CN109001974B - Position synchronization control method for networked large-association motion system based on generalized extended state observer - Google Patents
Position synchronization control method for networked large-association motion system based on generalized extended state observer Download PDFInfo
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Abstract
A position synchronization control method for a networked large-association motion system based on a generalized extended state observer is disclosed. Firstly, the uncertain dynamics of a system and the coupling part of each subsystem caused by time-varying delay are processed into the total disturbance of the system, a generalized extended state observer is designed, the total disturbance of the system is observed while the state of the system is observed, and then a large-correlation motion system position servo decoupling controller based on disturbance compensation is designed. And then, establishing a position synchronous coupling error model of the networked large-association motion system, designing a synchronous controller, and realizing position synchronous control of the networked large-association motion system. The invention can process the influence of mutual coupling and time delay among subsystems, ensures that the system has good anti-interference performance and robust performance, and realizes good position synchronous control performance while realizing good position servo decoupling control performance of the system.
Description
Technical Field
The invention is applied to the field of networked motion control, and relates to a position synchronization control method suitable for a networked large-association motion system.
Background
In modern intelligent manufacturing industry, the application of large-scale linkage motion systems is increasingly widespread, and complex equipment functions such as industrial robots, shaftless printing machines, textile machines, wire drawing machines and the like can be realized through the linkage between various subsystems. Such systems are comprised of many similar and adjacent sub-processes, which are affected only by their neighbors. Therefore, the adoption of an effective decoupling control method is a key factor for improving the control performance and the production quality of the system and reducing the production cost. Meanwhile, with the rapid development of network technology, the big-correlation motion system is developing towards networking and high-speed. The network is introduced into the large-association motion system, data communication is carried out between the controller and each subsystem through the Ethernet, the data transmission rate and reliability between the controller and each subsystem are greatly improved, the accurate synchronization function of the large-association motion system is realized, the system wiring is greatly reduced, and the system expansion capability is improved. The universal Ethernet has incomparable advantages in the aspects of bandwidth, cost, openness and the like compared with a field bus, and a large-association motion system developed based on the open universal Ethernet can well improve the flexibility, the rapidity and the control precision of equipment. Therefore, the control of large-association motion systems based on general ethernet has gradually become one of the core technologies of modern smart manufacturing.
However, although there are some commercial industrial ethernet technologies such as EtherCAT, SERCOS-III, POWERLINK, deterministic data transmission is mostly achieved by modifying the data link layer protocol. Therefore, these commercial ethernet networks can be considered as a high-speed field bus, and require a special chip to implement a protocol stack and special development software for system development, which is costly, difficult to authorize, and incompatible with standard ethernet networks. If a theory and a method for solving the influence of the uncertainty of the Ethernet information transmission on the performance of the motion control system can be provided from a control layer, the theory and the method have great theoretical significance and practical application value. Meanwhile, the realization of the position synchronous control of the large-correlation motion system is a core technology in the large-correlation coordinated motion control, and relates to the position servo decoupling control and the position synchronous control of each subsystem of the large-correlation motion system. The main objective of the position servo decoupling control is to improve the position tracking accuracy and anti-interference performance of each subsystem, and many advanced control methods, such as PID control with feedforward, sliding mode control, adaptive control, fuzzy control, etc., have been proposed. Although the transmission rate of the real-time ethernet has been improved to a great extent, the influence of sampling jitter brought by network-induced delay on the position tracking accuracy is still not negligible, and the existing position servo decoupling control method and position synchronization control method rarely consider these influences. In the field of networked control systems, a plurality of network-induced delay compensation methods such as predictive control and self-adaptive Smith predictor exist, but most algorithms are complex and are not suitable for industrial application. Particularly, a writer designs a networked multi-axis motion position synchronous control scheme based on an active disturbance rejection controller aiming at the problem of networked multi-axis motion synchronous control, so that a good time delay compensation effect is obtained, but aiming at a networked large-correlation motion system, mutual decoupling control among subsystems is realized, the influence of time delay is processed, certain limitation is caused, and further improvement is needed. At present, no good solution is provided for the problem of position synchronization control of a networked large-association motion system.
Disclosure of Invention
In order to overcome the defects of poor anti-interference performance, poor robust performance and poor decoupling control performance of a position synchronization control method in the conventional networked large-correlation motion system, the invention provides the position synchronization control method of the networked large-correlation motion system based on the generalized extended state observer, which has good anti-interference performance, good robust performance and good decoupling control performance.
In order to solve the technical problems, the invention adopts the following technical scheme:
a networked large-association motion system position synchronization control method based on a generalized extended state observer comprises the following steps:
step 1) under the condition that the network induced delay is less than a sampling period, establishing a large-correlation motion system model containing time-varying network induced delay, and dynamically processing system uncertainty caused by the time-varying delay into a part of system sum disturbance, so as to describe the networked large-correlation motion system as a discrete-time linear time invariant system, wherein the method comprises the following processes:
1.1) establishing a state space model of a large-correlation motion system:
according to the dynamic characteristics of the large-correlation motion system, the state space model of the system is
Wherein
Is the state vector for the ith subsystem,
is a domain parameter of the ith subsystem, and
for the j-th axis servo control input, i.e. the speed set point,
for an unknown and bounded amount of interference for the ith subsystem,
for the ith subsystem output value, i.e. position, Ai，Bij，CiAnd HiIs a system matrix;
1.2) establishing a large-correlation motion system model under the influence of time-varying network induced time delay:
the data packet has network-induced delay in the network transmission process, and the method is used
Represents a control input uj(t) to j-th axis, the system sensor node is driven by time, the controller node and the actuator node are driven by events, and the network delay is
Are all less than one sampling period T, and define network delay
The nominal part and the uncertainty part of (1) are respectively
And
then
The expression is as follows:
any sampling period (k, k +1)]In this case, the control input applied to the actuator is composed of two parts, one of which is the control input u calculated from the previous control cyclej(k-1) and the other part is a control input u calculated by the current control periodj(k) The form is expressed as follows:
therefore, according to equations (1) and (3), the model of the large-correlation motion control system discretized by the sampling period T and simplified correspondingly is:
wherein
d (k) is the system bounded sum perturbation expressed as
Wherein
Definition of x (k) ═ x1 T(k)...xi T(k)...]T,u(k)＝[u1 T(k)...uj T(k)...]TAnd d (k) ═ blockdiag { d1(k),...,di(k) ,.., the model of the system (1) can be expressed as follows
χ(k+1)＝Φ1χ(k)+Γu1u(k)+Γd1d(k) (6)
Wherein
Step 2) designing a tracking controller based on the generalized extended state observer;
and 3) establishing a position synchronous coupling error model of the networked large-association motion system, designing a synchronous controller, and realizing position synchronous control of the networked large-association motion system.
Further, the step 2) is to design a tracking controller process based on the generalized extended state observer as follows:
2.1) design generalized extended State observer
Defining a system expansion state xi (k) ═ χT(k),dT(k)]TAnd let h (k) d (k +1) -d (k), the augmentation system model is as follows
Wherein
Cp＝blockdiag{Cp1,...,Cpi,...}，Π(p×2n)＝[Cp 0p×n]；
The generalized extended state observer is designed as follows:
where L is the observer observation matrix and,
and
observed values for augmented systems ξ (k) and y (k), respectively;
the design of the large-correlation motion system stabilizing controller has the following two conditions:
a) when χ (k) is measurable, the system feedback controller is designed as follows:
b) when χ (k) is not measurable, the system feedback controller is designed as follows:
wherein, K ═ Kx Kd]Controller gain matrix, KxAnd KdRespectively, a controller feedback gain matrix and a disturbance compensation gain matrix.
Further, in the step 3), a position synchronization coupling error model of the networked great-correlation motion system is established, a synchronization controller is designed, and a process of realizing position synchronization control of the networked great-correlation motion system is as follows:
3.1) defining the i-th subsystem tracking position error as ei1(k)＝r0-xi1(k)，r0The position synchronization error model of the networked large-correlation motion system is
ε(k)＝Γe(k) (11)
Wherein ε (k) ═ ε1(k),…,εi(k),…,εn(k)]T，e(k)＝[e11(k),…,ei1(k),…,en1(k)]TRespectively a position synchronization error vector and a position error of a networked large-correlation motion systemDifference vector εi(k)、ei1(k) Respectively representing the ith subsystem position synchronization error and the ith subsystem position error, wherein gamma represents a synchronization transformation matrix;
the selected synchronous transformation matrix Γ is as follows:
i.e. the synchronization error is expressed as follows:
3.2) establishing a position synchronous coupling error model of the networked large-correlation motion system as
E(k)＝e(k)+αε(k) (14)
Wherein E (k) ═ E1(k),…,Ei(k),…,En(k)]And alpha is a diagonal and positive control gain matrix, and is obtained by substituting equation (11) into equation (14)
E(k)＝(I+αΓ)e(k) (15)
Wherein I represents a unit matrix, and when (I + α Γ) is invertible, e (k) → 0 can be derived from e (k) → 0, and further, ∈ (k) → 0 can be derived from e (k) → 0;
3.2) designing a synchronous controller based on the generalized extended state observer, eliminating the influence of time-varying delay on the system performance, and designing a synchronous control law as follows:
wherein, Kp、KdAnd KeFor synchronous control of the gain matrix ui(k) And controlling the input quantity for the synchronization error feedback of the ith subsystem of the networked large-correlation motion system.
In the invention, firstly, uncertain dynamics of a system and coupling parts of each subsystem caused by time-varying delay are processed into total disturbance of the system, a generalized extended state observer is further designed, the total disturbance of the system is observed while the state of the system is observed, and then a large-correlation motion system position servo decoupling controller based on disturbance compensation is designed. And secondly, establishing a synchronous error model, designing a position synchronous controller based on the generalized extended state observer, and realizing good position synchronous control performance while realizing that the system has good position servo tracking decoupling control performance.
Compared with the prior art, the invention has the beneficial effects that: the uncertain dynamics of the system and the coupling part of each subsystem caused by time-varying delay are processed into the total disturbance of the system, a generalized extended state observer is further designed, the total disturbance of the system is observed while the state of the system is observed, and then a position servo decoupling controller based on disturbance compensation is designed, so that good position servo decoupling control of a networked large-correlation motion system is achieved. And secondly, establishing a synchronous error model, designing a position synchronous controller of the generalized extended state observer, and realizing good position synchronous control performance. The scheme can effectively realize the position servo tracking decoupling control of a large-correlation motion system and the influence of processing time-varying delay on the system, and simultaneously realize the position synchronous control, so that the system has good robustness and has a prospect of being popularized to industrial application.
Drawings
Fig. 1 is a diagram of a position synchronization control structure of a networked large-correlation motion system based on a generalized extended state observer.
Fig. 2 is a diagram of a large-linkage motion system.
Fig. 3 is a diagram of the effect of the position synchronization control verified by the experiment.
Fig. 4 is an effect diagram of position decoupling control and observed values verified by experiments.
Fig. 5 is a diagram of the effect of position error experimentally verified.
FIG. 6 is a graph of experimentally verified position-coupled synchronization errors.
Fig. 7 is experimentally verified observed values of interference for each axis.
Detailed Description
In order to make the technical scheme and the design idea of the present invention clearer, the following detailed description is made with reference to the accompanying drawings.
Referring to fig. 1 to 7, a networked large-association motion system position synchronization control method based on a generalized extended state observer includes the following steps:
step 1) under the condition that the network induced delay is less than a sampling period, establishing a large-correlation motion system model containing time-varying network induced delay, and dynamically processing system uncertainty caused by the time-varying delay into a part of system sum disturbance, so as to describe the networked large-correlation motion system as a discrete-time linear time invariant system, wherein the method comprises the following processes:
1.1) establishing a state space model of a large-correlation motion system, as shown in FIG. 2:
according to the dynamic characteristics of the large-correlation motion system, the state space model of the system is
Wherein
Is the state vector for the ith subsystem,
is a domain parameter of the ith subsystem, and
for the j-th axis servo control input, i.e. the speed set point,
for an unknown and bounded amount of interference for the ith subsystem,
for the ith subsystem output value, i.e. position, Ai，Bij，CiAnd HiIs a system matrix;
1.2) establishing a large-correlation motion system model under the influence of time-varying network induced time delay:
the data packet has network-induced delay in the network transmission process, and the method is used
Represents a control input uj(t) to j-th axis, the system sensor node is driven by time, the controller node and the actuator node are driven by events, and the network delay is
Are all less than one sampling period T, and define network delay
The nominal part and the uncertainty part of (1) are respectively
And
then
The expression is as follows:
any sampling period (k, k +1)]In this case, the control input applied to the actuator is composed of two parts, one of which is the control input u calculated from the previous control cyclej(k-1) and the other part is a control input u calculated by the current control periodj(k) The form is expressed as follows:
therefore, according to equations (1) and (3), the model of the large-correlation motion control system discretized by the sampling period T and simplified correspondingly is:
wherein
d (k) is the system bounded sum perturbation expressed as
Wherein
Definition of x (k) ═ x1 T(k)...xi T(k)...]T,u(k)＝[u1 T(k)...uj T(k)...]TAnd d (k) ═ blockdiag { d1(k),...,di(k) ,.., the model of the system (1) can be expressed as follows
χ(k+1)＝Φ1χ(k)+Γu1u(k)+Γd1d(k) (6)
Wherein
Step 2) designing a tracking controller based on the generalized extended state observer;
and 3) establishing a position synchronous coupling error model of the networked large-association motion system, designing a synchronous controller, and realizing position synchronous control of the networked large-association motion system.
Further, the step 2) is to design a tracking controller process based on the generalized extended state observer as follows:
2.1) design generalized extended State observer
Defining a system expansion state xi (k) ═ χT(k),dT(k)]TAnd let h (k) d (k +1) -d (k), the augmentation system model is as follows
Wherein
Cp＝blockdiag{Cp1,...,Cpi,...}，Π(p×2n)＝[Cp 0p×n]；
The generalized extended state observer is designed as follows:
where L is the observer observation matrix and,
and
observed values for augmented systems ξ (k) and y (k), respectively;
the design of the large-correlation motion system stabilizing controller has the following two conditions:
c) when χ (k) is measurable, the system feedback controller is designed as follows:
d) when χ (k) is not measurable, the system feedback controller is designed as follows:
wherein, K ═ Kx Kd]Controller gain matrix, KxAnd KdRespectively, a controller feedback gain matrix and a disturbance compensation gain matrix.
Further, in step 3), as shown in fig. 1, a position synchronization coupling error model of the networked large-correlation motion system is established, and a synchronization controller is designed, so that the process of implementing position synchronization control of the networked large-correlation motion system is as follows:
3.1) defining the i-th subsystem tracking position error as ei1(k)＝r0-xi1(k)，r0The position synchronization error model of the networked large-correlation motion system is
ε(k)＝Γe(k) (11)
Wherein ε (k) ═ ε1(k),…,εi(k),…,εn(k)]T，e(k)＝[e11(k),…,ei1(k),…,en1(k)]TRespectively a position synchronization error vector and a position error vector of the networked large-correlation motion systemi(k)、ei1(k) Respectively representing the ith subsystem position synchronization error and the ith subsystem position error, wherein gamma represents a synchronization transformation matrix;
the selected synchronous transformation matrix Γ is as follows:
i.e. the synchronization error is expressed as follows:
3.2) establishing a position synchronous coupling error model of the networked large-correlation motion system as
E(k)＝e(k)+αε(k) (14)
Wherein E (k) ═ E1(k),…,Ei(k),…,En(k)]And alpha is a diagonal and positive control gain matrix, and is obtained by substituting equation (11) into equation (14)
E(k)＝(I+αΓ)e(k) (15)
Wherein I represents a unit matrix, and when (I + α Γ) is invertible, e (k) → 0 can be derived from e (k) → 0, and further, ∈ (k) → 0 can be derived from e (k) → 0;
3.2) designing a synchronous controller based on the generalized extended state observer, eliminating the influence of time-varying delay on the system performance, and designing a synchronous control law as follows:
wherein, Kp、KdAnd KeFor synchronous control of the gain matrix ui(k) And controlling the input quantity for the synchronization error feedback of the ith subsystem of the networked large-correlation motion system.
In order to verify the effectiveness and superiority of the method, the invention carries out experimental verification on a four-axis networked large-association motion system experimental platform, fig. 3 and 4 respectively show the position synchronization control effect and the position decoupling control and observation value effect of experimental research, fig. 5 shows the position error effect, and fig. 6 and 7 respectively show the coupling synchronization error and the interference observation value of each axis. As shown in fig. 3 to 6, by applying the position synchronization control method of the networked large-correlation motion control system based on the generalized extended state observer according to the present invention, even if there are time-varying network-induced delay and inter-coupling between subsystems, the large-correlation motion control system still has good synchronization performance, which indicates that the coupling part between the subsystem and the uncertain dynamics generated by the network-induced delay can be effectively compensated, and the performance of the large-correlation motion control system is not affected. The designed method can well observe the state and disturbance of the system, thereby realizing the position servo tracking decoupling control of the large-correlation motion system, simultaneously processing the influence of time-varying delay on the system, and finally realizing the good position synchronization control performance of the system.
The foregoing description of the invention has been presented to illustrate the invention and to best explain the advantages of the invention, it should be understood that this invention is not limited to the foregoing examples, but is capable of numerous modifications without departing from the basic inventive concepts and the scope of the invention as defined by the appended claims. The scheme designed by the invention can effectively solve the problem of position synchronization control of a networked large-association motion system, and realizes good position synchronization control performance while realizing good position servo tracking decoupling control performance of the system.
Claims (1)
1. A position synchronization control method of a networked large-association motion system based on a generalized extended state observer is characterized by comprising the following steps: the method comprises the following steps:
step 1) under the condition that the network induced delay is less than a sampling period, establishing a large-correlation motion system model containing time-varying network induced delay, and dynamically processing system uncertainty caused by the time-varying delay into a part of system sum disturbance, so as to describe the networked large-correlation motion system as a discrete-time linear time invariant system, wherein the method comprises the following processes:
1.1) establishing a state space model of a large-correlation motion system:
according to the dynamic characteristics of the large-correlation motion system, the state space model of the system is
Wherein
Is the state vector for the ith subsystem,
is a domain parameter of the ith subsystem, and
for controlling the output of the j-th axis servo systemAnd then, the speed set value is input,
for an unknown and bounded amount of interference for the ith subsystem,
for the ith subsystem output value, i.e. position, Ai，Bij，CiAnd HiIs a system matrix;
1.2) establishing a large-correlation motion system model under the influence of time-varying network induced time delay:
the data packet has network-induced delay in the network transmission process, and the method is used
Represents a control input uj(t) to j-th axis, the system sensor node is driven by time, the controller node and the actuator node are driven by events, and the network delay is
Are all less than one sampling period T, and define network delay
The nominal part and the uncertainty part of (1) are respectively
And
then
The expression is as follows:
any sampling period (k, k +1)]In this case, the control input applied to the actuator is composed of two parts, one of which is the control input u calculated from the previous control cyclej(k-1) and the other part is a control input u calculated by the current control periodj(k) The form is expressed as follows:
therefore, according to equations (1) and (3), the model of the large-correlation motion control system discretized by the sampling period T and simplified correspondingly is:
wherein
d (k) is the system bounded sum perturbation expressed as
Wherein
Definition of x (k) ═ x1 T(k) ... xi T(k) ...]T,u(k)＝[u1 T(k) ... uj T(k) ...]TAnd d (k) ═ blockdiag { d1(k),...,di(k) ,.., the model of the system (1) can be expressed as follows
χ(k+1)＝Φ1χ(k)+Γu1u(k)+Γd1d(k) (6)
Wherein
Step 2) designing a tracking controller based on the generalized extended state observer;
step 3), establishing a position synchronous coupling error model of the networked large-association motion system, designing a synchronous controller, and realizing position synchronous control of the networked large-association motion system:
in the step 2), designing a tracking controller based on the generalized extended state observer as follows:
2.1) design generalized extended State observer
Defining a system expansion state xi (k) ═ χT(k),dT(k)]TAnd let h (k) d (k +1) -d (k), the augmentation system model is as follows
Wherein
Cp＝blockdiag{Cp1,...,Cpi,...}，Π(p×2n)＝[Cp 0p×n]；
The generalized extended state observer is designed as follows:
where L is the observer observation matrix and,
and
observed values for augmented systems ξ (k) and y (k), respectively;
the design of the large-correlation motion system stabilizing controller has the following two conditions:
a) when χ (k) is measurable, the system feedback controller is designed as follows:
b) when χ (k) is not measurable, the system feedback controller is designed as follows:
wherein, K ═ Kx Kd]Controller gain matrix, KxAnd KdRespectively a controller feedback gain matrix and a disturbance compensation gain matrix;
in the step 3), a position synchronous coupling error model of the networked large-association motion system is established, a synchronous controller is designed, and the position synchronous control of the networked large-association motion system is realized by the following process:
3.1) defining the i-th subsystem tracking position error as ei1(k)＝r0-xi1(k)，r0The position synchronization error model of the networked large-correlation motion system is
ε(k)＝Γe(k) (11)
Wherein ε (k) ═ ε1(k),…,εi(k),…,εn(k)]T，e(k)＝[e11(k),…,ei1(k),…,en1(k)]TRespectively a position synchronization error vector and a position error vector of the networked large-correlation motion systemi(k)、ei1(k) Respectively representing the ith subsystem position synchronization error and the ith subsystem position error, wherein gamma represents a synchronization transformation matrix;
the selected synchronous transformation matrix Γ is as follows:
i.e. the synchronization error is expressed as follows:
3.2) establishing a position synchronous coupling error model of the networked large-correlation motion system as
E(k)＝e(k)+αε(k) (14)
Wherein E (k) ═ E1(k),…,Ei(k),…,En(k)]And alpha is a diagonal and positive control gain matrix, and is obtained by substituting equation (11) into equation (14)
E(k)＝(I+αΓ)e(k) (15)
Wherein I represents a unit matrix, and when (I + α Γ) is invertible, e (k) → 0 can be derived from e (k) → 0, and further, ∈ (k) → 0 can be derived from e (k) → 0;
3.2) designing a synchronous controller based on the generalized extended state observer, eliminating the influence of time-varying delay on the system performance, and designing a synchronous control law as follows:
wherein, Kp、KdAnd KeFor synchronous control of the gain matrix ui(k) And controlling the input quantity for the synchronization error feedback of the ith subsystem of the networked large-correlation motion system.
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