CN110824928A - Improved semi-active H infinity robust control method - Google Patents

Improved semi-active H infinity robust control method Download PDF

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CN110824928A
CN110824928A CN201911233952.7A CN201911233952A CN110824928A CN 110824928 A CN110824928 A CN 110824928A CN 201911233952 A CN201911233952 A CN 201911233952A CN 110824928 A CN110824928 A CN 110824928A
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林秀芳
郑祥盘
唐晓腾
王兆权
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Minjiang University
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Abstract

The invention relates to an improved semi-active H∞A robust control method. First, H will be based on interference suppression problem∞The design of control is converted into a mixed sensitivity solving problem, and a robust control theory is adopted to design a PSTH∞And (4) robust control. Then, performing band-constrained multi-objective optimization design on the mixed sensitivity weighting function of the robust controller by using a WOA algorithm, and using the designed mixed sensitivity H∞The controller calculates an active control force of the closed-loop control system. The active control force is then converted into a control signal for the MR damper using CVL law as the MR damper controller. Finally, outputting actual damping force based on the forward model of the MR damper to realize the semi-active WOA-PSTH based on the MR damper∞-CVL control. The invention not only can overcome H∞Conservatism of control system design and dependence on engineering experience can be realized, and active control force can be accurately calculated, so that control signals of the MR damper can be accurately controlled, and a good semi-active vibration damping control effect is achieved.

Description

Improved semi-active H infinity robust control method
Technical Field
The invention relates to the field of semi-active control, in particular to an improved semi-active H-infinity robust control method.
Background
The magnetorheological damper is an intelligent semi-active control device with a promising application prospect, has the advantages of strong adaptability of an active control device, high reliability of a passive control device and the like, and becomes a research hotspot in the field of structural vibration reduction. In order to fully exert the excellent damping characteristics of the Magnetorheological (MR) damper, semi-active control research based on the damper is still under way.
In recent years, H∞Research into robust control in MR damper semi-active vibration control is receiving increasing attention. However, in these studies, H∞Most of the control methods focus on solving the problem of robust stability, and the design of the controller is relatively conservative. Further, in these control methods, once the equation of state of the controlled system is determined, H∞The control law of the control is determined accordingly, so that the design of the controller is not flexible enough.
Disclosure of Invention
In view of the above, the present invention is directed to an improved semi-active H ∞ robust control method, which can overcome H ∞ robustness∞Conservatism of control system design and dependence on engineering experience can be realized, and active control force can be calculated more accurately, so that control signals of the MR damper can be controlled accurately, and finally a good semi-active vibration reduction control effect is achieved.
In order to achieve the purpose, the invention adopts the following technical scheme:
an improved semi-active H ∞ robust control method, comprising the steps of:
step S1: h to be based on interference suppression problem∞The design of control is converted into a mixed sensitivity solving problem, and a PS/T type mixed sensitivity H based on output feedback is constructed∞A robust controller;
step S2: performing band-constrained multi-objective optimization design on the mixed sensitivity weighting function of the robust controller by using a whale optimization algorithm to obtain an optimized robust controller;
step S3: calculating the active control force of the closed-loop control system according to the optimized robust controller;
step S4: converting the active control force into a control signal of the magneto-rheological damper by utilizing an amplitude limiting voltage law;
step S5: based on the control signal of the magneto-rheological damper, the phenomenon model is used as the forward model of the magneto-rheological damper, the damping force required by structural damping is calculated and output, and the semi-active WOA-PSTH based on the MR damper is realized∞-CVL control.
Further, said H∞A robust controller is a closed loop control system of the positive feedback type, whose closed loop transfer function can be expressed as:
Figure BDA0002304375920000021
where S is the sensitivity function and PS is the transfer function of excitation d to system output y; the system output y is not a full state variable, but rather an easily measured acceleration response; t is called a complementary sensitivity function and is a transfer function between the excitation d and the control force u; wsAnd WtIs a mixed sensitivity weighting function of the control system, which weights PS and T respectively; for a standard controlled system constructed, the output is defined as
Figure BDA0002304375920000022
Wherein z1 and z2 are evaluation signals.
Further, the step S2 is specifically:
step S21: an optimization objective function is determined as follows:
Obj＝wJ1+(1-w)J2
in the formula,
Figure BDA0002304375920000031
Figure BDA0002304375920000032
in the formula, Obj is a fitness function in a whale optimization algorithm; x is the number ofi(t) and
Figure BDA0002304375920000033
respectively, the displacement and absolute acceleration, x, of the ith floorunctrlAnd
Figure BDA0002304375920000034
maximum displacement and maximum absolute acceleration of the building when uncontrolled, respectively; w is reflection J1And J2A weight of relative importance;
step S22: determining the number of inputs and outputs of the control system according to the nominal controlled object, and determining the structure of the weighting function;
step S23: performing algorithm coding on the parameter to be optimized by adopting a real-value coding strategy, and defining a search space of the parameter to be optimized;
step S24: randomly generating position information X ═ X of whale individual1,…,XN]As initial parameters to be optimized, and initializing algorithm parameters;
step S25: cycle 1, start iterative calculations: first, a weighting function W is determinedsAnd WtThen calculating the standard H∞Each matrix in the control is solved for the controller K based on the LMI method, thereby calculating the active control fcAnd finally calculating the fitness F (X) according to the control systemi)。
Step S26: judging whether an algorithm termination condition is met: if the Cycle is satisfied>TmaxTerminating iteration and finding out an individual position with the optimal fitness value as an optimal position X; otherwise, the process advances to step S27;
step S27: updating each individual location:
step S28: calculating the updated population fitness, and replacing the optimal position in the original population by the updated optimal position if the fitness of the optimal individual in the updated population is superior to the fitness of the optimal individual in the original population; otherwise, keeping the optimal position of the original population unchanged;
step S29: and repeating the steps S26-S28 until the algorithm is finished, wherein the output optimal individual position is the optimization parameter of the mixed sensitivity weighting function.
Further, the weighting function WsAnd WtThe structure of (1) is in a first-order regular form, and a diagonalized real rational function matrix is adopted.
Further, in the step S25, the calculation fitness F (X) is calculatedi) First, PSTH is determined∞Whether the open loop system is stable or not, if the system is not stable, let F (X)i) Otherwise, continuously judging PSTH∞Whether the CVL closed-loop semi-active control system is stable, if not, let F (X)i) Otherwise, F (X) is calculated according to the formula defined in step S21i)。
Further, the step S27 is specifically:
when the probability p is less than 0.5, a shrink wrapping mechanism is adopted, specifically:
if | A | ≧ 1, randomly determining whale individual position X in current population rangei,randAnd updating the location of the individual using the following formula:
Figure BDA0002304375920000041
in the formula, A ═ 2 a ═ k1A, where a ∈ [0,2 ]]，k1∈[0,1]，C＝2×k2，k2∈[0,1]；
If | A | <1, the location of the individual is updated using the following equation:
Figure BDA0002304375920000043
in the formula,
Figure BDA0002304375920000044
wherein XleaderThe optimal individuals in the previous round are selected;
when the probability p is more than or equal to 0.5, executing spiral position updating, specifically:
Xi k+1＝D×eblcos(2πl)+Xleader；
wherein D ═ Xleader-Xi k|，b＝1,l＝(a2-1)×rand+1,a2∈[-2,-1]。
Further, after the position of each individual is updated in step S27, it is determined whether each parameter exceeds a preset value range, and if any parameter exceeds the value range, the parameter is made equal to the corresponding parameter of the previous iteration optimal solution.
Compared with the prior art, the invention has the following beneficial effects:
1. the invention provides PS/T type mixed sensitivity H in structural vibration reduction control based on a magneto-rheological damper∞Robust control, overcomes the conventional H∞The control rate of the control system is conservative as determined by the equation of state.
2. The invention combines whale optimization algorithm and PS/T type mixed sensitivity H∞The combination of robust control forms an improved robust control, which not only overcomes the mixed sensitivity H∞The dependence of the robust control design on engineering experience solves the problem that the weighting function is difficult to determine, and the active control force can be calculated more accurately.
3. The invention combines the improved robust control and the limiting voltage theorem, and can accurately control the control signal of the MR damper.
4. The invention improves the vibration reduction effect of the structure, and effectively reduces the displacement response, the interlayer displacement response and the acceleration response of the structure;
drawings
FIG. 1 shows an improved semi-active H according to an embodiment of the present invention∞A robust control block diagram;
FIG. 2 is a Kobe seismic time-course diagram of an embodiment of the invention;
FIG. 3 shows a PS/T implementation of the present inventionSensitivity of mixing H∞A control block diagram;
FIG. 4 shows the hybrid sensitivity H of an embodiment of the present invention∞Controlling a standard form;
FIG. 5 is a graph of the convergence of the whale optimization algorithm of an embodiment of the present invention;
FIG. 6 illustrates an algorithm principle of an optimal clipping control algorithm according to an embodiment of the present invention;
FIG. 7 is a graph comparing time course response of displacement of the top layer with and without control according to an embodiment of the present invention;
FIG. 8 is a graph comparing time-course responses of displacement between top layers with and without control according to an embodiment of the present invention;
FIG. 9 is a graph comparing the response of the acceleration time course of the top layer with and without control according to an embodiment of the present invention;
fig. 10 is a graph comparing displacement and acceleration response peaks for all floors in an embodiment of the present invention.
Detailed Description
The invention is further explained below with reference to the drawings and the embodiments.
Referring to fig. 1, the present invention provides an improved semi-active H ∞ robust control method, which includes the following steps:
step S1: h to be based on interference suppression problem∞The design of control is converted into a mixed sensitivity solving problem, and a PS/T type mixed sensitivity H based on output feedback is constructed∞A robust controller;
step S2: performing band-constrained multi-objective optimization design on the mixed sensitivity weighting function of the robust controller by using a whale optimization algorithm to obtain an optimized robust controller;
step S3: calculating the active control force of the closed-loop control system according to the optimized robust controller;
step S4: converting the active control force into a control signal of the magneto-rheological damper by utilizing an amplitude limiting voltage law;
step S5: based on the control signal of the magneto-rheological damper, the phenomenon model is used as the forward model of the magneto-rheological damper, the damping force required by the structural damping is calculated and output, and the MR-based damping is realizedSemi-active WOA-PSTH of damper∞-CVL control.
In this embodiment, the H∞A robust controller is a closed loop control system of the positive feedback type, whose closed loop transfer function can be expressed as:
where S is the sensitivity function and PS is the transfer function of excitation d to system output y; the system output y is not a full state variable, but rather an easily measured acceleration response; t is called a complementary sensitivity function and is a transfer function between the excitation d and the control force u; wsAnd WtIs a mixed sensitivity weighting function of the control system, which weights PS and T respectively; for a standard controlled system constructed, the output is defined as
Figure BDA0002304375920000062
Wherein z1 and z2 are evaluation signals.
In this embodiment, the step S2 specifically includes:
step S21: an optimization objective function is determined as follows:
Obj＝wJ1+(1-w)J2
in the formula,
Figure BDA0002304375920000071
Figure BDA0002304375920000072
in the formula, Obj is a fitness function in a whale optimization algorithm; x is the number ofi(t) and
Figure BDA0002304375920000073
respectively, the displacement and absolute acceleration, x, of the ith floorunctrlAnd
Figure BDA0002304375920000074
maximum displacement and maximum absolute acceleration of the building when uncontrolled, respectively; w is reflection J1And J2A weight of relative importance;
step S22: determining the number of inputs and outputs of the control system according to the nominal controlled object, and determining the structure of the weighting function;
step S23: performing algorithm coding on the parameter to be optimized by adopting a real-value coding strategy, and defining a search space of the parameter to be optimized;
step S24: randomly generating position information X ═ X of whale individual1,…,XN]As initial parameters to be optimized, and initializing algorithm parameters;
step S25: cycle 1, start iterative calculations: first, a weighting function W is determinedsAnd WtThen calculating the standard H∞Each matrix in the control is solved for the controller K based on the LMI method, thereby calculating the active control fcAnd finally calculating the fitness F (X) according to the control systemi)。
Step S26: judging whether an algorithm termination condition is met: if the Cycle is satisfied>TmaxTerminating iteration and finding out an individual position with the optimal fitness value as an optimal position X; otherwise, the process advances to step S27;
step S27: updating each individual location:
when the probability p is less than 0.5, a shrink wrapping mechanism is adopted, specifically:
if | A | ≧ 1, randomly determining whale individual position X in current population rangei,randAnd updating the location of the individual using the following formula:
Figure BDA0002304375920000075
in the formula, A ═ 2 a ═ k1A, where a ∈ [0,2 ]]，k1∈[0,1]，C＝2×k2，k2∈[0,1]；
If | A | <1, the location of the individual is updated using the following equation:
Figure BDA0002304375920000082
in the formula,
Figure BDA0002304375920000083
wherein XleaderThe optimal individuals in the previous round are selected;
when the probability p is more than or equal to 0.5, executing spiral position updating, specifically:
Xi k+1＝D×eblcos(2πl)+Xleader；
wherein D ═ Xleader-Xi k|，b＝1,l＝(a2-1)×rand+1,a2∈[-2,-1]；
Step S28: calculating the updated population fitness, and replacing the optimal position in the original population by the updated optimal position if the fitness of the optimal individual in the updated population is superior to the fitness of the optimal individual in the original population; otherwise, keeping the optimal position of the original population unchanged;
step S29: and repeating the steps S26-S28 until the algorithm is finished, wherein the output optimal individual position is the optimization parameter of the mixed sensitivity weighting function.
Preferably, in this embodiment, the weighting function WsAnd WtThe structure of (1) is in a first-order regular form, and a diagonalized real rational function matrix is adopted.
Preferably, in this embodiment, in the step S25, the calculation fitness F (X) is calculatedi) First, PSTH is determined∞Whether the open loop system is stable or not, if the system is not stable, let F (X)i) Otherwise, continuously judging PSTH∞Whether the CVL closed-loop semi-active control system is stable, if not, let F (X)i) Otherwise, F (X) is calculated according to the formula defined in step S21i)。
Preferably, in this embodiment, after the position update is completed in step S27, each individual determines whether each parameter exceeds a preset value range, and if any parameter exceeds the value range, the parameter is made equal to a corresponding parameter of the previous iteration optimal solution.
In this embodiment, in step S4, the core control law of the clip voltage law is: when the damping force f of the magneto-rheological damper is the active control force fcThen, the control voltage i maintains the original value; when f is<fcOr when the two forces have the same sign, in order to make f as much as possible equal to fcMatching, i is equal to imax(ii) a Otherwise, let i equal to 0.
In this embodiment, the damping force of the magnetorheological damper used in the amplitude-limiting voltage law is calculated by a forward model of the magnetorheological damper based on a phenomenon model.
In particular, in the embodiment, PS/T type hybrid sensitivity H is provided in the structural vibration damping control based on the magneto-rheological damper∞(PSTH∞) And (4) robust control. Optimizing algorithm and PSTH (particle swarm optimization) of whale∞The robust controls combine to form an improved robust control. And the improved robust control is combined with the amplitude limiting voltage law to form the vibration semi-active predictive control of the building structure based on the magneto-rheological damper. The method can ensure that the mixed sensitivity is H∞The design method is widely applied to semi-active control, can achieve an ideal structural vibration reduction control effect, and obtains considerable social and economic benefits.
The above embodiments are described in more detail below with reference to the accompanying drawings.
The damping object of the embodiment of the invention is a shear frame structure of a five-storey building, and the applied dynamic excitation is real Kobe seismic waves. FIG. 2 is a Kobe seismic time-course diagram of the present embodiment. Three MR dampers with the maximum output of 1000KN are respectively arranged on the 3 rd layer, the 4 th layer and the 5 th layer. The mass, stiffness and damping of the various layers of the structure are as follows:
Figure BDA0002304375920000091
FIG. 3 shows the PS/T hybrid sensitivity H of this example∞And (5) a control block diagram. In the figure, P is the nominal object, i.e. the real controlled system, K is the controller system, u is the control force generated by the controller, d is the seismic excitation, y is the measured structural seismic response, z is1And z2Is an evaluation signal, WsAnd WtWhich are weighting functions of the signals y and u, respectively.
With respect to FIG. 3, a standard controlled system can be constructed with an output defined as
Figure BDA0002304375920000101
The closed loop transfer function matrix from input d to output z is defined as:
Figure BDA0002304375920000102
where S is the sensitivity function, PS is the transfer function from the excitation d to the system output y, and T is the complementary sensitivity function, which is the transfer function between the excitation d and the control force u.
The purpose of this hybrid sensitivity design is to select an appropriate weighting function matrix W for the control object PsAnd WtA suitable controller K is found such that the closed loop system satisfies the following conditions:
Figure BDA0002304375920000103
to determine the controller K, the system is further modified to convert it into a mixing sensitivity H∞Standard form of control. FIG. 4 shows the hybrid sensitivity H of the present embodiment∞And controlling the standard form. P, W thereinsAnd WtForm the standard H∞Generalized object G in control.
Hybrid sensitivity H based on whale optimization algorithm∞The specific steps of the optimization design flow can be detailed as follows:
step 1: an optimization objective function is determined as follows:
Obj＝wJ1+(1-w)J2
in the formula,
Figure BDA0002304375920000105
wherein Obj is also the fitness function in the following whale optimization algorithm. This is to solve the minimization problem, and the smaller the fitness, the better the solution. x is the number ofi(t) and
Figure BDA0002304375920000106
respectively, the displacement and absolute acceleration, x, of the ith floorunctrlAnd
Figure BDA0002304375920000107
respectively the maximum displacement and the maximum absolute acceleration of the building when it is not controlled. w is reflection J1And J2The weight of relative importance is given by w equal to 0.7.
Step 2: determining the number of inputs and outputs of the control system according to the nominal controlled object, and determining the structure of the weighting function;
h of the embodiment of the invention∞The controller is a three-input-three-output system, three inputs are 3-5 layers of acceleration, and three outputs are 3-5 layers of active control force. WsAnd WtThe expression is as follows:
Figure BDA0002304375920000112
wherein,
Figure BDA0002304375920000113
Figure BDA0002304375920000114
where m and n are the number of inputs and outputs, respectively, of the control system, i.e. both 3.
Step 3: performing algorithm coding on the parameter to be optimized by adopting a real-value coding strategy, and defining a search space of the parameter to be optimized;
the coding structure of the parameter to be optimized is defined as:
H＝{w11,w12,w13,w21,w22,w23,w31,w32,w33,w41,w42,w43,k11,k12,k13,k21,k22,k23}
the search spaces for these parameters are:
Figure BDA0002304375920000115
w41,w42,w43∈[103,106],k11,k12,k13∈[10,103],k21,k22,k23∈[10-3,10-1]
step 4: algorithm initialization: randomly generating position information X ═ X of whale individual1,…,XN]As initial parameters to be optimized, and initializing algorithm parameters, making population size N and iteration number T max20 and 100, respectively;
step 5: cycle 1, start iterative calculations: first, a weighting function W is determinedsAnd WtThen calculating the standard H∞Each matrix in the control is solved based on an LMI method, and finally, the fitness F (X) is calculated according to the control systemi). Calculating the calculation fitness F (X)i) First, PSTH is determined∞In open loop systemsWhether any one of the control force components exceeds 106kN, if so, let F (X)i) 1 is ═ 1; otherwise, continuously judging the PSTH∞Whether the damping force of any MR damper in the CVL closed-loop semi-active control system exceeds the force range or not, and if so, enabling F (X)i) 1 is ═ 1; otherwise, F (X) is calculated according to the formula defined in Step1i)；
Step 6: judging whether an algorithm termination condition is met: if the Cycle is satisfied>TmaxTerminating iteration and finding out the individual position with the optimal (namely the minimum) fitness value as the optimal position X; otherwise, the process advances to step S27;
step 7: updating each individual location:
when the probability p is less than 0.5, a shrink wrapping mechanism is adopted, specifically:
if | A | ≧ 1, randomly determining whale individual position X in current population rangei,randAnd updating the location of the individual using the following formula:
Figure BDA0002304375920000121
in the formula, A ═ 2 a ═ k1A, where a ∈ [0,2 ]]，k1∈[0,1]，C＝2×k2，k2∈[0,1]；
If | A | <1, the location of the individual is updated using the following equation:
in the formula,wherein XleaderThe optimal individuals in the previous round are selected;
when the probability p is more than or equal to 0.5, executing spiral position updating, specifically:
Xi l+1＝D×eblcos(2πl)+Xleader；
wherein D ═ Xleader-Xi k|，b＝1,l＝(a2-1)×rand+1,a2∈[-2,-1]；
Step 8: and judging whether each parameter of each individual exceeds a preset value range, and if any parameter exceeds the value range, enabling the parameter to be equal to the corresponding parameter of the optimal solution of the previous iteration.
Step 9: referring to Step5, the updated population fitness is calculated. If the fitness of the optimal individual in the updated population is better than that of the optimal individual in the original population, replacing the optimal position in the original population with the updated optimal position; otherwise, keeping the optimal position of the original population unchanged;
step 10: and repeating the steps S26-S29 until the algorithm is finished, wherein the output optimal individual position is the optimization parameter of the mixed sensitivity weighting function.
Referring to fig. 6, in the present embodiment, the clipping voltage law is used to convert the active control force into the control voltage value of the MR damper, and the calculation expression is as follows:
i＝ImaxH{(fc-f)f}
wherein, ImaxIs the maximum voltage of the MR damper, H { } is a step function, fcIs the active control force and f is the control force of the MR damper. The core control law is as follows: when f is fcThen, controlling the current value to maintain the original value; when f is<fcOr when the two forces have the same sign, in order to make f as much as possible equal to fcMatching, I is equal to Imax(ii) a Otherwise, let i equal to 0. The damping force of the magneto-rheological damper used in the amplitude limiting voltage law is obtained by calculation of a forward model of the magneto-rheological damper based on a phenomenon model.
Referring to fig. 7-9, the semi-active H described in this embodiment∞Robust control can effectively reduce all responses at the top of the structure.
Referring to fig. 10, it can be seen that although the optimization targets are the maximum displacement peak and acceleration peak, the semi-active H described in the present embodiment∞The robust control can effectively reduce the displacement peak value and the acceleration peak value of all floors.
The above description is only a preferred embodiment of the present invention, and all equivalent changes and modifications made in accordance with the claims of the present invention should be covered by the present invention.

Claims (7)

1. Improved semi-active H∞The robust control method is characterized in that: the method comprises the following steps:
step S1: h to be based on interference suppression problem∞The design of control is converted into a mixed sensitivity solving problem, and a PS/T type mixed sensitivity H based on output feedback is constructed∞A robust controller;
step S2: performing band-constrained multi-objective optimization design on the mixed sensitivity weighting function of the robust controller by using a whale optimization algorithm to obtain an optimized robust controller;
step S3: calculating the active control force of the closed-loop control system according to the optimized robust controller;
step S4: converting the active control force into a control signal of the magneto-rheological damper by utilizing an amplitude limiting voltage law;
step S5: based on the control signal of the magneto-rheological damper, the phenomenon model is used as the forward model of the magneto-rheological damper, the damping force required by structural damping is calculated and output, and the semi-active WOA-PSTH based on the MR damper is realized∞-CVL control.
2. An improved semi-active H according to claim 1∞Robust control method, characterized in that said H∞A robust controller is a closed loop control system of the positive feedback type, whose closed loop transfer function can be expressed as:
Figure FDA0002304375910000011
where S is the sensitivity function and PS is the transfer function of excitation d to system output y; the system output y is not a full state variable, but rather an easily measured acceleration response; t is called the complementary sensitivity function, and is the excitation d and controlThe transfer function between forces u; wsAnd WtIs a mixed sensitivity weighting function of the control system, which weights PS and T respectively; for a standard controlled system constructed, the output is defined as
Figure FDA0002304375910000012
Wherein z1 and z2 are evaluation signals.
3. An improved semi-active H according to claim 1∞The robust control method is characterized in that the step S2 specifically includes:
step S21: an optimization objective function is determined as follows:
Obj＝wJ1+(1-w)J2
in the formula,
Figure FDA0002304375910000021
Figure FDA0002304375910000022
in the formula, Obj is a fitness function in a whale optimization algorithm; x is the number ofi(t) andrespectively, the displacement and absolute acceleration, x, of the ith floorunctrlAnd
Figure FDA0002304375910000024
maximum displacement and maximum absolute acceleration of the building when uncontrolled, respectively; w is reflection J1And J2A weight of relative importance;
step S22: determining the number of inputs and outputs of the control system according to the nominal controlled object, and determining the structure of the weighting function;
step S23: performing algorithm coding on the parameter to be optimized by adopting a real-value coding strategy, and defining a search space of the parameter to be optimized;
step S24: randomly generating position information X ═ X of whale individual1,…,XN]As initial parameters to be optimized, and initializing algorithm parameters;
step S25: cycle 1, start iterative calculations: first, a weighting function W is determinedsAnd WtThen calculating the standard H∞Each matrix in the control is solved for the controller K based on the LMI method, thereby calculating the active control fcAnd finally calculating the fitness F (X) according to the control systemi)。
Step S26: judging whether an algorithm termination condition is met: if the Cycle is satisfied>TmaxTerminating iteration and finding out an individual position with the optimal fitness value as an optimal position X; otherwise, the process advances to step S27;
step S27: updating each individual location:
step S28: calculating the updated population fitness, and replacing the optimal position in the original population by the updated optimal position if the fitness of the optimal individual in the updated population is superior to the fitness of the optimal individual in the original population; otherwise, keeping the optimal position of the original population unchanged;
step S29: and repeating the steps S26-S28 until the algorithm is finished, wherein the output optimal individual position is the optimization parameter of the mixed sensitivity weighting function.
4. An improved semi-active H according to claim 3∞The robust control method is characterized in that: the weighting function WsAnd WtThe structure of (1) is in a first-order regular form, and a diagonalized real rational function matrix is adopted.
5. An improved semi-active H according to claim 3∞The robust control method is characterized in that: in step S25, the calculation fitness F (X) is calculatedi) First, PSTH is determined∞Whether the open loop system is stable or not, if the system is not stable, let F (X)i) 1, noThen, continue to judge PSTH∞Whether the CVL closed-loop semi-active control system is stable, if not, let F (X)i) Otherwise, F (X) is calculated according to the formula defined in step S21i)。
6. An improved semi-active H according to claim 3∞The robust control method is characterized in that: the step S27 specifically includes:
when the probability p is less than 0.5, a shrink wrapping mechanism is adopted, specifically:
if | A | ≧ 1, randomly determining whale individual position X in current population rangei,randAnd updating the location of the individual using the following formula:
Figure FDA0002304375910000031
in the formula, A ═ 2 a ═ k1A, where a ∈ [0,2 ]]，k1∈[0,1]，
Figure FDA0002304375910000032
C＝2×k2，k2∈[0,1]；
If | A | <1, the location of the individual is updated using the following equation:
Figure FDA0002304375910000033
in the formula,
Figure FDA0002304375910000041
wherein XleaderThe optimal individuals in the previous round are selected;
when the probability p is more than or equal to 0.5, executing spiral position updating, specifically:
Xi k+1＝D×eblcos(2πl)+Xleader；
wherein D ═ Xleader-Xi k|，b＝1,l＝(a2-1)×rand+1,a2∈[-2,-1]。
7. An improved semi-active H according to claim 6∞The robust control method is characterized in that: after the position of each individual is updated in step S27, it is determined whether each parameter exceeds a preset value range, and if any parameter exceeds the value range, the parameter is made equal to the corresponding parameter of the optimal solution in the previous iteration.
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Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111722533A (en) * 2020-06-29 2020-09-29 南京航空航天大学 Sliding mode prediction fault-tolerant control method for multi-time-lag system containing sensor faults
CN115421372A (en) * 2022-08-31 2022-12-02 广东电网有限责任公司 Process signal accelerator and acceleration observation method
CN116243606A (en) * 2023-03-03 2023-06-09 中国华能集团清洁能源技术研究院有限公司 Fan side robust controller configuration method and system based on sensitivity controller

Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110442020A (en) * 2019-06-28 2019-11-12 南京航空航天大学 A kind of novel fault tolerant control method based on whale optimization algorithm

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110442020A (en) * 2019-06-28 2019-11-12 南京航空航天大学 A kind of novel fault tolerant control method based on whale optimization algorithm

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
LIN, XF等: "A shuffled frog-leaping algorithm based mixed-sensitivity H control of a seismically excited structural building using MR dampers", 《JOURNAL OF VIBRATION AND CONTROL》 *
王杰等: "基于约束多目标免疫算法的H_∞混合灵敏度加权阵选择", 《电力自动化设备》 *
颜桂云等: "MR阻尼器对建筑结构地震反应的半主动H_∞控制", 《工程力学》 *

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111722533A (en) * 2020-06-29 2020-09-29 南京航空航天大学 Sliding mode prediction fault-tolerant control method for multi-time-lag system containing sensor faults
CN115421372A (en) * 2022-08-31 2022-12-02 广东电网有限责任公司 Process signal accelerator and acceleration observation method
CN115421372B (en) * 2022-08-31 2024-07-23 广东电网有限责任公司 Process signal accelerator and acceleration observation method
CN116243606A (en) * 2023-03-03 2023-06-09 中国华能集团清洁能源技术研究院有限公司 Fan side robust controller configuration method and system based on sensitivity controller

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