two parameters: observer bandwidthAnd controller bandwidthWherein
The step S2 is specific as follows:
For object (1), if it is known that we can utilize this information in the design by the model of u (t) to y (t).
Here, suppose that the transfer function model of controlled device P (s) is
Assuming thatState beSo its corresponding controllable state space is realized
For Cm(sI-Am)-1Bm, wherein
Unknown broad sense interference f (t) will be estimated using extended state observer (ESO) below.It is defined as follows broad sense pair
As:
Wherein
And
Wherein 0 indicate the zero vector being adapted with dimension.
Similar to the design procedure of traditional LADRC, GADRC has following state space realization form
HereFor broad sense reference signal, determined by Nonlinear Tracking Differentiator (TD) (Effect will be carried out below
It discusses).Feedback control gain is defined as
Obvious GADRC has two groups of gains to need to adjust: the observer gain of ESOAnd feedback control
Device gain processedThis two groups of gains all bandwidth (Feedback controller bandwidth,Observer bandwidth) think of
Want to be adjusted.
For ESO,Characteristic equation are as follows:
Wherein coefficient l1,l2,l3By a0,a1, b0,b1AndIt determines.Assuming that all poles of observer are respectively positioned onI.e. characteristic equation (20) can be write as againWhereinFor optimum wideband.Then, according to Ackerman
Theorem, observer gain vector are as follows:
If general disturbance f (t) is adequately compensated for, original controlled device is then reduced to 2 rank linear objectsIf
StateAlso accurately estimated, then final feedback control system are as follows:
Similarly, if all closed-loop poles are placed in(in addition to origin), i.e.,
So
This is allowed forBecome the parameter for uniquely needing to adjust in STATE FEEDBACK CONTROL.
Laplace transformation is carried out to the state space realization of 2 rank GADRC, is had
WhereinIt isLaplace transformation,It isLaplace transformation can be obtained by (25)
Wherein
Preferably closed-loop system is
WhenIt can achieve " optimal " tracking.Here it takesFor filter, to make control system obtain nothing
Difference tracking an adequate condition be
For the sake of simplicity, if not needing additional dynamic to set point filter can enable
It can be seen that GADRC is a kind of general control structure, it can be the multidate information of controlled device (including pole
Point, zero point and/or delay) it is added in the design of LADRC.Model information, which is added, in GADRC can reduce the burden of ESO, therefore can be with
It is expected that obtaining than traditional LADRC better performance.Moreover, the design of GADRC controller need to only adjust two parameters (With),
Therefore easily understood by Practical Project controllers.
The step S3 is specifically included:
For the state-space model (4) of object (1), it is written as follow form
Wherein, x1=y can measure,Accordingly
Can be estimated using following RESO controlled device state and unknown general disturbance.
Observer gain L at this timeoAre as follows:
Lo=[β1 β2]T(35)；
The general disturbance of state and estimation based on controlled device achieved above, using following Linear State Feedback control
Rate control processed:
Wherein
In summary, linear active disturbance rejection controller has following state space realization
The step S4 is specifically included:
Laplace transformation is carried out to formula (38), it is available
Wherein, the Laplace that Z (s) is z (t) is converted,ForLaplace transformation.
The Laplace that wherein R (s) is reference signal r (t) is converted.Remove intermediate variable, it is available
It is equivalent compound that the above RADRC can become two degrees of freedom.
To feedback controller C2(s) (41) carry out analysis and solution, available
Wherein numerator coefficients can be calculate by the following formula
Denominator coefficients can be calculate by the following formula
Obviously, C2It (s) is the 2 rank canonical transmission functions with integral.
The step S5 is specifically included:
For the feedback controller of GADRCConsider that a kind of RADRC is approached, wherein RADRC parameter KoAnd LoBy controlling
Device bandwidth omegacWith observer bandwidth omegaoIt determines.
Controller gain K hereinoA parameter ζ is increased, for eliminating the oscillation of response.
Notice that the feedback transfer function (46) of second order RADRC is equal to
In order to approach the feedback controller of GADRC with the transmission function(28), consider the two zero point having the same,
To have
Wherein α is an adjustable constant.It is available by the first two equation of (47)
(48) are brought into the third equation of (47), are obtained
Work as LoBy observer bandwidth omegaoWhen determining, β1,β2It is provided by (45), so that above-mentioned equation becomes
In order to approach the feedback controller of GADRCThe observer bandwidth omega of second order RADRCoIt must satisfy equation
(50).The equation has 4 solutions, can guarantee that solution is positive real solution by choosing sufficiently large α.It, can be with when there are multiple positive real solutions
Take it is maximum that as observer bandwidth.
Observer bandwidth omega has been determinedo, available by (47,45)
Above-mentioned steps ensure that the feedback controller of second order RADRC and GADRCWith same zero point.Due to second order
RADRC includes also three poles in addition to origin, in order to guarantee the feedback controller of RADRC (46) integral gain Yu original GADRCIntegral gain is identical, adjustable parameter b0Even
To b0It can be set to
The gain may insure the integral gain of RADRC (46) and the feedback controller of GADRCIntegral gain is identical.
In conclusion general industry process control objects are directed to, according to the GADRC feedback controller parameter benefit of known object
The parameter ω of the available second order RADRC of the method provided by the inventiono, ωc, ζ, bo.The second order obtained by above step
RADRC can obtain anti-interference similar with GADRC and robust performance, be controlled using obtained RADRC controller parameter,
Necessary on-line tuning can be carried out when needing to obtain ideal control performance.
Embodiment:
Giving controlled device transmission function is
Use GADRC controller parameter for
Its feedback controller is
By step S5 the method, α=10 are taken4, obtain RADRC controller parameter are as follows:
b0=9.56, ωo=9.38, ωc=0.24, ζ=5.65
Control emulation is carried out to practical controlled device by controller architecture shown in attached drawing 1, obtains system tracking and anti-interference
As a result as shown in Figure 2.
Embodiment described above, only one kind of the present invention more preferably specific embodiment, those skilled in the art
The usual variations and alternatives that member carries out within the scope of technical solution of the present invention should be all included within the scope of the present invention.
Claims (8)
1. a kind of method using known models information adjusting depression of order automatic disturbance rejection controller parameter, which is characterized in that the method
GADRC feedback controller is approached using the feedback controller transmission function of RADRC, according to the feedback controller of RADRC and
GADRC feedback controller zero point having the same, guarantee two kinds of feedback controllers have similar Immunity Performance, thus obtain with
Two bandwidth parameters of traditional RADRC of bandwidth-version adjusting.
2. the method according to claim 1, wherein the described method includes:
S1: traditional LADRC controller architecture and bandwidth setting method are provided；
S2: providing the GADRC controller architecture and bandwidth setting method that model information is added, and provides its traditional two degrees of freedom shape
Formula；
S3: by being analyzed to obtain the controller architecture of RADRC to the LADRC structure in S1；
S4: equivalent traditional feedback control structure of RADRC is obtained by being analyzed the RADRC structure in S3, and is provided
RADRC feedback controller transmission function C2(s) between the feedback control gain and observer gain of molecule denominator and RADRC
Relationship；
S5: the feedback controller transmission function by the way that the feedback controller transmission function of RADRC in S3 to be approached to GADRC is examined
Consider the two zero point having the same, guarantee that the two has similar Immunity Performance, to obtain the tradition adjusted with bandwidth-version
Two bandwidth parameters of RADRC；To make traditional RADRC identical as the feedback control integral gain of GADRC, traditional RADRC is obtained
Parameter b0。
3. according to the method described in claim 2, it is characterized in that, the S1 is specifically included:
S11: assuming that object is
Conventional linear Active Disturbance Rejection Control is using series connection integrator model, it is assumed that the model of controlled device (1) is as follows
In formula,For the estimation of object model high-frequency gain, y (t) is system output, and u (t) is system input, and f (t) is that system is total
Disturbance；
S12: the state of controlled device and unknown wide is estimated in linear active disturbance rejection control using linear extended state observer
Justice disturbance；
Wherein
According to the state-space model of (4), whereinAnd
Wherein
For selected state andFor observer gain:
Under the hypothesis of general disturbance f (t) bounded, whenWhen asymptotically stability, z1(t),z2(t) level off to output y (t) andAnd z3(t) f (t) is leveled off to；
S13: z is utilized3(t) controlled, inhibit f (t) quickly, the state based on controlled device achieved above with
And the general disturbance of estimation, it is controlled using following linear state feedback control rate
Wherein r (t) is the reference signal to be tracked,To combine reference signal r (t) and its derivativeBroad sense with reference to letter
Number
And state feedback oscillatorIt is defined as
S14: linear active disturbance rejection controller is according to following state space realization
By the above design process it is found that a linear active disturbance rejection control needs to design following three groups of parameters:The observer of ESO
GainAnd 2 rank Integrating control gainWhereinValue should approximation system as far as possible practical high-frequency gain b, usuallySmaller, control action is stronger, but stability margin is smaller, aboutAndIt, will using bandwidth TuningAndAdjusting turn
Turn to the adjusting of two parameters: observer bandwidthAnd controller bandwidthWherein
4. according to the method described in claim 3, it is characterized in that, the S2 is specifically included:
S21: for object (1), if it is known that by the model of u (t) to y (t), it is assumed that the transfer function model of controlled device P (s)
For
Assuming thatState beIts corresponding controllable state space is embodied as Cm(sI-
Am)-1Bm, wherein
Unknown broad sense interference f (t) will be estimated using extended state observer (ESO) below, is defined as follows generalized object:
Wherein
And
Wherein 0 indicate the zero vector being adapted with dimension；
GADRC has following state space realization form:
WhereinFor broad sense reference signal, feedback control gain is defined as
For ESO,Characteristic equation are as follows:
Wherein coefficient l1,l2,l3By a0,a1, b0,b1AndIt determines, it is assumed that all poles of observer are respectively positioned onFeature
Equation (20) write as again forWhereinFor optimum wideband, according to Ackerman theorem, observer gain is sweared
Amount are as follows:
If general disturbance f (t) is adequately compensated for, original controlled device is reduced to 2 rank linear objectsIf state
Accurately estimated, then final feedback control system is
Similarly, if all closed-loop poles are placed inExcept origin, i.e.,
ThereforeFor the parameter for uniquely needing to adjust in STATE FEEDBACK CONTROL.
S22: Laplace transformation is carried out to the state space realization of 2 rank GADRC, is had
WhereinIt isLaplace transformation,It isLaplace transformation, can be obtained by (25)
Wherein
Preferably closed-loop system is
WhenReach " optimal " tracking, takesFor filter, to make control system obtain one of no error following
Adequate condition is
Not needing additional dynamic to set point filter can enable
5. according to the method described in claim 4, it is characterized in that, the S3 is specifically included:
S31: the state-space model (4) of object (1) is as follows:
Wherein, x1=y can measure,Accordingly
Estimated using following RESO controlled device state and unknown general disturbance；
Observer gain L at this timeoAre as follows:
Lo=[β1 β2]T(35)；
S32: the general disturbance of state and estimation based on controlled device achieved above, using following Linear State Feedback control
Rate control processed
Wherein
The following state space realization of S33:RADRC controller:
6. according to the method described in claim 5, it is characterized in that, the S4 is specifically included:
S41: Laplace transformation is carried out to formula (38):
Wherein, the Laplace that Z (s) is z (t) is converted,ForLaplace transformation；
The Laplace that wherein R (s) is reference signal r (t) is converted, and removes intermediate variable:
It is equivalent compound that RADRC is become into two degrees of freedom；
S42: to feedback controller C2(s) (41) carry out analysis and solution:
Wherein numerator coefficients are calculate by the following formula
Denominator coefficients can be calculate by the following formula
C2It (s) is the 2 rank canonical transmission functions with integral.
7. according to the method described in claim 6, it is characterized in that, the S5 is specifically included:
S51:RADRC parameter KoAnd LoBy controller bandwidth omegacWith observer bandwidth omegaoIt determines
Controller gain KoA parameter ζ is increased, for eliminating the oscillation of response；
The feedback transfer function (46) of second order RADRC is equal to
S52: the feedback controller of GADRC is approached with feedback transfer function (46)(28), consider the two having the same zero
Point, to have
Wherein α is an adjustable constant, is obtained by the first two equation of (47)
(48) are brought into the third equation of (47), are obtained
Work as LoBy observer bandwidth omegaoWhen determining, β1,β2It is provided by (45), so that above-mentioned equation becomes
Equation (50) has 4 solutions, guarantees that the solution real solution that is positive takes maximum when there are multiple positive real solutions by choosing sufficiently large α
As observer bandwidth；
S53: observer bandwidth omega has been determinedo, obtained by (47,45)
Above-mentioned steps ensure that the feedback controller of second order RADRC and GADRCWith same zero point, second order RADRC is except original
Outer point also includes three poles, for the feedback controller for guaranteeing RADRC (46) integral gain and original GADRCIntegral gain phase
Together, adjustment parameter b0, enable
To b0It is set as
The gain ensures the integral gain of RADRC (46) and the feedback controller of GADRCIntegral gain is identical.
8. the method according to the description of claim 7 is characterized in that the method is directed to general industry process control objects, root
The parameter ω of second order RADRC is obtained using the method according to the GADRC feedback controller parameter of known objecto, ωc, ζ, bo, warp
It crosses the second order RADRC that above step obtains and obtains anti-interference similar with GADRC and robust performance, controlled using obtained RADRC
Device parameter is controlled, and can carry out necessary on-line tuning when needed to obtain ideal control performance.
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