CN108732933B - Time-varying continuous controller design of periodic segmented vibration cooperative system based on LMI - Google Patents

Time-varying continuous controller design of periodic segmented vibration cooperative system based on LMI Download PDF

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CN108732933B
CN108732933B CN201810559202.8A CN201810559202A CN108732933B CN 108732933 B CN108732933 B CN 108732933B CN 201810559202 A CN201810559202 A CN 201810559202A CN 108732933 B CN108732933 B CN 108732933B
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segmented vibration
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CN108732933A (en
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鲁仁全
李博
李攀硕
李鸿一
吴元清
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Guangdong University of Technology
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Abstract

The invention provides a time-varying continuous controller design of a periodic segmented vibration cooperative system based on an LMI, which comprises the following steps: establishing a periodic segmented vibration system model; and calculating a controller parameter K (t) at each moment through an LMI tool box according to parameters in the periodic segmented vibration system model, so that the controller calculates a controller output u (t) (K (t) x (t)) according to the controller parameter K (t) and a system state variable x (t), generates an acting force and acts on the periodic segmented vibration system. The invention also provides a corresponding device. In the invention, the controller parameter K (t) at each moment is solved by the LMI toolbox, so that the controller can calculate the controller parameter K (t) at each moment in real time according to the parameters in the periodic segmented vibration system model, and when the parameters in the model change, the controller parameters can be corrected in real time, thereby enabling the system to be more stable, being more adaptive to environmental change, reducing the vibration amplitude of the system and having better flexibility. In addition, the invention also provides a corresponding device.

Description

Time-varying continuous controller design of periodic segmented vibration cooperative system based on LMI
Technical Field
The invention relates to the technical field of program control devices, in particular to a time-varying continuous controller design of a periodic segmented vibration cooperative system based on an LMI.
Background
Periodic vibration systems are widespread in nature, such as rotary wing systems, sun black activities, and the like. In engineering, for such systems, in the prior art, some damping elements are mostly added to the system to damp the vibration of the system. Although the cost of the vibration system is low, the vibration system is lack of flexibility, the vibration reduction effect is inflexible, and the vibration system cannot adapt to changeable environments.
Therefore, the existing damping system lacks flexibility, has inflexible damping effect, and cannot adapt to variable environments, which is a technical problem to be solved by technical personnel in the field.
Disclosure of Invention
Aiming at the defects of the existing vibration reduction technology, the invention provides a time-varying continuous controller design of a periodic segmented vibration cooperative system based on LMI. Aiming at a periodic sectional vibration system, the method changes the parameters of the controller in real time by means of an LMI toolbox in Matlab software, so that the system is stable, the vibration amplitude of the system is reduced, and the performance of the vibration system is improved. The present invention is not limited to a specific system environment, and has a great flexibility compared with the prior art.
The invention provides a time-varying continuous controller design of a periodic segmented vibration cooperative system based on an LMI, which comprises the following steps:
establishing a periodic segmented vibration system model;
and calculating a controller parameter K (t) at each moment through an LMI tool box according to parameters in the periodic segmented vibration system model, so that the controller calculates a controller output u (t) (K (t) x (t)) according to the controller parameter K (t) and a system state variable x (t), generates an acting force and acts on the periodic segmented vibration system.
Preferably, the establishing a periodic segmented vibration system model comprises:
establishing a state space expression of the system as follows:
Figure BDA0001682782890000011
z(t)＝Cx(t)+Du(t)+Dw w(t)；
take the state variable of the system as
Figure BDA0001682782890000021
Figure BDA0001682782890000022
C＝[1 0]，D＝0，Dw＝0；
Dividing the system into S subsystems according to a period segmentation principle, wherein the periods of the S subsystems are respectively T1,T2,...,TSThe system period is T ═ T1+T2+...+TSSetting t0＝0，t1＝T1，t2＝T1+T2，…，ts＝T1+T2+...+TST and satisfies:
Figure BDA0001682782890000023
therefore, the expression of the periodic segmented vibration system model is as follows:
Figure BDA0001682782890000024
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 mass of the periodic sectional vibration system, q is displacement, w (t) is system disturbance, k and c are spring coefficient and damping coefficient in the vibration system, u (t) is output by the controller, Ai、Bi、Ci、Di、Bwi、DwiIs the system parameter of the ith subsystem.
It should be noted that, in the model expression,
Figure BDA0001682782890000025
Ci＝[1 0]，Di＝0，D wi0, where i denotes the ith subsystem.
Preferably, the calculating, by the LMI toolbox, the controller parameter k (t) at each time according to the parameters in the periodic segmented vibration system model specifically includes:
establishing a linear matrix inequality according to parameters in the periodic segmented vibration system model and parameters of an LMI tool box:
Figure BDA0001682782890000026
Figure BDA0001682782890000031
QS+1＝Q1；
US+1＝U1；
wherein λ isiAnd γ is a predetermined parameter of the LMI toolset, I is the identity matrix, UiAnd QiIs the matrix calculated by the LMI toolset, sym (A) ═ A + ATDenotes symmetry;
solving to obtain K (t) ═ U (t) Q-1(t) wherein,
Figure BDA0001682782890000032
Figure BDA0001682782890000033
preferably, the periodic segmented vibration system model is exponentially stabilized, that is, after the acting force is generated and acts on the periodic segmented vibration system (after the controller acts on the periodic segmented vibration system), the method further includes:
and detecting whether the system is stable at a speed greater than or equal to a preset exponential function convergence rate, and if not, judging that the system is not in accordance with the condition of stable exponential.
Preferably, the periodic segmented vibration system model adopts H∞The performance index, after the acting force is generated and acts on the periodic segmented vibration system (after the controller acts on the periodic segmented vibration system), also comprises:
detecting whether the energy output by the system is less than or equal to the disturbance energy multiplied by a preset constant systemThe product of numbers, if not, then the system is judged not to satisfy H∞Performance index.
The invention provides a time-varying continuous control device of a periodic segmented vibration cooperative system based on LMI, which comprises:
the model establishing module is used for establishing a periodic sectional vibration system model;
and the controller parameter calculation module is used for calculating a controller parameter K (t) at each moment through an LMI tool box according to parameters in the periodic segmented vibration system model, so that the controller calculates the controller output u (t) ═ K (t) × (t) according to the controller parameter K (t) and the system state variable x (t), generates an acting force and acts on the periodic segmented vibration system.
Preferably, the model building module is specifically configured to:
establishing a state space expression of the system as follows:
Figure BDA0001682782890000041
z(t)＝Cx(t)+Du(t)+Dw w(t)；
take the state variable of the system as
Figure BDA0001682782890000042
Figure BDA0001682782890000043
C＝[1 0]，D＝0，Dw＝0；
Dividing the system into S subsystems according to a period segmentation principle, wherein the periods of the S subsystems are respectively T1,T2,...,TSThe system period is T ═ T1+T2+...+TSSetting t0＝0，t1＝T1，t2＝T1+T2，…，ts＝T1+T2+...+TST and satisfies:
Figure BDA0001682782890000044
therefore, the expression of the periodic segmented vibration system model is as follows:
Figure BDA0001682782890000045
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 mass of the periodic sectional vibration system, q is displacement, w (t) is system disturbance, k and c are spring coefficient and damping coefficient in the vibration system, u (t) is output by the controller, Ai、Bi、Ci、Di、Bwi、DwiIs the system parameter of the ith subsystem.
Preferably, the controller parameter calculation module includes:
the linear matrix inequality establishing unit is used for establishing a linear matrix inequality according to parameters in the periodic segmented vibration system model and parameters of the LMI toolbox:
Figure BDA0001682782890000046
Figure BDA0001682782890000047
QS+1＝Q1；
US+1＝U1；
wherein λ isiAnd γ is a predetermined parameter of the LMI toolset, I is the identity matrix, UiAnd QiIs the matrix calculated by the LMI toolset, sym (A) ═ A + ATDenotes symmetry;
a controller parameter solving unit for solving to obtain K (t) ═ U (t) Q-1(t) wherein,
Figure BDA0001682782890000051
the invention provides a time-varying continuous controller of a periodic segmented vibration cooperative system based on LMI, which comprises:
a memory to store instructions;
a processor coupled to the memory, the processor configured to execute a time-varying continuous controller design implementing an LMI based periodically segmented vibration coordination system as described above based on instructions stored by the memory.
The present invention provides a computer readable storage medium having stored thereon a computer program which, when executed by a processor, implements a time-varying continuous controller design of an LMI based periodically segmented vibration coordination system as described above.
According to the technical scheme, the embodiment of the invention has the following advantages:
the invention provides a time-varying continuous controller design of a periodic segmented vibration cooperative system based on an LMI, which comprises the following steps: establishing a periodic segmented vibration system model; and calculating a controller parameter K (t) at each moment through an LMI tool box according to parameters in the periodic segmented vibration system model, so that the controller calculates a controller output u (t) (K (t) x (t)) according to the controller parameter K (t) and a system state variable x (t), generates an acting force and acts on the periodic segmented vibration system. The invention also provides a corresponding device. In the invention, the controller parameter K (t) at each moment is solved by the LMI toolbox, so that the controller can calculate the controller parameter K (t) at each moment in real time according to the parameters in the periodic segmented vibration system model, and when the parameters in the model change, the controller parameters can be corrected in real time, thereby enabling the system to be more stable, being more adaptive to environmental change, reducing the vibration amplitude of the system and having better flexibility.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without inventive exercise.
FIG. 1 is a flow diagram of one embodiment of a time-varying continuum controller design for an LMI-based periodically segmented vibration coordination system provided by the present invention;
FIG. 2 is a flow diagram of another embodiment of a time-varying continuum controller design of an LMI-based periodically segmented vibration coordination system provided by the present invention;
FIG. 3 is a simplified diagram of a periodically segmented vibratory system in accordance with an embodiment of the present invention;
FIG. 4 is a conceptual diagram of a periodically segmented vibratory system in a state space representation according to an embodiment of the present invention;
FIG. 5 is a diagram illustrating vibration amplitudes of a periodic segmented vibration system in an embodiment of the present invention;
FIG. 6 is a diagram illustrating a variation of the controller gain K (t) according to an embodiment of the present invention;
FIG. 7 shows the time variation of the output u (t) of the controller according to the embodiment of the present invention.
Detailed Description
Aiming at the defects of the existing vibration reduction technology, the invention provides a time-varying continuous controller design of a periodic segmented vibration cooperative system based on LMI. Aiming at a periodic sectional vibration system, the method changes the parameters of the controller in real time by means of an LMI toolbox in Matlab software, so that the system is stable, the vibration amplitude of the system is reduced, and the performance of the vibration system is improved. The present invention is not limited to a specific system environment, and has a great flexibility compared with the prior art.
In order to make the objects, features and advantages of the present invention more obvious and understandable, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the embodiments described below are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The system corresponding to the time-varying continuous controller design of the LMI-based periodic segmented vibration cooperative system can be used as a single intelligent system of a multi-intelligent-agent system and applied to a self-organizing cooperative system.
Referring to fig. 1, an embodiment of a time-varying continuous controller design of an LMI-based periodic segmented vibration cooperative system according to the present invention includes:
101. establishing a periodic segmented vibration system model;
102. and calculating a controller parameter K (t) at each moment through an LMI tool box according to parameters in the periodic segmented vibration system model, so that the controller calculates a controller output u (t) (K (t) x (t)) according to the controller parameter K (t) and a system state variable x (t), generates an acting force and acts on the periodic segmented vibration system.
In the invention, the controller parameter K (t) at each moment is solved by the LMI toolbox, so that the controller can calculate the controller parameter K (t) at each moment in real time according to the parameters in the periodic segmented vibration system model, and when the parameters in the model change, the controller parameters can be corrected in real time, thereby enabling the system to be more stable, being more adaptive to environmental change, reducing the vibration amplitude of the system and having better flexibility.
The above is a detailed description of an embodiment of a time-varying continuous controller design of an LMI-based periodic segmented vibration cooperative system, and the following is a detailed description of another embodiment of a time-varying continuous controller design of an LMI-based periodic segmented vibration cooperative system.
Referring to fig. 2, another embodiment of a time-varying continuous controller design of an LMI-based periodic segmented vibration cooperative system according to the present invention includes:
201. the method for establishing the periodic segmented vibration system model comprises the following steps:
referring first to fig. 3, fig. 3 is a simplified diagram of a periodic segmented vibration system, w being the system disturbance (typically noise or displacement disturbance), m being the mass of the system, q being the displacement of m, and k and c being the spring and damping coefficients of the vibration system. And u is a controller.
Referring to fig. 3, according to the simplified diagram of the periodic segmented vibration system shown in fig. 3, the output z of the system is the displacement q of the mass block, and a state space expression of the system can be written, and the state space expression of the system is established as follows:
Figure BDA0001682782890000071
z(t)＝Cx(t)+Du(t)+Dw w(t)；
take the state variable of the system as
Figure BDA0001682782890000072
Figure BDA0001682782890000073
C＝[1 0]，D＝0，Dw＝0；
The periodic sectional vibration system is essentially a vibration system with periodic structure or periodic parameter components. The periodic segmented vibration system can be regarded as an approximation of a periodic vibration system, and the system has a plurality of subsystems in each period, and the parameter of each subsystem can be an average value of the parameter in the time period or a parameter of a real subsystem with periodic segmented characteristics. Such systems are abundant in the real world, such as bio-predation systems, dc-dc converters, vibrating platforms for flow-line production, etc. Any system of this type or which can be viewed as an approximation of such a system may use the controller set forth herein. In particular, a general periodic vibration system can be regarded as a periodic segmented vibration system with only one subsystem. Let m, k, c all have the property of periodic segmentation, as explained above and without loss of generality. The periodic segmented vibration cooperative system in the invention indicates that the system can be applied to a self-organizing cooperative system and acts as an independent intelligent agent subsystem, so that the system is called a cooperative system.
Therefore, the system can be divided into S subsystems according to the period segmentation principle, and the periods of the S subsystems are respectively T1,T2,...,TSThe system period is T ═ T1+T2+...+TSSetting t0＝0，t1＝T1，t2＝T1+T2，…，ts＝T1+T2+...+TST and satisfies:
Figure BDA0001682782890000081
referring to fig. 4, fig. 4 is a conceptual diagram of a periodic segmented vibration system expressed in a state space expression. It can be seen that in one period TPIn the system, there are S subsystems, each subsystem has its own system parameter Ai，Bi，Ci，Di。
Therefore, the expression of the periodic segmented vibration system model is as follows:
Figure BDA0001682782890000082
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 mass of the periodic sectional vibration system, q is displacement, w (t) is system disturbance, k and c are spring coefficient and damping coefficient in the vibration system, u (t) is output by the controller, Ai、Bi、Ci、Di、Bwi、DwiIs the system parameter of the ith subsystem.
It should be noted that, in the model expression,
Figure BDA0001682782890000083
Ci＝[10]，Di＝0，D wi0, where i denotes the ith subsystem.
202. According to parameters in the periodic segmented vibration system model, a controller parameter K (t) at each moment is calculated through an LMI tool box, and the method specifically comprises the following steps:
aiming at the periodic segmented vibration system, the output of the controller is u (t) ═ K (t) × (t), and a linear matrix inequality is established according to parameters in a periodic segmented vibration system model and parameters of an LMI tool box:
Figure BDA0001682782890000091
Figure BDA0001682782890000092
QS+1＝Q1；
US+1＝U1；
wherein λ isiAnd γ is a predetermined parameter of the LMI toolset, I is the identity matrix, UiAnd QiIs the matrix calculated by the LMI toolset, sym (A) ═ A + ATDenotes symmetry;
the system has H∞When the performance index is obtained, solving the performance index to obtain K (t) ═ U (t) Q-1(t) wherein,
Figure BDA0001682782890000093
it should be noted that, in the following description,
Figure BDA0001682782890000094
and
Figure BDA0001682782890000095
are all linear convex functions and are artificially selected.
203. And the controller calculates controller output u (t) K (t) x (t) according to the controller parameter K (t) and the system state variable x (t), generates acting force and acts on the periodic segmented vibration system.
The invention adopts the most common state feedback control in a control system, the output of a controller is u (t) ═ K (t) × (t), wherein K (t) is a controller parameter, and x (t) is a state variable, and the state variable is selected in the system, such as the embodiment, the state feedback control is performed
Figure BDA0001682782890000096
Is a two-dimensional vector containing system displacement and acceleration. Therefore, the invention changes K (t) in real time and further changes the output of the controller. The controller can be understood as a generator of force, except that the amount of force it generates needs to be calculated by means of the LMI toolbox in MATLAB.
It should be noted that, the controller designed by the present invention has a periodic characteristic in the controller parameter k (t), but the system state variable x (t) becomes smaller and smaller, so the force output by the controller is not periodic. Once the parameters of the system are determined, the LMI toolbox can be used for directly calculating K (t) of the whole period, and if the system parameters change at a certain moment, the LMI toolbox can calculate a new group of K (t), which is the real-time change of the parameters.
204. And detecting whether the system is stable at a speed greater than or equal to a preset exponential function convergence rate, and if not, judging that the system is not in accordance with the condition of stable exponential.
The exponent adopted in the periodic segmented vibration system model of the invention is stable. Exponential stabilization has a faster stabilization rate than general asymptotic stabilization, which requires the system to stabilize at a rate greater than or equal to the rate of convergence of some exponential function. The stability requirement is smooth and fast, and has stronger engineering significance.
205. Detecting whether the energy output by the system is less than or equal to the product of the disturbance energy multiplied by a preset constant coefficient, and if not, judging that the system does not meet H∞Performance index.
As regards the performance index, H is used here∞Performance index. Such asThe performance intelligence requires that the energy output by the system is less than or equal to the disturbance energy multiplied by a constant coefficient. In general, in engineering, the disturbances that have a large impact on the system performance are energy-bounded, based on which H is chosen∞The performance index can better reflect the reality.
It should be noted that, steps 204 and 205 are to detect the control effect of the controller after the controller is added. The system determined is referred to as a periodic segmented vibration system.
Referring to fig. 5, fig. 6 and fig. 7, according to the present embodiment, a specific periodic segmented vibration system is adopted (T is 15, T)1＝T2＝T35), in the case of a zero initial state, finite time (2 cycles) white noise disturbance input, the system outputs a change in amplitude. A perturbation input of white noise of limited time may ensure that the perturbation is energy bounded. It can be seen from fig. 5 that the vibration of the system is relatively severe before the controller is added, and the vibration amplitude of the system is greatly reduced after the controller is added. It is noted in particular that during the second period (15-30), the vibration of the system is already almost 0, although there is still white noise disturbance.
Fig. 6 shows the variation of the controller gain k (t) in the simulation process. It can be seen that k (t) is a continuous cycle, and when the system state variable x (t) is also continuous, from u (t) k (t) x (t), the output force of the controller is continuous.
Fig. 7 shows the time variation of the output u (t) of the controller in the simulation process.
The abscissa of fig. 5, 6 and 7 is the time t and the ordinate is the corresponding value.
An embodiment of the time-varying continuous control device of the periodic segmented vibration cooperative system based on the LMI according to the present invention will be described in detail below.
The device can be used as a single intelligent system of a multi-intelligent system and applied to an ad hoc cooperative system.
The invention provides an embodiment of a time-varying continuous control device of a periodic segmented vibration cooperative system based on LMI, which comprises the following components:
the model establishing module is used for establishing a periodic sectional vibration system model;
and the controller parameter calculation module is used for calculating a controller parameter K (t) at each moment through an LMI tool box according to parameters in the periodic segmented vibration system model, so that the controller calculates the controller output u (t) ═ K (t) × (t) according to the controller parameter K (t) and the system state variable x (t), generates an acting force and acts on the periodic segmented vibration system.
Further, the model building module is specifically configured to:
establishing a state space expression of the system as follows:
Figure BDA0001682782890000111
z(t)＝Cx(t)+Du(t)+Dw w(t)；
take the state variable of the system as
Figure BDA0001682782890000112
Figure BDA0001682782890000113
C＝[1 0]，D＝0，Dw＝0；
Dividing the system into S subsystems according to a period segmentation principle, wherein the periods of the S subsystems are respectively T1,T2,...,TSThe system period is T ═ T1+T2+...+TSSetting t0＝0，t1＝T1，t2＝T1+T2，…，ts＝T1+T2+...+TST and satisfies:
Figure BDA0001682782890000114
therefore, the expression of the periodic segmented vibration system model is as follows:
Figure BDA0001682782890000115
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 mass of the periodic sectional vibration system, q is displacement, w (t) is system disturbance, k and c are spring coefficient and damping coefficient in the vibration system, u (t) is output by the controller, Ai、Bi、Ci、Di、Bwi、DwiIs the system parameter of the ith subsystem.
Further, the controller parameter calculation module includes:
the linear matrix inequality establishing unit is used for establishing a linear matrix inequality according to parameters in the periodic segmented vibration system model and parameters of the LMI toolbox:
Figure BDA0001682782890000121
Figure BDA0001682782890000122
QS+1＝Q1；
US+1＝U1；
wherein λ isiAnd γ is a predetermined parameter of the LMI toolset, I is the identity matrix, UiAnd QiIs the matrix calculated by the LMI toolset, sym (A) ═ A + ATDenotes symmetry;
a controller parameter solving unit for solving to obtain K (t) ═ U (t) Q-1(t) wherein,
Figure BDA0001682782890000123
one embodiment of the time-varying continuous controller of the present invention providing an LMI based periodically segmented vibration system will now be described in detail.
The invention provides one embodiment of a time-varying continuous controller of an LMI-based periodic segmented vibration cooperative system, comprising:
a memory to store instructions;
a processor coupled to the memory, the processor configured to execute, based on instructions stored by the memory, a time-varying continuous controller design implementing an LMI-based periodically-segmented vibration coordination system as described above.
The present invention will be described in detail below with respect to providing a computer-readable storage medium.
The present invention provides a computer readable storage medium having stored thereon a computer program which, when executed by a processor, implements a time-varying continuous controller design of an LMI based periodically segmented vibration cooperative system as described above.
The above-mentioned embodiments are only used for illustrating the technical solutions of the present invention, and not for limiting the same; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.

Claims (8)

1. A time-varying continuous controller design for an LMI-based periodic segmented vibration coordinated system, comprising:
establishing a periodic segmented vibration system model;
calculating a controller parameter K (t) at each moment through an LMI tool box according to parameters in a periodic segmented vibration system model, so that the controller calculates a controller output u (t) (K (t) x (t)) according to the controller parameter K (t) and a system state variable x (t), generates an acting force and acts on the periodic segmented vibration system;
the calculating the controller parameter k (t) at each moment through the LMI toolbox according to the parameters in the periodic segmented vibration system model specifically includes:
establishing a linear matrix inequality according to parameters in the periodic segmented vibration system model and parameters of an LMI tool box:
Figure FDA0002820960130000011
Figure FDA0002820960130000012
QS+1＝Q1；
US+1＝U1；
wherein λ isiAnd γ is a predetermined parameter of the LMI toolset, I is the identity matrix, UiAnd QiIs the matrix calculated by the LMI toolset, sym (A) ═ A + ATDenotes symmetry;
solving to obtain K (t) ═ U (t) Q-1(t) wherein,
Figure FDA0002820960130000013
Figure FDA0002820960130000014
2. an LMI-based time-varying continuum controller design of a periodic segmented vibration cooperative system as recited in claim 1, wherein the modeling the periodic segmented vibration system comprises:
establishing a state space expression of the system as follows:
Figure FDA0002820960130000015
z(t)＝Cx(t)+Du(t)+Dww(t)；
take the state variable of the system as
Figure FDA0002820960130000016
Figure FDA0002820960130000021
C＝[1 0]，D＝0，Dw＝0；
Dividing the system into S subsystems according to a period segmentation principle, wherein the periods of the S subsystems are respectively T1,T2,...,TSThe system period is T ═ T1+T2+...+TSSetting t0＝0，t1＝T1，t2＝T1+T2，…，ts＝T1+T2+...+TST and satisfies:
Figure FDA0002820960130000022
therefore, the expression of the periodic segmented vibration system model is as follows:
Figure FDA0002820960130000023
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 mass of the periodic sectional vibration system, q is displacement, w (t) is system disturbance, k and c are spring coefficient and damping coefficient in the vibration system, u (t) is output by the controller, Ai、Bi、Ci、Di、Bwi、DwiIs the system parameter of the ith sub-system,
it should be noted that, in the model expression,
Figure FDA0002820960130000024
Ci＝[1 0]，Di＝0，Dwi0, where i denotes the ith subsystem.
3. An LMI-based time-varying continuum controller design of a periodic segmented vibration cooperative system as recited in claim 2, wherein the periodic segmented vibration system model is exponentially stabilized, i.e. after generating a force and acting on the periodic segmented vibration system, further comprising:
and detecting whether the system is stable at a speed greater than or equal to a preset exponential function convergence rate, and if not, judging that the system is not in accordance with the condition of stable exponential.
4. The LMI-based time-varying continuum controller design of the CFM cooperative system as recited in claim 2, wherein the CFM model employs H∞The performance indexes, namely after the acting force is generated and acts on the periodic segmented vibration system, also comprise:
detecting whether the energy output by the system is less than or equal to the product of the disturbance energy multiplied by a preset constant coefficient, and if not, judging that the system does not meet H∞Performance index.
5. An LMI-based time-varying continuous control device for a periodic segmented vibration cooperative system, comprising:
the model establishing module is used for establishing a periodic sectional vibration system model;
the controller parameter calculation module is used for calculating a controller parameter K (t) at each moment through an LMI tool box according to parameters in the periodic segmented vibration system model, so that the controller calculates the controller output u (t) ═ K (t) × (t) according to the controller parameter K (t) and a system state variable x (t), generates an acting force and acts on the periodic segmented vibration system;
the controller parameter calculation module includes:
the linear matrix inequality establishing unit is used for establishing a linear matrix inequality according to parameters in the periodic segmented vibration system model and parameters of the LMI toolbox:
Figure FDA0002820960130000031
Figure FDA0002820960130000032
QS+1＝Q1；
US+1＝U1；
wherein λ isiAnd γ is a predetermined parameter of the LMI toolset, I is the identity matrix, UiAnd QiIs the matrix calculated by the LMI toolset, sym (A) ═ A + ATDenotes symmetry;
a controller parameter solving unit for solving to obtain K (t) ═ U (t) Q-1(t) wherein,
Figure FDA0002820960130000033
6. the LMI-based time-varying continuous control device of the periodic segmented vibration cooperative system as claimed in claim 5, wherein the model building module is specifically configured to:
establishing a state space expression of the system as follows:
Figure FDA0002820960130000034
z(t)＝Cx(t)+Du(t)+Dww(t)；
take the state variable of the system as
Figure FDA0002820960130000035
Figure FDA0002820960130000041
C＝[1 0]，D＝0，Dw＝0；
Dividing the system into S subsystems according to a period segmentation principle, wherein the periods of the S subsystems are respectively T1,T2,...,TSThe system period is T ═ T1+T2+...+TSSetting t0＝0，t1＝T1，t2＝T1+T2，…，ts＝T1+T2+...+TST and satisfies:
Figure FDA0002820960130000042
therefore, the expression of the periodic segmented vibration system model is as follows:
Figure FDA0002820960130000043
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 mass of the periodic sectional vibration system, q is displacement, w (t) is system disturbance, k and c are spring coefficient and damping coefficient in the vibration system, u (t) is output by the controller, Ai、Bi、Ci、Di、Bwi、DwiIs the system parameter of the ith subsystem.
7. A time-varying continuous controller for an LMI-based periodic segmented vibration coordinated system, comprising:
a memory to store instructions;
a processor coupled to the memory, the processor configured to execute, based on instructions stored by the memory, a time-varying continuous controller design implementing an LMI based periodically-segmented vibration coordination system as claimed in any of claims 1 to 4.
8. A computer readable storage medium having stored thereon a computer program which, when executed by a processor, implements a time-varying continuous controller design for an LMI-based periodically-segmented vibration cooperative system as claimed in any one of claims 1 to 4.
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