CN107037726A - It is a kind of non-with first new fractional-order system synovial membrane interference observer design method - Google Patents
It is a kind of non-with first new fractional-order system synovial membrane interference observer design method Download PDFInfo
- Publication number
- CN107037726A CN107037726A CN201610969568.3A CN201610969568A CN107037726A CN 107037726 A CN107037726 A CN 107037726A CN 201610969568 A CN201610969568 A CN 201610969568A CN 107037726 A CN107037726 A CN 107037726A
- Authority
- CN
- China
- Prior art keywords
- order
- fractional
- synovial membrane
- interference observer
- disturbance
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
Classifications
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
- G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
- G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
- G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
- G05B13/045—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance using a perturbation signal
Landscapes
- Engineering & Computer Science (AREA)
- Health & Medical Sciences (AREA)
- Artificial Intelligence (AREA)
- Computer Vision & Pattern Recognition (AREA)
- Evolutionary Computation (AREA)
- Medical Informatics (AREA)
- Software Systems (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Automation & Control Theory (AREA)
- Feedback Control In General (AREA)
Abstract
Non- with first new fractional-order system synovial membrane interference observer design method the invention discloses one kind, its specific steps includes：Excitation system obtains related data, and off-line identification system is non-with first fractional model, then according to the non-with first fractional order order of system, designs the disturbance at synovial membrane interference observer online observation current time.The invention also discloses the product that application correlation method is designed.The invention also discloses application corresponding product to the non-method being controlled with first new fractional-order system.Relative to traditional disturbance rejection method, the inventive method improves the degree of accuracy of disturbance observation using the non-design that synovial membrane interference observer is carried out with first new fractional-order system model；Can be in Finite-time convergence, it is ensured that the real-time of observed result；In the presence of strong jamming is run into, strengthen non-robustness and stability with first new fractional-order system, further it is proposed that method be also applied for first new fractional-order system.
Description
Technical field
The invention belongs to control technology field, and in particular to a kind of non-with first new fractional-order system synovial membrane interference observer design
Method.
Background technology
Fractional calculus provides more perfect mathematical modeling for complicated dynamical system.At present, using fractional order mould
Type can reach purpose more accurate to portraying for fractional order object, succinct.Fractional model is the expansion of conventional integer rank model
Exhibition, is difficult to have good fitting effect with the system of integer model rank accurate description, fractional model for some.With use
The modeling of integer rank is compared, and fractional model has the advantages that lower exponent number, less parameter, higher modeling accuracy.
It is whether identical according to the fractional order order of new fractional-order system in actual research process, system can be divided into non-
With first (order is differed) with member (order is identical) new fractional-order system.At present for many driver's physical systems, system
Fractional order characteristic all have it is non-with member characteristic, such as electronic manufacture equipment in flexible swing arm system Power Flow and machinery
The fractional order order of energy storage link is inconsistent, therefore the fractional order characteristic of the system has the non-feature with member.On the other hand, outside
The multifarious disturbances such as portion's disturbance, the perturbation of system model parameter, frictional force and ripple thrust can have a strong impact on the control of system
Performance processed.The motion requirement of high speed and super precision requires that controlled system should possess very strong robustness to tackle multifarious disturbance.
In practice in disturbance rejection strategy, the method existed can be summarized as following two：The passive strategy that suppresses is with actively pressing down
Method processed.The strategy passively suppressed ensures the performance of dynamic tracking of system, such as iteration by using advanced control algolithm
Study control, fuzzy control and Self Adaptive Control etc..This kind of method is adjusted according to system tracking error using relatively slow feedback
Perfect square formula eliminates influence of the disturbance to systematic function.Therefore these methods can cause the dynamic response performance of difference, in strong disturbance
In the case of, it is more likely to result in controlled system unstable.Active inhibition method is then that observer accurately estimates disturbance first
Then size directly eliminates the influence of disturbance by feedforward compensation.This method has the performance of preferable disturbance rejection, in control
Field is widely used.
The method for the active suppression disturbance being widely used at present is only applicable to the system with same first fractional order characteristic, therefore
It is not particularly suited for the non-system with first fractional order characteristic.On the other hand, for the system with fractional order characteristic, mesh
Preceding Disturbance Rejection method is it cannot be guaranteed that the finite time convergence of disturbance observation error.
Such as paper " Second-order sliding mode approaches to disturbance estimation
and fault detection in fractional-order systems”(Pisano A,M,Usai E,et
al.IFAC Proceedings Volumes,2011,44(1):2436-2441.), disclose a kind of for new fractional-order system
Sliding formwork disturbance-observer design method.But there is following defect or deficiency in design method disclosed in the document：
(1) it is only applicable to first new fractional-order system；
(2) the Infinite Time convergence of disturbance observation error is only ensure that, finite time convergence control can not be further ensured that
Property.
The content of the invention
For the disadvantages described above or Improvement requirement of prior art, the present invention provides a kind of non-same first new fractional-order system synovial membrane and done
Design of Observer method is disturbed, the purpose is to by the non-with first fractional order state-space model of identification system, using non-with member point
Number rank order design sliding mode observer, the size of the actual disturbance of accurate measuring systems, then by feedforward path, by the survey of observation
Value is added in the input control quantity of system, directly eliminates influence of the disturbance to systematic function, realizes to new fractional-order system
Control.
To achieve these goals, it is non-with first new fractional-order system synovial membrane there is provided one kind according to one aspect of the present invention
Interference observer design method, this method comprises the following steps：
S1：Selection pumping signal is non-with first new fractional-order system to encourage, input signal and output signal required for collection；
S2：Using optimized algorithm to described non-with first new fractional-order system progress Stute space model identification, the state sky
Between model be：
Wherein,(t) } be system state variable, A1,A2, K is the parameter of system；D (t)=Δ Ax
(t)+de(t) the actual comprehensive disturbance of system is represented, u (t) is the input signal of system；Y (t) is the output signal of system, Δ A
It is the Uncertainty of system model parameter, de(t) unknown disturbance that the system represented is present, h (x (t)) is system model
Present in non-linear factor, ξ and υ are the fractional order orders of system model, and D is fractional order differential operator；
S3：State-space model according to step S2, designs synovial membrane interference observer, comprises the following steps：
S11：Calculating speed tracking error e (t)：
E (t)=y (t)-r (t)
Wherein, r (t) is given reference velocity；
S12：According to the non-with first fractional order order ξ and υ of system, tracking error e (t) the progress fractional order to system is micro-
Point：
Wherein, C is real number set in advance；
S13：Integer rank differential is carried out to the tracking error e (t)：
S14：According to non-with first fractional order order ξ and υ, virtual synovial membrane inspection surface is chosen：
Wherein, z1For the intermediate variable of selection, σ is the virtual synovial membrane face of design,Observed for the sliding mode observer of design
Actual disturbance；
S15：Differential is carried out to the virtual synovial membrane inspection surface σ：
Wherein,- d (t) is the observation error of system disturbance；
S16：The single order synovial membrane differential equation is chosen to estimateValue：
Wherein, ρσ1,ρσ2For the state variable of the synovial membrane differential equation,For pre-defined arithmetic number, sign is symbol
Number function；
It can be represented by the formula
In formula, λ is the error that the differential equation is estimated；
S17：Define correlated variablesThe following synovial membrane interference observer of design, can obtain observation system
Actually the variable quantity of disturbance is：
Wherein, TsIt it is the sampling time, P (σ ') is the function on σ '.
Further, the fractional order differential operator definitions are：
Wherein, α is fractional order order, and n is the minimum positive integer bigger than α fractional order orders, and I is fractional order integration operator；
Further, the fractional order integration operator is：
Wherein, α is fractional order order, and t is the time of integration, and what x (t) was represented is to be integrated function, and what Γ was represented is gamma
Function.
Further, the optimized algorithm is particle cluster algorithm：
Wherein, k ' represents current iteration number of times；I=1,2,3 ... be the numbering of particle；A represents systematic parameter to be identified,What is represented is the position for being currently located at solution space；What is represented is current translational speed, c1,c2It is acceleration constant；
rand1,rand2For 0 to 1 random number, pbestijAnd gbestijLocally optimal solution and globally optimal solution are represented respectively.
Further, the non-input instruction with first new fractional-order system is：
Further, the variable quantity of the actual disturbance of the observation system meets following perturbation nonlinear differential equation and determined
Reason：
Wherein,X is the state of system, μ1And μ2It is the parameter of the differential equation,
μ2>=1.1M, TsIt it is the sampling time, ξ (t) is unknown system disturbance, and M represents the coboundary of shock wave amount.
Further, the synovial membrane interference observer meets following relation：
Wherein：μ′1=CKA1μ1,μ′2=CKA1μ2,
According to it is described perturbation nonlinear differential equation theorem, it is known that the synovial membrane interference observer variable σ ' of design andCan be
Finite time convergence control is zero, is obtained：
So that sliding formwork interference observer can be in finite time by the non-disturbance essence with first new fractional-order system
Really pick out and.
Further, the pumping signal is the white Gaussian noise of amplitude distribution Gaussian distributed.
According to another aspect of the present invention, there is provided non-with first new fractional-order system synovial membrane disturbance-observer described in a kind of application
The product of device design method design.
According to another aspect of the present invention, there is provided a kind of the non-with first new fractional-order system controlling party of the product described in application
Method, it is characterised in that：The disturbance that the synovial membrane interference observer is observed, which is added to, controls speed end, is controlled by fractional order PI
Device realizes that, to the non-control with first new fractional-order system, its transmission function is represented by：
In formula, KpIt is the proportionality coefficient of PI controllers, KiIt is the integral coefficient of PI controllers, λ is fractional order order, and s is multiple
Variable.
In general, by the contemplated above technical scheme of the present invention compared with prior art, it can obtain down and show
Beneficial effect：
(1) method of the invention describes new fractional-order system with first fractional order state-space model by non-first, can be with
Effect more more accurate than integer model is obtained, controlled device can be preferably represented, therefore based on non-with first fractional order order
The synovial membrane interference observer of design can obtain higher observation effect.
(2) method of method active suppression of the invention disturbance, this method considered system model parameter drift, outer
The comprehensive disturbance such as portion's disturbance, disturbance that can be to system in finite time is observed, with very high real-time, and
The stability of system is can guarantee that when running into strong disturbance.
(3) synovial membrane interference observer proposed by the invention is applicable not only to non-same first new fractional-order system, and is applied to
With member new fractional-order system.
Brief description of the drawings
Fig. 1 for the embodiment of the present invention it is a kind of it is non-with first new fractional-order system synovial membrane interference observer design method be related to it is soft
Property swing arm system control process figure；
Fig. 2 for the embodiment of the present invention it is a kind of it is non-with first new fractional-order system synovial membrane interference observer design method be related to it is soft
Property swing arm system structure diagram；
Fig. 3 for the embodiment of the present invention it is a kind of it is non-with first new fractional-order system synovial membrane interference observer design method be related to it is soft
Property swing arm system control block figure；
Fig. 4 for the embodiment of the present invention it is a kind of it is non-with first new fractional-order system synovial membrane interference observer design method be related to it is soft
Property swing arm system synovial membrane interference observer design procedure schematic diagram；
Fig. 5 for the embodiment of the present invention it is a kind of it is non-with first new fractional-order system synovial membrane interference observer design method be related to it is soft
Property swing arm system synovial membrane interference observer observation effect schematic diagram.
Embodiment
In order to make the purpose , technical scheme and advantage of the present invention be clearer, it is right below in conjunction with drawings and Examples
The present invention is further elaborated.It should be appreciated that specific embodiment described herein is only to explain the present invention, not
For limiting the present invention.As long as in addition, technical characteristic involved in each embodiment of invention described below that
Not constituting conflict between this can just be mutually combined.
For the flexible swing arm system of the critical component in electronic manufacture equipment, the inductive circuit of system is due to discharge and recharge
Unintentional nonlinearity, these characteristics can preferably be described using fractional model；The Mass Distribution of other flexible load is not
, the features such as nonlinear elasticity deformation and suffered frictional force strictly can not be directly proportional to speed, it will cause system to be produced
Raw fractional order dynamic characteristic.
Fig. 2 for the embodiment of the present invention it is a kind of it is non-with first new fractional-order system synovial membrane interference observer design method be related to it is soft
Property swing arm system structure diagram.Flexible swing arm system in die grading device mainly realizes the pickup and sorting to chip, its
Primary structure schematic diagram is as shown in Figure 2.Flexible swing arm system mainly includes permagnetic synchronous motor 1 and flexible structure two parts group
Into wherein flexible structure contains shaft coupling 2, transmission device 3 and swing arm structure 4 etc..
With the development of electronic manufacture equipment technology, its operating efficiency requires more and more higher, and frequency is more and more faster, and swing arm is got over
Come more long, while positioning accuracy request also more and more higher.And in the motion control of swing arm, the angular displacement of swing arm motor passes through pendulum
The amplification of arm mechanism, is converted to swing arm tip displacement, and therefore, motion frequency is higher, and swing arm is longer so that end positioning precision is got over
It is difficult.The swing arm system of electronic manufacture equipment is generally divided into simple pendulum arm, double pendulum arm configuration, and passes through transmission link more with servomotor
Drive swing arm motion；The transmission link of this structure is more, inertia is big, flexible strong, and therefore, control difficulty is big.
When being controlled to flexible swing arm system, its structure can be considered answering for permagnetic synchronous motor and time-varying
The combination of miscellaneous load.It just can so be attributed to the control of flexible swing arm system the control to a complicated servo drive system to ask
Topic.The present invention is directed being controlled to the speed ring of flexible swing arm system, the purpose of control is not flexible swing arm system
Stable speed output is provided, smooth track is produced in environment complicated and changeable, is optimal the control performance of system.
Fig. 3 for the embodiment of the present invention it is a kind of it is non-with first new fractional-order system synovial membrane interference observer design method be related to it is soft
Property swing arm system control block figure；Fig. 4 is a kind of non-with first new fractional-order system synovial membrane interference observer design of the embodiment of the present invention
The flexible swing arm system synovial membrane interference observer design procedure schematic diagram that method is related to.As shown in Figure 3 and Figure 4, the present invention is proposed
The non-design method with the flexible swing arm system synovial membrane interference observer of first fractional order mainly include the contents of three parts：Flexibility pendulum
Non- same first fractional order Stute space model identification of arm system；The design of fractional order synovial membrane interference observer in observation system to deposit
Actual disturbance；The disturbance of observation is incorporated into the instruction of the input current of system, shadow of the disturbance to systematic function is eliminated
Ring.Its major design step is summarized as follows：
The first step：White Gaussian noise incentive object simultaneously gathers signal
Firstly the need of the motor speed feedback y (t) and input current value signal u (t) in collection servo-drive system speed ring.For
This needs to select the pumping signal of suitable form to encourage speed ring controlled device, so as to obtain required signal, set up from
Line database.Selected pumping signal should be able to fully encourage servo-drive system, each frequency band of covering servo-drive system work.This implementation
The white Gaussian noise of prioritizing selection amplitude distribution Gaussian distributed in example, its mean power is close to be uniformly distributed, and is had
It is without memory.The discrete form of white noise signal is referred to as white noise sequence, the input of system is disturbed only it is small, amplitude, the cycle, when
Clock beat is easily controlled, and can meet optimal input signal requirement.AC servo drive system is encouraged using white Gaussian noise, is obtained
The sampled value of flexible swing arm system rotating speed and electric current.
For various disturbances present in flexible swing arm system, choose the disturbance with following expression and be added to flexible swing arm
System is non-with first fractional order state-space model：
Wherein：ω1=1, ω2=0.2.
The present embodiment completes the identification of system fractional model parameter, particle using particle cluster algorithm using particle cluster algorithm
Iterative operation each time be intended to be updated the state of particulate by location updating formula and speed more new formula, for this
For embodiment, A represents to treat the state-space model parameter that optimizing is solved, and formula is as follows：
Wherein, k ' represents current iteration number of times；I=1,2,3 ... be the numbering of particle；A represents systematic parameter to be identified,What is represented is the position for being currently located at solution space；What is represented is current translational speed, c1,c2It is acceleration constant；
rand1,rand2For 0 to 1 random number, pbestijAnd gbestijLocally optimal solution and globally optimal solution are represented respectively.
The non-with first fractional order state-space model expression formula correlation model parameters of the system of obtaining can be recognized：
It can obtain A1=1, A2=-0.2xξ(t)-0.5xυ(t), h (x (t))=0, υ=0.2928, ξ=0.9752, K=
143.7275。
Second step：Design the synovial membrane interference observer based on fractional order, the design of virtual sliding-mode surface, by tracking error
Signal carries out fractional calculus computing so that synovial membrane interference observer can observe the reality of actual disturbance in finite time
When numerical value, its specific design step be divided into it is following some：
S11：Calculating speed tracking error e (t)：
E (t)=y (t)-r (t) (6)
Wherein, r (t) is given reference velocity；
S2：Fractional order differential is carried out to the tracking error signal of system：
Wherein：C is set as that 1, D is fractional order differential operator, and order is the ＜ 1 of 0 ＜ ξ+υ -1；
The fractional order differential operator definitions are：
Wherein, n is the minimum positive integer bigger than α fractional order orders, and I is fractional order integration operator；
The fractional order integration operator is：
Wherein, α is fractional order order, and t is the time of integration, and what x (t) was represented is to be integrated function, and what Γ was represented is gamma
Function.
S3：Integer rank differential is carried out to above-mentioned error signal：
S4：Choose virtual synovial membrane inspection surface：
Wherein, z1For the intermediate variable of selection, σ is the virtual synovial membrane face of design,Observed for the sliding mode observer of design
Actual disturbance；
Differential is carried out to the virtual synovial membrane inspection surface σ：
Wherein,For the observation error of system disturbance.
S5：The following single order synovial membrane differential equation is chosen to estimate unknown variable
Wherein：ρσ1,ρσ2For the state of synovial membrane equation,To be set as 20 and 10.
Therefore it can be represented by the formula
In formula：λ is the error that the differential equation is estimated.
S6：Define correlated variablesThe synovial membrane interference observer of response is designed, the reality of observation system is can obtain
Border disturbance variable quantity be：
3rd step：Flexible swing arm system is controlled using PI controllers the most frequently used in engineering, its transmission function can
It is expressed as：
In formula, KpIt is the proportionality coefficient of PI controllers, KiIt is the integral coefficient of PI controllers, λ is fractional order order.
In view of the feedforward compensation of disturbance, the current-order that finally enters that can obtain system is：
Proved for the finite time convergence control of system, use following perturbation nonlinear differential equation：
Wherein：X is the state of system；μ1And μ2It is the parameter of the differential equation, TsIt is sampling
Time, ξ (t) is unknown system disturbance.
For above-mentioned equation, if can meetμ2>=1.1M, then the derivative of system state variablesWill
In finite time convergence control to zero.
Therefore for synovial membrane interference observer, second dervative is definedIt can be derived by：
The associated expression for the disturbance observed according to sliding formwork interference unit, it is known that：
In formula：μ′1=CKA1μ1,μ′2=CKA1μ2,
It can further be derived by：
According to perturbation nonlinear differential equation theorem, it is known that the synovial membrane interference observer variable σ ' of design andWill have
Zero is converged between in limited time, therefore is derived by：
Therefore the present invention based on the non-sliding formwork interference observer with first fractional order order design can in finite time incite somebody to action
The disturbance of system, which is accurately picked out, to be come.
Fig. 5 for the embodiment of the present invention it is a kind of it is non-with first new fractional-order system synovial membrane interference observer design method be related to it is soft
Property swing arm system synovial membrane interference observer observation effect schematic diagram.As shown in Figure 5, it can be seen that design synovial membrane interference observer energy
Obtain good effect.
The control rate at system current time is finally given by above-mentioned steps, that is to say that input current is instructed, realize to soft
The speed control of property swing arm system.
The controller parameter adjusted by the present invention results in good position tracking performance and mapping.Not inclined
Appropriate deformation can be made on the premise of from essence spirit of the present invention and without departing from scope involved by substantive content of the present invention to it to be subject to
Implement.
Relative to traditional disturbance rejection method, the inventive method is done using the non-of system with first fractional order order progress synovial membrane
Disturb the design of observer, improve the degree of accuracy of disturbance observation, can be in Finite-time convergence, it is ensured that observed result it is real-time
Property, and it is suitable for member new fractional-order system.Thus disturbing in the non-flexible swing arm system with first fractional order is solved
Dynamic suppression problem.
The present invention carries out setting for synovial membrane interference observer using the non-same member of flexible swing arm system fractional model order
Meter, can be carried out in real time to the disturbance such as external disturbance, sensor noise and parameter drift that includes in flexible swing arm system
Observation and compensation, suppression system disturb the influence to systematic function.
As it will be easily appreciated by one skilled in the art that the foregoing is merely illustrative of the preferred embodiments of the present invention, it is not used to
The limitation present invention, any modifications, equivalent substitutions and improvements made within the spirit and principles of the invention etc., it all should include
Within protection scope of the present invention.
Claims (10)
1. it is a kind of non-with first new fractional-order system synovial membrane interference observer design method, it is characterised in that：This method includes following step
Suddenly：
S1：Selection pumping signal is non-with first new fractional-order system to encourage, input signal and output signal required for collection；
S2：Using optimized algorithm to described non-with first new fractional-order system progress Stute space model identification, the state space mould
Type is：
Wherein,It is the state variable of system, A1,A2, K is the parameter of system；D (t)=Δ Ax (t)+de
(t) the actual comprehensive disturbance of system is represented, u (t) is the input signal of system；Y (t) is the output signal of system, and Δ A is system
The Uncertainty of model parameter, de(t) represent system exist unknown disturbance, h (x (t)) be system model in exist
Non-linear factor, ξ and υ are the fractional order orders of system model, and D is fractional order differential operator；
S3：State-space model according to step S2, designs synovial membrane interference observer, comprises the following steps：
S11：Calculating speed tracking error e (t)：
E (t)=y (t)-r (t)
Wherein, r (t) is given reference velocity；
S12：According to the non-with first fractional order order ξ and υ of system, fractional order differential is carried out to the tracking error e (t) of system：
Wherein, C is real number set in advance；
S13：Integer rank differential is carried out to the tracking error e (t)：
S14：According to non-with first fractional order order ξ and υ, virtual synovial membrane inspection surface is chosen：
Wherein, z1For the intermediate variable of selection, σ is the virtual synovial membrane face of design,The reality observed for the sliding mode observer of design
Border is disturbed；
S15：Differential is carried out to the virtual synovial membrane inspection surface σ：
Wherein,For the observation error of system disturbance；
S16：The single order synovial membrane differential equation is chosen to estimateValue：
Wherein, ρσ1,ρσ2For the state variable of the synovial membrane differential equation,For pre-defined arithmetic number, sign is symbol letter
Number；
It can be represented by the formula
In formula, λ is the error that the differential equation is estimated；
S17：Define correlated variablesThe following synovial membrane interference observer of design, can obtain the reality of observation system
The variable quantity of disturbance is：
Wherein, TsIt it is the sampling time, P (σ ') is the function on σ '.
2. one kind according to claim 1 is non-with first new fractional-order system synovial membrane interference observer design method, its feature exists
In：The fractional order differential operator definitions are：
Wherein, α is fractional order order, and n is the minimum positive integer bigger than α fractional order orders, and I is fractional order integration operator.
3. one kind according to claim 1 or 2 is non-with first new fractional-order system synovial membrane interference observer design method, its feature
It is：The fractional order integration operator is：
Wherein, α is fractional order order, and t is the time of integration, and what x (t) was represented is to be integrated function, and what Γ was represented is gamma function.
4. it is a kind of non-with first new fractional-order system synovial membrane interference observer design side according to any one of claim 1-3
Method, it is characterised in that：The optimized algorithm is particle cluster algorithm：
Wherein, k ' represents current iteration number of times；I=1,2,3 ... be the numbering of particle；A represents systematic parameter to be identified,Table
What is shown is the position for being currently located at solution space；What is represented is current translational speed, c1,c2It is acceleration constant；rand1,
rand2For 0 to 1 random number, pbestijAnd gbestijLocally optimal solution and globally optimal solution are represented respectively.
5. it is a kind of non-with first new fractional-order system synovial membrane interference observer design side according to any one of claim 1-4
Method, it is characterised in that：The non-input instruction with first new fractional-order system is：
6. it is a kind of non-with first new fractional-order system synovial membrane interference observer design side according to any one of claim 1-5
Method, it is characterised in that：The variable quantity of the actual disturbance of the observation system meets following perturbation nonlinear differential equation theorem：
Wherein,X is the state of system, μ1And μ2It is the parameter of the differential equation,
TsIt it is the sampling time, ξ (t) is unknown system disturbance, and M represents the coboundary of shock wave amount.
7. it is a kind of non-with first new fractional-order system synovial membrane interference observer design side according to any one of claim 1-6
Method, it is characterised in that：The synovial membrane interference observer meets following relation：
Wherein：μ′1=CKA1μ1,μ′2=CKA1μ2,
According to it is described perturbation nonlinear differential equation theorem, it is known that the synovial membrane interference observer variable σ ' of design andCan be limited
Time Convergence is zero, is obtained：
So that sliding formwork interference observer can accurately be distinguished the non-disturbance with first new fractional-order system in finite time
Knowledge comes out.
8. one kind according to claim 1 is non-with first new fractional-order system synovial membrane interference observer design method, its feature exists
In：The pumping signal is the white Gaussian noise of amplitude distribution Gaussian distributed.
9. a kind of non-same first new fractional-order system synovial membrane interference observer design applied according to any one of claim 1-8
The product of method design.
10. a kind of non-same first new fractional-order system control method of the product described in application claim 9, it is characterised in that：By institute
The disturbance for stating the observation of synovial membrane interference observer is added to control speed end, is realized by fractional order PI controllers to described non-with member
The control of new fractional-order system, its transmission function is represented by：
In formula, KpIt is the proportionality coefficient of PI controllers, KiIt is the integral coefficient of PI controllers, λ is fractional order order, and s is multiple change
Amount.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201610969568.3A CN107037726B (en) | 2016-10-31 | 2016-10-31 | It is a kind of non-with first new fractional-order system synovial membrane interference observer design method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201610969568.3A CN107037726B (en) | 2016-10-31 | 2016-10-31 | It is a kind of non-with first new fractional-order system synovial membrane interference observer design method |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN107037726A true CN107037726A (en) | 2017-08-11 |
| CN107037726B CN107037726B (en) | 2019-08-13 |
Family
ID=59530543
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201610969568.3A Active CN107037726B (en) | 2016-10-31 | 2016-10-31 | It is a kind of non-with first new fractional-order system synovial membrane interference observer design method |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN107037726B (en) |
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111030534A (en) * | 2019-12-20 | 2020-04-17 | 东南大学 | Parameter identification method for permanent magnet synchronous motor in steady-state operation mode |
| CN111506996A (en) * | 2020-04-15 | 2020-08-07 | 郑州轻工业大学 | Self-adaptive identification method of turntable servo system based on identification error limitation |
| CN112631132A (en) * | 2020-12-22 | 2021-04-09 | 山东建筑大学 | Adaptive fault-tolerant control method based on fractional order disturbance observer |
| CN113791542A (en) * | 2021-09-17 | 2021-12-14 | 广州市香港科大***研究院 | Servo motor rotating speed control method, system and device based on two-dimensional system |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102591207A (en) * | 2012-03-01 | 2012-07-18 | 北京航空航天大学 | Sliding form control method of flexible joint mechanical arm based on disturbance observer |
| CN103406909A (en) * | 2013-07-24 | 2013-11-27 | 黑龙江科技大学 | Tracking control device and method of mechanical arm system |
| CN104260107A (en) * | 2014-09-04 | 2015-01-07 | 北京邮电大学 | Method for achieving tooth space compensation for flexible joint of space manipulator |
-
2016
- 2016-10-31 CN CN201610969568.3A patent/CN107037726B/en active Active
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102591207A (en) * | 2012-03-01 | 2012-07-18 | 北京航空航天大学 | Sliding form control method of flexible joint mechanical arm based on disturbance observer |
| CN103406909A (en) * | 2013-07-24 | 2013-11-27 | 黑龙江科技大学 | Tracking control device and method of mechanical arm system |
| CN104260107A (en) * | 2014-09-04 | 2015-01-07 | 北京邮电大学 | Method for achieving tooth space compensation for flexible joint of space manipulator |
Non-Patent Citations (2)
| Title |
|---|
| SHIQI ZHENG 等: "Virtual Reference Feedback Tuning of a Fractional Order PI Controller", 《2015 2ND INTERNATIONAL CONFERENCE ON INTELLIGENT MATERIALS AND MECHATRONICS》 * |
| 王欢 等: "带有干扰观测器的分数阶滑模控制", 《电光与控制》 * |
Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111030534A (en) * | 2019-12-20 | 2020-04-17 | 东南大学 | Parameter identification method for permanent magnet synchronous motor in steady-state operation mode |
| CN111030534B (en) * | 2019-12-20 | 2021-07-13 | 东南大学 | Parameter identification method for permanent magnet synchronous motor in steady-state operation mode |
| CN111506996A (en) * | 2020-04-15 | 2020-08-07 | 郑州轻工业大学 | Self-adaptive identification method of turntable servo system based on identification error limitation |
| CN111506996B (en) * | 2020-04-15 | 2024-05-03 | 郑州轻工业大学 | Identification error limitation-based turntable servo system self-adaptive identification method |
| CN112631132A (en) * | 2020-12-22 | 2021-04-09 | 山东建筑大学 | Adaptive fault-tolerant control method based on fractional order disturbance observer |
| CN113791542A (en) * | 2021-09-17 | 2021-12-14 | 广州市香港科大***研究院 | Servo motor rotating speed control method, system and device based on two-dimensional system |
Also Published As
| Publication number | Publication date |
|---|---|
| CN107037726B (en) | 2019-08-13 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Madoński et al. | Survey on methods of increasing the efficiency of extended state disturbance observers | |
| CN106325073B (en) | Position Closed Loop for Servo System IP controller model-free automatic correcting method based on fractional order | |
| Sira-Ramírez et al. | Algebraic identification and estimation methods in feedback control systems | |
| CN107037726A (en) | It is a kind of non-with first new fractional-order system synovial membrane interference observer design method | |
| JP2763832B2 (en) | Control device and method for plant including unknown dynamics | |
| CN108958032B (en) | Total amount cooperative and consistent control method of nonlinear multi-agent system | |
| Li et al. | Fuzzy adaptive dynamic surface control for a single-link flexible-joint robot | |
| Chang et al. | Robust tracking control for a class of electrically driven flexible-joint robots without velocity measurements | |
| CN108908338A (en) | Robot end's jitter suppression method and its system based on ZVD reshaper | |
| CN111965976B (en) | Robot joint sliding mode control method and system based on neural network observer | |
| Huang et al. | A FAT-based adaptive controller for robot manipulators without regressor matrix: theory and experiments | |
| CN105929865A (en) | Linear servo system mechanical resonance control method | |
| CN115946120A (en) | Mechanical arm control method, device, equipment and medium | |
| CN107659241B (en) | Servo motor control unit and method, computer-readable storage medium | |
| Xue-Jun et al. | Mathematical theories and applications for nonlinear control systems | |
| CN114274148B (en) | Track planning method and device, electronic equipment and storage medium | |
| CN113486523B (en) | Global identification method for linear variable parameter vibration system | |
| CN114147710B (en) | Robot control method and device, robot and storage medium | |
| Silva et al. | Performance analysis of path planning techniques based on potential fields | |
| Tang et al. | Adaptive chattering-free terminal sliding mode control for a coordinate measuring machine system | |
| Cao et al. | Optimization of X-axis servo drive performance using PSO fuzzy control technique for double-axis dicing saw | |
| Song et al. | Flexible joint parameters identification method based on improved tracking differentiator and adaptive differential evolution | |
| Iqbal et al. | Predictive time domain passivity control for delayed teleoperation using energy derivatives | |
| Lee | Constraints identification in time-varying obstacle avoidance for mechanical manipulators | |
| Li et al. | Parameter identification based on PSO algorithm for piezoelectric actuating system with rate-dependent Prandtl-Ishlinskii hysteresis modeling method |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |