CN108732933A - The time-varying continuous controller design of periodic segment vibration cooperative system based on LMI - Google Patents
The time-varying continuous controller design of periodic segment vibration cooperative system based on LMI Download PDFInfo
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Abstract
A kind of time-varying continuous controller design of periodic segment vibration cooperative system based on LMI provided by the invention, including：Establish periodic segment vibration system model；According to the parameter in periodic segment vibration system model, each moment controller parameter K (t) is calculated by the tool boxes LMI, so that controller acts power and is applied in periodic segment vibrational system according to controller parameter K (t) and system state variables x (t) computing controllers output u (t)=K (t) * x (t).The present invention also provides corresponding devices.In the present invention, the controller parameter K (t) at each moment is solved by the tool boxes LMI, controller is allow to calculate each moment controller parameter K (t) according to the parameter in periodic segment vibration system model in real time, when the Parameters variation in model, controller parameter can be also modified in real time, so that system is more stablized, be better able to adapt to environmental change, the vibration amplitude of reduction system has better flexibility.In addition, the present invention also provides corresponding devices.
Description
Technical field
The present invention relates to presetting apparatus technical fields, more particularly to the periodic segment based on LMI vibrates cooperative system
Time-varying continuous controller design.
Background technology
Periodic vibration system is widely present in nature, such as rotary wings system, Sunspot Activities etc..In engineering
For this kind of system, existing technology is that some damping elements are added in systems mostly, carrys out the vibration of relieving system.In this way
Although vibrational system cost it is relatively low, be the absence of flexibility, effectiveness in vibration suppression is dumb, can not adapt to changeable environment.
Therefore, existing shock mitigation system lacks flexibility, and effectiveness in vibration suppression is dumb, and it is ability that can not adapt to changeable environment
Field technique personnel's technical issues that need to address.
Invention content
For the deficiency of existing damping technology, the present invention provides a kind of, and the periodic segment based on LMI vibrates cooperative system
Time-varying continuous controller design.This method is directed to periodic segment vibrational system, by means of the tool boxes LMI in Matlab softwares,
Change controller parameter in real time, so that system is reached stable, reduce the vibration amplitude of system, promote the performance of vibrational system.This item
Invention is not limited to specific system environments, and more previous technology is compared, and has prodigious flexibility.
A kind of time-varying continuous controller design of periodic segment vibration cooperative system based on LMI provided by the invention, packet
It includes：
Establish periodic segment vibration system model；
According to the parameter in periodic segment vibration system model, each moment controller is calculated by the tool boxes LMI and is joined
Number K (t) so that controller is according to controller parameter K (t) and system state variables x (t) computing controllers output u (t)=K
(t) * x (t) act power and are applied in periodic segment vibrational system.
Preferably, the periodic segment vibration system model of establishing includes：
The state-space expression for establishing system is：
Z (t)=Cx (t)+Du (t)+Dww(t)；
The state variable of system is taken to be
C=[1 0], D=0, Dw=0；
System is divided into S subsystem according to periodic segment principle, the period of S subsystem is respectively T1,T2,...,TS,
The system period is T=T1+T2+...+TS, set t0=0, t1=T1, t2=T1+T2..., ts=T1+T2+...+TS=T and full
Foot：
Therefore the expression formula of periodic segment vibration system model is：
Z (t)=Cix(t)+Diu(t)+Dwiw(t)；
t∈(nT+ti-1,nT+ti), n=0,1,2 ..., i=1,2 ..., S；
Wherein, m is the quality of periodic segment vibrational system, and q is displacement, and w (t) is system disturbance, and k and c are vibrational system
In spring constant and damped coefficient, u (t) in order to control device export, Ai、Bi、Ci、Di、Bwi、DwiFor the system ginseng of i-th of subsystem
Number.
It should be noted that in model expression,Ci=
[1 0], Di=0, Dwi=0, wherein i indicate i-th of subsystem.
Preferably, the parameter in the vibration system model according to periodic segment, when calculating each by the tool boxes LMI
Controller parameter K (t) is carved to specifically include：
According in periodic segment vibration system model parameter and the tool boxes LMI parameter establish linear matrix inequality：
QS+1=Q1；
US+1=U1；
Wherein, λiIt is the previously given parameter in the tool boxes LMI with γ, I is unit matrix, UiAnd QiIt is by the tool boxes LMI
The matrix calculated, sym (A)=A+AT, * expressions are symmetrically；
Solution obtains K (t)=U (t) Q-1(t), wherein
Preferably, the periodic segment vibration system model uses Exponential Stability, that is, acts power and be applied to the period
Further include (after in controller action to periodic segment vibrational system) after in segmentation vibrational system：
Whether detecting system with the speed more than or equal to a preset exponential function convergency factor reaches stable, if it is not,
Then decision-making system does not meet the case where Exponential Stability.
Preferably, the periodic segment vibration system model uses H∞Performance indicator acts power and is applied to week
Further include (after in controller action to periodic segment vibrational system) after in phase segmentation vibrational system：
Whether the energy of detecting system output is less than or equal to the product that disturbance energy is multiplied by a default constant coefficient, if it is not,
Then decision-making system is unsatisfactory for H∞Performance indicator.
A kind of time-varying continuous control device of periodic segment vibration cooperative system based on LMI provided by the invention, including：
Model building module, for establishing periodic segment vibration system model；
Controller parameter computing module, for according to the parameter in periodic segment vibration system model, passing through the tool boxes LMI
Calculate each moment controller parameter K (t) so that controller is counted according to controller parameter K (t) and system state variables x (t)
Controller output u (t)=K (t) * x (t) are calculated, power is acted and is applied in periodic segment vibrational system.
Preferably, the model building module is specifically used for：
The state-space expression for establishing system is：
Z (t)=Cx (t)+Du (t)+Dww(t)；
The state variable of system is taken to be
C=[1 0], D=0, Dw=0；
System is divided into S subsystem according to periodic segment principle, the period of S subsystem is respectively T1,T2,...,TS,
The system period is T=T1+T2+...+TS, set t0=0, t1=T1, t2=T1+T2..., ts=T1+T2+...+TS=T and full
Foot：
Therefore the expression formula of periodic segment vibration system model is：
Z (t)=Cix(t)+Diu(t)+Dwiw(t)；
t∈(nT+ti-1,nT+ti), n=0,1,2 ..., i=1,2 ..., S；
Wherein, m is the quality of periodic segment vibrational system, and q is displacement, and w (t) is system disturbance, and k and c are vibrational system
In spring constant and damped coefficient, u (t) in order to control device export, Ai、Bi、Ci、Di、Bwi、DwiFor the system ginseng of i-th of subsystem
Number.
Preferably, the controller parameter computing module includes：
Linear matrix inequality establishes unit, for according to the parameter and LMI tools in periodic segment vibration system model
Case parameter establishes linear matrix inequality：
QS+1=Q1；
US+1=U1；
Wherein, λiIt is the previously given parameter in the tool boxes LMI with γ, I is unit matrix, UiAnd QiIt is by the tool boxes LMI
The matrix calculated, sym (A)=A+AT, * expressions are symmetrically；
Controller parameter solves unit, and K (t)=U (t) Q are obtained for solving-1(t), wherein
The present invention provides a kind of time-varying continuous controller of the periodic segment vibration cooperative system based on LMI, including：
Memory, for storing instruction；
Processor, is coupled to the memory, and the processor is configured as holding based on the instruction that the memory stores
Row realizes the time-varying continuous controller design such as a kind of above-mentioned periodic segment vibration cooperative system based on LMI.
The present invention provides a kind of computer readable storage medium, and computer is stored on the computer readable storage medium
Program is realized when the computer program is executed by processor such as a kind of above-mentioned periodic segment vibration collaboration system based on LMI
The time-varying continuous controller of system designs.
As can be seen from the above technical solutions, the embodiment of the present invention has the following advantages：
A kind of time-varying continuous controller design of periodic segment vibration cooperative system based on LMI provided by the invention, packet
It includes：Establish periodic segment vibration system model；According to the parameter in periodic segment vibration system model, pass through the tool boxes LMI meter
Calculate each moment controller parameter K (t) so that controller is calculated according to controller parameter K (t) and system state variables x (t)
Controller exports u (t)=K (t) * x (t), acts power and is applied in periodic segment vibrational system.The present invention also provides
Corresponding device.In the present invention, the controller parameter K (t) at each moment is solved by the tool boxes LMI so that controller can be with
Each moment controller parameter K (t) is calculated according to the parameter in periodic segment vibration system model in real time, when the ginseng in model
When number variation, controller parameter can be also modified in real time, so that system is more stablized, be better able to adapt to environment change
Change, reduce the vibration amplitude of system, there is better flexibility.
Description of the drawings
In order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, to embodiment or will show below
There is attached drawing needed in technology description to be briefly described, it should be apparent that, the accompanying drawings in the following description is only this
Some embodiments of invention without having to pay creative labor, may be used also for those of ordinary skill in the art
To obtain other attached drawings according to these attached drawings.
Fig. 1 is that the time-varying continuous controller that a kind of periodic segment based on LMI provided by the invention vibrates cooperative system is set
The flow chart of one embodiment of meter；
Fig. 2 is that the time-varying continuous controller that a kind of periodic segment based on LMI provided by the invention vibrates cooperative system is set
The flow chart of another embodiment of meter；
Fig. 3 is the simplification figure of periodic segment vibrational system in the embodiment of the present invention；
Fig. 4 is the concept map that periodic segment vibrational system is indicated with state-space expression in the embodiment of the present invention；
Fig. 5 is periodic segment vibrational system vibration amplitude situation map in the embodiment of the present invention；
Fig. 6 is the figure of changing of controller gain K (t) in the embodiment of the present invention；
Fig. 7 is that the output u (t) of controller in the embodiment of the present invention changes with time situation.
Specific implementation mode
For the deficiency of existing damping technology, the present invention provides a kind of, and the periodic segment based on LMI vibrates cooperative system
Time-varying continuous controller design.This method is directed to periodic segment vibrational system, by means of the tool boxes LMI in Matlab softwares,
Change controller parameter in real time, so that system is reached stable, reduce the vibration amplitude of system, promote the performance of vibrational system.This item
Invention is not limited to specific system environments, and more previous technology is compared, and has prodigious flexibility.
In order to make the invention's purpose, features and advantages of the invention more obvious and easy to understand, below in conjunction with the present invention
Attached drawing in embodiment, technical scheme in the embodiment of the invention is clearly and completely described, it is clear that disclosed below
Embodiment be only a part of the embodiment of the present invention, and not all embodiment.Based on the embodiments of the present invention, this field
All other embodiment that those of ordinary skill is obtained without making creative work, belongs to protection of the present invention
Range.
The time-varying continuous controller of periodic segment vibration cooperative system provided by the invention based on LMI designs corresponding system
System can be applied as the single multiagent system of multi-agent system in self-organizing cooperative system.
Referring to Fig. 1, a kind of time-varying continuous control of periodic segment vibration cooperative system based on LMI provided by the invention
One embodiment of device design, including：
101, periodic segment vibration system model is established；
102, according to the parameter in periodic segment vibration system model, each moment control is calculated by the tool boxes LMI
Device parameter K (t) so that controller according to controller parameter K (t) and system state variables x (t) computing controllers output u (t)=
K (t) * x (t) act power and are applied in periodic segment vibrational system.
In the present invention, the controller parameter K (t) at each moment is solved by the tool boxes LMI so that controller can be real-time
Each moment controller parameter K (t) is calculated according to the parameter in periodic segment vibration system model, when the parameter in model becomes
When change, controller parameter can be also modified in real time, so that system is more stablized, be better able to adapt to environmental change, be subtracted
The vibration amplitude of few system, has better flexibility.
It is to a kind of time-varying continuous controller of the periodic segment vibration cooperative system based on LMI provided by the invention above
One embodiment of design is described in detail, below will be to a kind of periodic segment vibration based on LMI provided by the invention
Another embodiment of the time-varying continuous controller design of cooperative system is described in detail.
Referring to Fig. 2, a kind of time-varying continuous control of periodic segment vibration cooperative system based on LMI provided by the invention
Another embodiment of device design, including：
201, periodic segment vibration system model is established, is included the following steps：
Referring initially to Fig. 3, Fig. 3 is the simplification figure of periodic segment vibrational system, w be system disturbance (generally noise or
Person's shift perturbation), m is the quality of system, and q is the displacement of m, and k and c are spring constant and damped coefficient in vibrational system.U is
Controller.
Referring to Fig. 3, periodic segment vibrational system simplification figure according to Fig.3, the output z of system is the position of mass block
Q is moved, can be with the state-space expression of write through system, the state-space expression for establishing system：
Z (t)=Cx (t)+Du (t)+Dww(t)；
The state variable of system is taken to be
C=[1 0], D=0, Dw=0；
Periodic segment vibrational system, essence are a kind of vibrational systems with periodic structure or cycle parameter component.
A kind of approximation of periodic vibration system, this kind of system have within each period when periodic segment vibrational system can be regarded as
The parameter of several subsystems, each subsystem can be average value of the parameter within the period, can also be to have week
The parameter of phase segmented characterizing true subsystem.This kind of system is a large amount of existing, such as microorganism predation system in real world
System, DC-to-dc converter, the shaking platform etc. of flow production line.As long as this kind of system or can approximation regard this as
The system of class system can use controller proposed in this paper.It especially says, general periodic vibration system can be regarded as
It is the periodic segment vibrational system of only one subsystem.As specified above and without loss of generality, enable m, k, c that all there is the period
The characteristic of segmentation.Periodic segment vibration cooperative system in topic of the present invention shows that this kind of system can be applied and is cooperateed in self-organizing
In system, an independent intelligent body subsystem, thus referred to as cooperative system are served as.
Therefore system can be divided into S subsystem according to periodic segment principle, the period of S subsystem is respectively T1,
T2,...,TS, the system period is T=T1+T2+...+TS, set t0=0, t1=T1, t2=T1+T2..., ts=T1+T2+...+TS
=T and satisfaction：
Referring to Fig. 4, Fig. 4 is the concept map that periodic segment vibrational system is indicated with state-space expression.It can be seen that
In a cycle TPIt is interior, there are S subsystem, each subsystem to have the systematic parameter A of oneselfi, Bi, Ci, Di。
Therefore the expression formula of periodic segment vibration system model is：
Z (t)=Cix(t)+Diu(t)+Dwiw(t)；
t∈(nT+ti-1,nT+ti), n=0,1,2 ..., i=1,2 ..., S；
Wherein, m is the quality of periodic segment vibrational system, and q is displacement, and w (t) is system disturbance, and k and c are vibrational system
In spring constant and damped coefficient, u (t) in order to control device export, Ai、Bi、Ci、Di、Bwi、DwiFor the system ginseng of i-th of subsystem
Number.
It should be noted that in model expression,Ci=
[10], Di=0, Dwi=0, wherein i indicate i-th of subsystem.
202, according to the parameter in periodic segment vibration system model, each moment control is calculated by the tool boxes LMI
Device parameter K (t) is specifically included：
For periodic segment vibrational system, the output of controller is u (t)=K (t) * x (t), according to periodic segment vibration system
Parameter and the tool boxes LMI parameter in system model establish linear matrix inequality：
QS+1=Q1；
US+1=U1；
Wherein, λiIt is the previously given parameter in the tool boxes LMI with γ, I is unit matrix, UiAnd QiIt is by the tool boxes LMI
The matrix calculated, sym (A)=A+AT, * expressions are symmetrically；
The system has H∞When performance indicator, solution obtains K (t)=U (t) Q-1(t), wherein
It should be noted thatWith
All it is linear convex function, is the Certain function summary artificially chosen.
203, controller is according to controller parameter K (t) and system state variables x (t) computing controllers output u (t)=K
(t) * x (t) act power and are applied in periodic segment vibrational system.
The present invention is u (t)=K using most common STATE FEEDBACK CONTROL inside control system, controller output
(t) * x (t), wherein device parameter, x (t) are state variable to K (t) in order to control, it is chosen in this class system, such as the present embodiment
In, it isIt is a bivector for including system displacement and acceleration.So the present invention is real-time change K (t),
And then change controller output.Controller can be understood as the generator of a meeting power, the size for the power that only it is generated
It is to need to calculate by the tool boxes LMI in MATLAB.
It should be noted that the controller that the present invention designs, its controller parameter K (t) is also to have cyclophysis,
But system state variables x (t) can be smaller and smaller, so the power of controller output is not the period.The parameter of system once it is determined that,
The K (t) of whole cycle can be directly calculated with the tool boxes LMI, if some time etching system parameter changes, the tool boxes LMI are just
One group of new K (t) can be calculated, changes parameter here it is real-time.
204, whether detecting system with the speed more than or equal to a preset exponential function convergency factor reaches stable, if
It is no, then the case where decision-making system does not meet Exponential Stability.
Using Exponential Stability in the periodic segment vibration system model of the present invention.Exponential Stability is gradually than general significance
There is faster stabilized speed into stablizing, it requires system to reach steady with the speed more than or equal to some exponential function convergency factor
It is fixed.This stability requirement, it is not only smooth but also quick, there is stronger engineering significance.
205, whether the energy of detecting system output is less than or equal to the product that disturbance energy is multiplied by a default constant coefficient, if
No, then decision-making system is unsatisfactory for H∞Performance indicator.
About performance indicator, herein using H∞Performance indicator.This performance intelligently requires the energy of system output small
In the range of being multiplied by a constant coefficient equal to disturbance energy.Generally, it in engineering, is disturbed to what system performance was affected
Dynamic is energy bounded, is based on this, selects H∞Performance indicator can preferably reflect reality.
It should be noted that step 204 and step 205 are the detection being added after controller to its control effect.Judgement
System refers to periodic segment vibrational system.
Fig. 5, Fig. 6 and Fig. 7 are please referred to, according to the present embodiment, for specific periodic segment vibrational system (T=15, T1=
T2=T3=5), in the case of the disturbance input of zero original state finite time (2 periods) white noise, system output amplitude
Situation of change.The disturbance input of finite time white noise can ensure that disturbance is energy bounded.Do not have as can be seen from Figure 5
Before adding controller, the vibration of system is more violent, and after having added controller, the vibration amplitude of system substantially reduces.It is important to
Illustrate, in second period (15-30), although there is also white noise acoustic disturbance, the vibration of system has been almost 0.
Fig. 6 is the situation of change of controller gain K (t) in above-mentioned simulation process.As can be seen that K (t) is to connect in the period
Continuous, it is also continuous in system state variables x (t), according to u (t)=K (t) * x (t), it is known that, the output of controller
Active force is continuous.
Fig. 7 is in above-mentioned simulation process, and the output u (t) of controller changes with time situation.
The abscissa of Fig. 5, Fig. 6 and Fig. 7 are all time t, and ordinate is all corresponding value.
It below will be to a kind of time-varying continuous control dress of the periodic segment vibration cooperative system based on LMI provided by the invention
The one embodiment set is described in detail.
The device can be applied as the single multiagent system of multi-agent system in self-organizing cooperative system.
One of the time-varying continuous control device of a kind of periodic segment vibration cooperative system based on LMI provided by the invention
Embodiment, including：
Model building module, for establishing periodic segment vibration system model；
Controller parameter computing module, for according to the parameter in periodic segment vibration system model, passing through the tool boxes LMI
Calculate each moment controller parameter K (t) so that controller is counted according to controller parameter K (t) and system state variables x (t)
Controller output u (t)=K (t) * x (t) are calculated, power is acted and is applied in periodic segment vibrational system.
Further, model building module is specifically used for：
The state-space expression for establishing system is：
Z (t)=Cx (t)+Du (t)+Dww(t)；
The state variable of system is taken to be
C=[1 0], D=0, Dw=0；
System is divided into S subsystem according to periodic segment principle, the period of S subsystem is respectively T1,T2,...,TS,
The system period is T=T1+T2+...+TS, set t0=0, t1=T1, t2=T1+T2..., ts=T1+T2+...+TS=T and full
Foot：
Therefore the expression formula of periodic segment vibration system model is：
Z (t)=Cix(t)+Diu(t)+Dwiw(t)；
t∈(nT+ti-1,nT+ti), n=0,1,2 ..., i=1,2 ..., S；
Wherein, m is the quality of periodic segment vibrational system, and q is displacement, and w (t) is system disturbance, and k and c are vibrational system
In spring constant and damped coefficient, u (t) in order to control device export, Ai、Bi、Ci、Di、Bwi、DwiFor the system ginseng of i-th of subsystem
Number.
Further, controller parameter computing module includes：
Linear matrix inequality establishes unit, for according to the parameter and LMI tools in periodic segment vibration system model
Case parameter establishes linear matrix inequality：
QS+1=Q1；
US+1=U1；
Wherein, λiIt is the previously given parameter in the tool boxes LMI with γ, I is unit matrix, UiAnd QiIt is by the tool boxes LMI
The matrix calculated, sym (A)=A+AT, * expressions are symmetrically；
Controller parameter solves unit, and K (t)=U (t) Q are obtained for solving-1(t), wherein
One of a kind of time-varying continuous controller of the periodic segment vibrational system based on LMI will be provided to the present invention below
Embodiment is described in detail.
The present invention provides a kind of implementation of the time-varying continuous controller of the periodic segment vibration cooperative system based on LMI
Example, including：
Memory, for storing instruction；
Processor, is coupled to memory, and the instruction execution that processor is configured as storing based on memory is realized as above-mentioned
It is a kind of based on LMI periodic segment vibration cooperative system time-varying continuous controller design.
A kind of computer readable storage medium will be provided the present invention below to be described in detail.
The present invention provides a kind of computer readable storage medium, and computer journey is stored on computer readable storage medium
Sequence, realized when computer program is executed by processor as a kind of above-mentioned periodic segment vibration cooperative system based on LMI when
Become continuous controller design.
The above, the above embodiments are merely illustrative of the technical solutions of the present invention, rather than its limitations；Although with reference to before
Stating embodiment, invention is explained in detail, it will be understood by those of ordinary skill in the art that：It still can be to preceding
The technical solution recorded in each embodiment is stated to modify or equivalent replacement of some of the technical features；And these
Modification or replacement, the spirit and scope for various embodiments of the present invention technical solution that it does not separate the essence of the corresponding technical solution.
Claims (10)
1. a kind of time-varying continuous controller design of the periodic segment vibration cooperative system based on LMI, which is characterized in that including：
Establish periodic segment vibration system model；
According to the parameter in periodic segment vibration system model, each moment controller parameter K is calculated by the tool boxes LMI
(t) so that controller is according to controller parameter K (t) and system state variables x (t) computing controllers output u (t)=K (t) * x
(t), it acts power and is applied in periodic segment vibrational system.
2. a kind of time-varying continuous controller of periodic segment vibration cooperative system based on LMI according to claim 1 is set
Meter, which is characterized in that the periodic segment vibration system model of establishing includes：
The state-space expression for establishing system is：
Z (t)=Cx (t)+Du (t)+Dww(t)；
The state variable of system is taken to be
System is divided into S subsystem according to periodic segment principle, the period of S subsystem is respectively T1,T2,...,TS, system
Period is T=T1+T2+...+TS, set t0=0, t1=T1, t2=T1+T2..., ts=T1+T2+...+TS=T and satisfaction：
Therefore the expression formula of periodic segment vibration system model is：
Z (t)=Cix(t)+Diu(t)+Dwiw(t)；
t∈(nT+ti-1,nT+ti), n=0,1,2 ..., i=1,2 ..., S；
Wherein, m is the quality of periodic segment vibrational system, and q is displacement, and w (t) is system disturbance, and k and c are in vibrational system
Spring constant and damped coefficient, device exports u (t) in order to control, Ai、Bi、Ci、Di、Bwi、DwiFor the systematic parameter of i-th of subsystem.
It should be noted that in model expression,Ci=[1
0], Di=0, Dwi=0, wherein i indicate i-th of subsystem.
3. a kind of time-varying continuous controller of periodic segment vibration cooperative system based on LMI according to claim 2 is set
Meter, which is characterized in that the parameter in the vibration system model according to periodic segment, when calculating each by the tool boxes LMI
Controller parameter K (t) is carved to specifically include：
According in periodic segment vibration system model parameter and the tool boxes LMI parameter establish linear matrix inequality：
QS+1=Q1；
US+1=U1；
Wherein, λiIt is the previously given parameter in the tool boxes LMI with γ, I is unit matrix, UiAnd QiIt is to be calculated by the tool boxes LMI
Matrix out, sym (A)=A+AT, * expressions are symmetrically；
Solution obtains K (t)=U (t) Q-1(t), wherein
4. a kind of time-varying continuous controller of periodic segment vibration cooperative system based on LMI according to claim 2 is set
Meter, which is characterized in that the periodic segment vibration system model uses Exponential Stability, that is, acts power and be applied to the period point
Further include after in section vibrational system：
Whether detecting system with the speed more than or equal to a preset exponential function convergency factor reaches stable, if it is not, then sentencing
Determine the case where system does not meet Exponential Stability.
5. a kind of time-varying continuous controller of periodic segment vibration cooperative system based on LMI according to claim 2 is set
Meter, which is characterized in that the periodic segment vibration system model uses H∞Performance indicator acts power and is applied to the period
Further include after in segmentation vibrational system：
Whether the energy of detecting system output less than or equal to disturbance energy is multiplied by the product of a default constant coefficient, if it is not, then sentencing
Determine system and is unsatisfactory for H∞Performance indicator.
6. a kind of time-varying continuous control device of the periodic segment vibration cooperative system based on LMI, which is characterized in that including：
Model building module, for establishing periodic segment vibration system model；
Controller parameter computing module, for according to the parameter in periodic segment vibration system model, being calculated by the tool boxes LMI
Go out each moment controller parameter K (t) so that controller calculates control according to controller parameter K (t) and system state variables x (t)
Device output u (t)=K (t) * x (t) processed, act power and are applied in periodic segment vibrational system.
7. a kind of time-varying continuous control device of periodic segment vibration cooperative system based on LMI according to claim 6,
It is characterized in that, the model building module is specifically used for：
The state-space expression for establishing system is：
Z (t)=Cx (t)+Du (t)+Dww(t)；
The state variable of system is taken to be
System is divided into S subsystem according to periodic segment principle, the period of S subsystem is respectively T1,T2,...,TS, system
Period is T=T1+T2+...+TS, set t0=0, t1=T1, t2=T1+T2..., ts=T1+T2+...+TS=T and satisfaction：
Therefore the expression formula of periodic segment vibration system model is：
Z (t)=Cix(t)+Diu(t)+Dwiw(t)；
t∈(nT+ti-1,nT+ti), n=0,1,2 ..., i=1,2 ..., S；
Wherein, m is the quality of periodic segment vibrational system, and q is displacement, and w (t) is system disturbance, and k and c are in vibrational system
Spring constant and damped coefficient, device exports u (t) in order to control, Ai、Bi、Ci、Di、Bwi、DwiFor the systematic parameter of i-th of subsystem.
8. a kind of time-varying continuous control device of periodic segment vibration cooperative system based on LMI according to claim 7,
It is characterized in that, the controller parameter computing module includes：
Linear matrix inequality establishes unit, for according to the parameter and the tool boxes LMI ginseng in periodic segment vibration system model
Number establishes linear matrix inequality：
QS+1=Q1；
US+1=U1；
Wherein, λiIt is the previously given parameter in the tool boxes LMI with γ, I is unit matrix, UiAnd QiIt is to be calculated by the tool boxes LMI
Matrix out, sym (A)=A+AT, * expressions are symmetrically；
Controller parameter solves unit, and K (t)=U (t) Q are obtained for solving-1(t), wherein
9. a kind of time-varying continuous controller of the periodic segment vibration cooperative system based on LMI, which is characterized in that including：
Memory, for storing instruction；
Processor is coupled to the memory, and it is real that the processor is configured as the instruction execution stored based on the memory
Now a kind of time-varying of periodic segment vibration cooperative system based on LMI as described in any one of claim 1 to 5 is continuously controlled
Device design processed.
10. a kind of computer readable storage medium, which is characterized in that be stored with computer on the computer readable storage medium
Program realizes that one kind as described in any one of claim 1 to 5 is based on when the computer program is executed by processor
The time-varying continuous controller design of the periodic segment vibration cooperative system of LMI.
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