CN110865541B - Structure semi-active optimal prediction control method - Google Patents
Structure semi-active optimal prediction control method Download PDFInfo
- Publication number
- CN110865541B CN110865541B CN201911198626.7A CN201911198626A CN110865541B CN 110865541 B CN110865541 B CN 110865541B CN 201911198626 A CN201911198626 A CN 201911198626A CN 110865541 B CN110865541 B CN 110865541B
- Authority
- CN
- China
- Prior art keywords
- optimal
- control
- acceleration
- lqg
- controller
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000000034 method Methods 0.000 title claims abstract description 35
- 241000283153 Cetacea Species 0.000 claims abstract description 50
- 230000004044 response Effects 0.000 claims abstract description 49
- 238000005457 optimization Methods 0.000 claims abstract description 35
- 238000004422 calculation algorithm Methods 0.000 claims abstract description 28
- 238000013461 design Methods 0.000 claims abstract description 23
- 230000007246 mechanism Effects 0.000 claims abstract description 6
- 230000001537 neural effect Effects 0.000 claims abstract description 4
- 230000001133 acceleration Effects 0.000 claims description 68
- 238000006073 displacement reaction Methods 0.000 claims description 64
- 230000006870 function Effects 0.000 claims description 31
- 238000013016 damping Methods 0.000 claims description 26
- 238000012549 training Methods 0.000 claims description 26
- 239000010410 layer Substances 0.000 claims description 23
- 239000011229 interlayer Substances 0.000 claims description 15
- 230000002441 reversible effect Effects 0.000 claims description 13
- 239000011159 matrix material Substances 0.000 claims description 12
- 238000005070 sampling Methods 0.000 claims description 12
- 230000008569 process Effects 0.000 claims description 8
- 238000004364 calculation method Methods 0.000 claims description 7
- 238000009825 accumulation Methods 0.000 claims description 6
- 230000003044 adaptive effect Effects 0.000 claims description 4
- 238000005259 measurement Methods 0.000 claims description 4
- 241000170545 Iago Species 0.000 claims description 3
- 230000009471 action Effects 0.000 claims description 3
- 230000003111 delayed effect Effects 0.000 claims description 3
- 238000011161 development Methods 0.000 claims description 3
- 230000002087 whitening effect Effects 0.000 claims description 3
- 229910052731 fluorine Inorganic materials 0.000 claims description 2
- 125000001153 fluoro group Chemical group F* 0.000 claims description 2
- 230000000694 effects Effects 0.000 abstract description 10
- 230000007547 defect Effects 0.000 abstract description 2
- 230000002401 inhibitory effect Effects 0.000 abstract description 2
- 238000010586 diagram Methods 0.000 description 15
- 238000004590 computer program Methods 0.000 description 7
- 238000012545 processing Methods 0.000 description 5
- 238000011160 research Methods 0.000 description 4
- 230000008901 benefit Effects 0.000 description 3
- 238000003860 storage Methods 0.000 description 3
- 230000002068 genetic effect Effects 0.000 description 2
- 230000004048 modification Effects 0.000 description 2
- 238000012986 modification Methods 0.000 description 2
- 238000010521 absorption reaction Methods 0.000 description 1
- 230000002411 adverse Effects 0.000 description 1
- 238000013528 artificial neural network Methods 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000008859 change Effects 0.000 description 1
- 239000000470 constituent Substances 0.000 description 1
- 230000008602 contraction Effects 0.000 description 1
- 238000009795 derivation Methods 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 230000005284 excitation Effects 0.000 description 1
- 238000001914 filtration Methods 0.000 description 1
- 230000000670 limiting effect Effects 0.000 description 1
- 238000004519 manufacturing process Methods 0.000 description 1
- 230000004060 metabolic process Effects 0.000 description 1
- 230000003287 optical effect Effects 0.000 description 1
- 230000036961 partial effect Effects 0.000 description 1
- 230000009467 reduction Effects 0.000 description 1
- 230000002829 reductive effect Effects 0.000 description 1
- 230000035939 shock Effects 0.000 description 1
Images
Classifications
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
- G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
- G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
Landscapes
- Engineering & Computer Science (AREA)
- Health & Medical Sciences (AREA)
- Artificial Intelligence (AREA)
- Computer Vision & Pattern Recognition (AREA)
- Evolutionary Computation (AREA)
- Medical Informatics (AREA)
- Software Systems (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Automation & Control Theory (AREA)
- Feedback Control In General (AREA)
Abstract
The invention relates to a structure semi-active optimal predictive control method, which comprises the steps of firstly introducing a gray prediction system to predict the input of an LQG controller, then carrying out optimal design on the parameters of the LQG controller by utilizing a whale optimization algorithm, and finally realizing the semi-active predictive control of a structure by combining with a self-adaptive neural fuzzy inference system. The invention not only can effectively solve the problem that the weighting function of the active controller is difficult to determine, make up for the defect of insufficient control effect of the traditional LQG, but also can improve the control signal precision of the MR damper. In addition, the invention can effectively compensate the time lag in the system through a prediction mechanism, thereby enabling the control system to fully exert the performance of the magneto-rheological damper and finally realizing the purpose of effectively inhibiting the response of the building structure.
Description
Technical Field
The invention relates to the technical field of civil structure seismic design, in particular to a structure semi-active optimal predictive control method.
Background
The superiority and inferiority of the earthquake resistance of the civil structure concern the safety of human life and property, and how to improve the earthquake resistance of the civil structure is always a research focus in the engineering field. The magnetorheological damper is an intelligent semi-active control device with a promising application prospect, has the advantages of an active control device and a passive control device, and has a research hotspot in the field of civil engineering based on the building structure damping technology. In order to fully exert the excellent damping characteristic of the magnetorheological damper, the semi-active control research based on the MR damper still needs to be further developed.
A linear quadratic gaussian controller (LQG) is a highly suitable optimal control, and has been widely used in vibration control. It can also be used in semi-active control of structures as the active controller responsible for calculating the desired control force. The LQG adopts a filtering observer capable of estimating the full-state Kalman according to partial states, so that the problem that a plurality of states are difficult to measure is avoided, and the risk of sensor failure possibly caused by the need of using a large number of sensors is reduced to a great extent. This largely remedies the drawbacks of the Linear Quadratic Regulator (LQR), since LQR is a full-state feedback controller.
The selection of the weighting matrix (especially Q and R) in the controller LQG has a great influence on the control effect, but the determination of the weighting matrix depends on expert experience, and the manual design method is not only inefficient, but also has limited control effect and even has adverse effect on the controlled system. Currently, it has become a research hotspot to adjust the weighting matrix by using an evolutionary algorithm. It has been proposed to use genetic algorithms to adjust the weighting matrices Q and R of the linear quadratic optimal controller (see for example european patent CN106707752A) to ensure good dynamic performance of the control voltage source STATCOM. However, the genetic algorithm is a traditional random optimization algorithm and is easy to fall into a local optimal solution.
In addition, in order to further improve the effect of semi-active control, a relatively accurate inverse model of the magnetorheological damper needs to be adopted, and the function of the inverse model is to calculate the control signal of the damper according to the ideal control force. As a non-parametric intelligent modeling strategy, the Adaptive Neural Fuzzy Inference System (ANFIS) has the advantages of both a neural network and a fuzzy system, and the modeling precision of the ANFIS is often superior to that of parametric modeling.
On the other hand, besides improving the control effect of the control algorithm, the influence of the time lag problem on the control algorithm is still under deep study. The time lag can affect the performance of a control system to different degrees, and the larger time lag can reduce the shock absorption effect of the structure and even amplify the earthquake response of the structure.
Disclosure of Invention
In view of this, the present invention aims to provide a structural semi-active optimal predictive control method, which can not only effectively solve the problem that the weighting function of the active controller is difficult to determine, make up for the defect of insufficient control effect of the conventional LQG, but also improve the control signal accuracy of the MR damper. In addition, the invention can effectively compensate the time lag in the system through a prediction mechanism, thereby enabling the control system to fully exert the performance of the magneto-rheological damper and finally realizing the purpose of effectively inhibiting the response of the building structure.
The invention is realized by adopting the following scheme: a semi-active optimal predictive control method for a structure includes the steps of firstly introducing a gray prediction system to predict input of an LQG controller, then carrying out optimization design on parameters of the LQG controller by utilizing a whale optimization algorithm, and finally combining an adaptive neural fuzzy inference system to achieve semi-active predictive control of the structure.
Further, the method specifically comprises the following steps:
step S1: connecting a gray prediction system to the output end of the acceleration sensor, so that the gray prediction system corrects the delayed acceleration response in real time and outputs a predicted value of the acceleration response;
step S2: calculating the full-state response of the building structure, namely the displacement and the speed of all floors according to the predicted value of the acceleration response by using a Kalman filter observer of the controller LQG;
step S3: performing constrained multi-objective optimization design on the controller LQG by utilizing a whale optimization algorithm, and optimizing the feedback gain of the LQG;
step S4: calculating the ideal control force of the control system by using the controller LQG optimized in the step S3 based on the full-state response;
step S5: training an ANFIS reverse model based on the forward model of the magnetorheological damper, so that the ideal control force obtained in the step S4 is converted into a control signal of the magnetorheological damper;
step S6: and taking the control signal as the input of the forward model of the magnetorheological damper, and calculating by using the forward model of the magnetorheological damper to obtain the damping force required by the structural damping.
The invention combines whale optimization algorithm with LQG controller to form an improved quadratic Gaussian optimal control. And the optimal control is combined with an ANFIS reverse model of the magneto-rheological damper to form a semi-active control of structural vibration based on the magneto-rheological damper. In addition, a grey prediction system is introduced on the basis of the semi-active control, so that a predicted semi-active control is formed.
Further, step S1 specifically includes the following steps:
step S11: generating the original sequence of numbers: is provided withThe model dimension of the grey prediction system is m, and the acceleration x of the ith floor at the current moment is acquired i (n) and acceleration x at m-1 moments before it i (n-1)，x i (n-2)，…x i (n-m +1), generating a raw data sequence:
in the formula,
is the ith layer acceleration data sequence of m-dimensional discrete sampling, and n is the current sampling moment;
step S12: the raw data is preprocessed as follows:
in the formula, d i Is the maximum value of the absolute value of the acceleration of the ith floor;
step S13: performing accumulation operation on the preprocessed data to generate
Wherein AGO represents an accumulation operation;
step S14: generating a sequence of adjacent mean numbers:
step S15: gray modeling was performed and the following whitening equation was solved:
in the formula, parameter A gi And B gi Are respectively as
The development coefficient vector and the gray action vector of (1);
step S16: and (4) accumulating and subtracting to generate a predicted value of the step r:
in the formula, IAGO represents the subtraction operation;
step S17: and (3) restoring the data to obtain a final predicted value of the step r:
step S18: judging whether k is equal to m, if so, ending the process, otherwise, making k equal to k +1, updating the sequence by the concept of equal dimension innovation and adopting the following formula, and returning to the step S12:
further, in step S11, the gray prediction system uses an equal-dimensional innovation model, and the original data in the model is updated in real time; the acceleration at the oldest moment is continuously eliminated while the acceleration at the newest moment is supplemented in each sampling; if the first digit of the generated original digit sequence is equal to 0, the collection is carried out again until a value which is not 0 is collected.
Further, step S3 specifically includes the following steps:
step S31: determining a weighting matrix Q of a Kalman filter observer in a controller LQG e And R e ；
Step S32: an optimization objective function is determined as follows:
Obj＝β×J 1 +(α-β)×J 2 +(1-α)×J 3 ；
wherein,
in the formula, Obj is also a fitness function in the following whale optimization algorithm. x is the number of i (t)、x di (t) and
the relative displacement, the interlayer displacement and the absolute acceleration of the ith layer are controlled respectively; x is the number of unc 、x d,unc And
the maximum relative displacement, the maximum interlayer displacement and the maximum absolute acceleration when the control is not carried out are respectively obtained; j. the design is a square 1 、J 2 And J 3 Is a single objective function that minimizes maximum relative displacement, maximum interlayer displacement, and maximum absolute acceleration, respectively, and α and β are weight coefficients reflecting relative importance;
step S33: determining the structures of weighting matrixes Q and R of the optimal feedback gain of the LQG controller according to the attributes and the control target of the controlled object, and determining the number and the value range of the parameters to be optimized in the matrixes;
step S34: randomly generating position information X ═ X of whale individual 1 ，...，X N ]Initializing population size N and number of iterations T max ；
Step S35: calculating the optimal feedback gain G, feedback control force and fitness function value f (X) of each individual of the LQG controller i ) (ii) a Then finding out an individual position with the optimal fitness value as an optimal position X; let j equal to 1, and proceed to step S36;
step S36: performing iterative calculation to make j equal to j +1, updating a and k 1 、A、C、D、l；
Step S37: when the probability p is less than 0.5, adopting a contraction surrounding mechanism, specifically:
if | A | ≧ 1, randomly determining whale individual position X in current population range i，rand And updating the location of the individual using the following formula:
in the formula, A ═ 2a ═ k 1 A, where a ∈ [0,2 ]]，k 1 ∈[0，1]，
k 2 ∈[0，1]；
If | A | <1, the location of the individual is updated using the following equation:
in the formula (I), wherein,
wherein X leader The 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:
X i k+1 ＝D×e bl cos(2πl)+X leader ；
wherein D ═ X leader -X i k |，b＝1，l＝(a 2 -1)×rand+1，a 2 ∈[-2，-1]；
Step S38: after each individual completes position updating, judging whether the position exceeds a preset value range, if the updated parameter is larger than an upper limit value, taking the upper limit value, and if the parameter is smaller than a lower limit value, taking the lower limit value;
step S39: calculating the updated population fitness, and replacing the optimal whale position in the original population with the optimal whale position in the new population if the fitness of the optimal whale individual in the new population is better than that of the optimal whale individual in the original population; otherwise, keeping the position of the optimal whale in the original population unchanged;
step S310: recording the position and fitness of the optimal whale individual at the moment; if j < T max Returning to step S36, otherwise, proceeding to step S311;
step S311: and outputting the optimal individual positions, namely the optimal parameters of the weighting matrixes Q and R.
Further, in step S35, if the feedback control force exceeds the maximum range of the magnetorheological damper, the fitness function value f (X) is set to make the feedback control force be the ideal control force in the semi-active closed-loop control system i )＝1。
Further, step S4 specifically includes the following steps:
step S41: the predicted value of the acceleration output from the gray prediction system in step S1 and the ideal control force (i.e., the feedback control force f) output from the LQG controller are compared d (t)) as an input to the Kalman filter observer of the controller LQG, Q is set based on S31 e And R e The filter observer is made to output an estimated value of the full-state response z (t)
The constructed Kalman filter observer is expressed as:
in the formula, K e Is the gain of a Kalman filter observer, represented by Q e And R e Jointly determining;
is a measurement output consisting of n layers of acceleration,
is an estimate of Y (t); A. b and C are system equation of state matrices, f d (t) is a feedback control force, i.e. said desired control force;
step S42: let the control targets of LQG be:
in the formula, q 1 、q 2 And r i Respectively, the maximum relative displacement x max Maximum absolute acceleration
And feedback control component force f di N is the amount of control force, and T is the sampling period. The core of the control is to make the performance index J reach the minimum value by solving the optimal feedback controller. Rewrite J to:
wherein Q is a state variable
R is the feedback control force f d (f d Is formed by the above-mentioned N pieces of f di Constituent diagonal matrices), the parameters of the two weighting matrices are optimally determined based on step S3.
Step S43: according to the optimal control law, the feedback control force of the controller is obtained as follows:
where G is the optimal feedback gain and P is found by the following Riccati equation:
-PA-A T P+PBR -1 B T P-Q＝0
wherein A and B are state equation matrixes of the controlled system and are determined by structural parameters.
Further, in step S5: in the training of ANFIS reverse model, the displacement x (k), speed at the current time
The damping force f (k) output by the forward model of the magnetorheological damper and the voltage u (k-1) at the previous moment serve as input, so that the predictive voltage is output
The training objective is to make the predicted voltage
And the voltage u (k) at the given current instant. When the ANFIS inverse model is trained, it is used in a closed loop control system. At this time, the feedback control force f, which is originally one of the inputs of the ANFIS inverse model, calculated by the WOA-LQG controller d (i.e., ideal control force) replacement, the displacement, velocity, and voltage at the previous time used to train the ANFIS inverse model are replaced with the corresponding actual values in the closed-loop control system.
Further, in steps S5 and S6, the forward model of the magnetorheological damper adopts a phenomenon model.
Further, the displacement, velocity and voltage in the input parameters when training the ANFIS inverse model are obtained from the following signals: generating the displacement of training data by adopting a width-limited white noise signal with the amplitude of-1 m to 1m and the frequency of 0 to 9 Hz; the speed signal is obtained by differentiating the displacement signal; the control voltage is generated by a width-limited white noise signal with the amplitude of 0-10V and the frequency of 0-6 Hz.
Compared with the prior art, the invention has the following beneficial effects:
1. the invention introduces a gray prediction system into the magneto-rheological damper-based linear optimal control (LQG), and solves the time lag problem of the control system to a great extent.
2. The invention solves the problems that the weighting matrix is difficult to determine and the controller can not accurately predict the control force.
3. The four-input-single-output ANFIS reverse model adopted by the invention accurately predicts the control signal of the magnetorheological damper. The reverse model is combined with an improved LQG controller, so that the semi-active control effect based on the magneto-rheological damper is improved.
4. The improved semi-active controller provided by the invention can fully play the vibration damping role of the magnetorheological damper. Although the maximum displacement response, the interlayer displacement response and the acceleration response of the structure are taken as the optimization targets of the LQG, the controller also effectively reduces various responses of other layers of the structure.
5. The design method of the semi-active controller is simple and feasible and is easy to widely popularize.
Drawings
Fig. 1 is a block diagram of a structural semi-active predictive control based on a magnetorheological damper according to an embodiment of the invention.
FIG. 2 is a flow chart of the design of an acceleration response gray prediction system according to an embodiment of the present invention.
FIG. 3 is a flow chart of an LQG optimization design algorithm based on a whale optimization algorithm according to an embodiment of the invention.
FIG. 4 is a graph of the convergence of the whale optimization algorithm of an embodiment of the present invention.
FIG. 5 is a schematic diagram of a four-input-single-output ANFIS inverse model training of a magnetorheological damper according to an embodiment of the invention.
FIG. 6 is a time chart of predicted voltage and target voltage for ANFIS training data in accordance with an embodiment of the present invention.
FIG. 7 is a time-course plot of predicted damping force and target damping force for ANFIS training data in accordance with an embodiment of the present invention.
FIG. 8 is a graph comparing time-course response of top-level displacement with control (no dead time) and without control according to an embodiment of the present invention.
FIG. 9 is a graph comparing time-course response of top layer displacement with control (no dead time) and without control according to an embodiment of the present invention.
FIG. 10 is a graph comparing the response of the acceleration time course of the top layer with control (no time lag) and without control according to the embodiment of the present invention.
Fig. 11 is a comparison graph of the response peaks of all floors according to the embodiment of the present invention. Wherein, (a) is displacement, (b) is interlayer displacement, and (c) is acceleration.
FIG. 12 is a response graph of top level displacement time course in the prediction control according to the embodiment of the present invention.
Fig. 13 is a response diagram of the top acceleration time course in the prediction control according to the embodiment of the present invention.
Detailed Description
The invention is further explained below with reference to the drawings and the embodiments.
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the disclosure herein. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments according to the present application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
As shown in fig. 1, the present embodiment provides a structure semi-active optimal predictive control method, which includes firstly introducing a gray prediction system to predict input of an LQG controller, then performing optimal design on parameters of the LQG controller by using whale optimization algorithm, and finally implementing semi-active predictive control of a structure by combining an adaptive neuro-fuzzy inference system.
In this embodiment, the method specifically includes the following steps:
step S1: connecting a gray prediction system to the output end of the acceleration sensor, so that the gray prediction system corrects the delayed acceleration response in real time and outputs a predicted value of the acceleration response;
step S2: calculating the full-state response of the building structure, namely the displacement and the speed of all floors according to the predicted value of the acceleration response by using a Kalman filter observer of the controller LQG;
step S3: performing constrained multi-objective optimization design on the controller LQG by utilizing a whale optimization algorithm, and optimizing the feedback gain of the LQG;
step S4: calculating the ideal control force of the control system by using the controller LQG optimized in the step S3 based on the full-state response;
step S5: training an ANFIS reverse model based on the forward model of the magnetorheological damper, so that the ideal control force obtained in the step S4 is converted into a control signal of the magnetorheological damper;
step S6: and taking the control signal as the input of the forward model of the magnetorheological damper, and calculating by using the forward model of the magnetorheological damper to obtain the damping force required by the structural damping.
The embodiment combines a whale optimization algorithm with an LQG controller to form an improved quadratic Gaussian optimal control. And the optimal control is combined with an ANFIS reverse model of the magneto-rheological damper to form a semi-active control of structural vibration based on the magneto-rheological damper. In addition, a grey prediction system is introduced on the basis of the semi-active control, and a predicted semi-active control is formed.
In this embodiment, step S1 specifically includes the following steps: the acceleration of the building structure is predicted by adopting a metabolism GM (1, 1) model, taking the acceleration of a first layer as an example, the design flow of a grey prediction system is as follows:
step S11: generating the original sequence of numbers: setting the model dimension of the gray prediction system as m, aiming at the ith floor, acquiring the acceleration x at the current moment i (n) and accelerations x (n-1), x (n-2), … x (n-m +1) at m-1 moments before it, to generate a raw data series:
in the formula,
is the ith layer acceleration data sequence of m-dimensional discrete sampling, and n is the current sampling moment;
step S12: the raw data is preprocessed as follows:
in the formula (d) i Is the maximum value of the absolute value of the acceleration of the ith floor;
step S13: performing accumulation operation on the preprocessed data to generate
Wherein AGO represents an accumulation operation;
step S14: generating a sequence of adjacent mean numbers:
step S15: gray modeling was performed and the following whitening equation was solved:
in the formula, parameter A gi And B gi Are respectively as
The development coefficient vector and the gray action vector of (1);
step S16: and (4) accumulating and subtracting to generate a predicted value of the step r:
in the formula, IAGO represents the subtraction operation;
step S17: and (3) restoring the data to obtain a final predicted value of the step r:
step S18: judging whether k is equal to m, if so, ending the process, otherwise, making k equal to k +1, updating the sequence by the concept of equal dimension innovation and adopting the following formula, and returning to the step S12:
in this embodiment, in step S11, the gray prediction system uses an equal-dimensional innovation model, and the original data in this model is updated in real time; the acceleration at the oldest moment is continuously eliminated while the acceleration at the newest moment is supplemented in each sampling; and if the first digit of the generated original number sequence is equal to 0, performing collection again until a non-0 value is collected. Furthermore, generating a non-zero first digit is an important prerequisite for generating a valid original digit sequence, since if the first digit of the digit sequence is equal to 0, a large prediction error will occur. Therefore, in step S11, if the first digit of the generated original sequence is equal to 0, the collection is performed again until a value other than 0 is collected.
In this embodiment, step S3 specifically includes the following steps:
step S31: determining a weighting matrix Q for a Kalman filter in a controller LQG e And R e ；
Step S32: an optimization objective function is determined as follows:
Obj＝β×J 1 +(α-β)×J 2 +(1-α)×J 3 ；
wherein,
in the formula, Obj is also a fitness function in the following whale optimization algorithm. Since this is a problem of solving a minimum solution, the smaller the fitness in the optimization process, the better; x is a radical of a fluorine atom i (t)、x di (t) and
the relative displacement, the interlayer displacement and the absolute acceleration of the ith layer under control are respectively; x is the number of unc 、x d,unc And
the maximum relative displacement, the maximum interlayer displacement and the maximum absolute acceleration when the control is not carried out are respectively obtained; j is a unit of 1 、J 2 And J 3 Is a single objective function that minimizes maximum relative displacement, maximum interlayer displacement, and maximum absolute acceleration, respectively, and α and β are weight coefficients reflecting relative importance;
step S33: determining the structures of weighting matrixes Q and R of optimal feedback gains of the LQG controller according to the attributes and the control targets of the controlled objects, and determining the number and value range of parameters to be optimized in the matrixes;
step S34: randomly generating position information X ═ X of whale individual 1 ,...,X N ]Initializing population size N and number of iterations T max ；
Step S35: calculating the optimal feedback gain G, feedback control force and fitness function value f (X) of each individual of the LQG controller i ) (ii) a Then finding out an individual position with the optimal fitness value as an optimal position X; let j equal to 1, and proceed to step S36;
step S36: performing iterative calculation to make j equal to j +1, and updating a and k 1 、A、C、D、l；
Step S37: 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 range i,rand And updating the location of the individual using the following formula:
in the formula, A ═ 2a ═ k 1 A, where a ∈ [0,2 ]]，k 1 ∈[0,1]，
C＝2×k 2 ，k 2 ∈[0,1]；
If | A | <1, the location of the individual is updated using the following equation:
in the formula (I), wherein,
wherein X leader The optimal individuals of the previous round are obtained;
when the probability p is more than or equal to 0.5, executing spiral position updating, specifically:
X i k+1 ＝D×e bl cos(2nl)+X leader ；
wherein D ═ X leader -X i k |，b＝1，l＝(a 2 -1)×rand+1，a 2 ∈[-2，-1]；
Step S38: after each individual completes position updating, judging whether the position exceeds a preset value range, if the updated parameter is larger than an upper limit value, taking the upper limit value, and if the parameter is smaller than a lower limit value, taking the lower limit value;
step S39: calculating the updated population fitness, and replacing the optimal whale position in the original population with the optimal whale position in the new population if the fitness of the optimal whale individual in the new population is better than that of the optimal whale individual in the original population; otherwise, keeping the position of the optimal whale in the original population unchanged;
step S310: recording the position and fitness of the optimal whale individual at the moment; if j is<T max Returning to step S36, otherwise, proceeding to step S311;
step S311: and outputting the optimal individual positions, namely the optimal parameters of the weighting matrixes Q and R.
In the present embodiment, in step S35, if the feedback control force is the ideal control force in the semi-active closed-loop control system, the feedback control force is determined to be the ideal control forceIf the control force exceeds the maximum range of the magneto-rheological damper, the fitness function value f (X) is adjusted i )＝1。
In this embodiment, step S4 specifically includes the following steps:
step S41: the predicted value of the acceleration output from the gray prediction system in step S1 and the ideal control force (i.e., the feedback control force f) output from the LQG controller are compared d (t)) as an input to the Kalman filter observer of the controller LQG, based on Q set at S31 e And R e The filter observer is made to output an estimated value of the full-state response z (t)
The constructed Kalman filter observer is expressed as:
in the formula, K e Is the gain of a Kalman filter observer, represented by Q e And R e Jointly determining;
is a measurement output consisting of n layers of acceleration,
is an estimate of Y (t); A. b and C are the system equation of state matrix, f d (t) is a feedback control force, i.e. said desired control force;
step S42: let the control targets of LQG be:
in the formula, q 1 、q 2 And r i Respectively, the maximum relative displacement x max Maximum absolute acceleration
And feedback controlComponent force f di N is the amount of control force, and T is the sampling period. The core of the control is that the performance index J reaches the minimum value by solving the optimal feedback controller, and the J is rewritten as follows:
wherein Q is a state variable
R is the feedback control force f d (f d Is formed by the above-mentioned N pieces of f di A diagonal matrix formed), wherein the parameters of the weighting matrices Q and R are determined by the optimization of step S3;
step S43: according to the optimal control law, the feedback control force of the controller is obtained as follows:
where G is the optimal feedback gain and P is found by the following Riccati equation:
-PA-A T P+PBR -1 B T P-Q＝0
wherein A and B are state equation matrixes of the controlled system and are determined by structural parameters.
In the present embodiment, in step S5: in the training of ANFIS reverse model, the displacement x (k), speed at the current time
The damping force f (k) output by the forward model of the magnetorheological damper and the voltage u (k-1) at the previous moment are used as input, so that the damping force f (k) and the voltage u (k-1) at the previous moment are output to be predicted voltage
The training objective is to make the predicted voltage
And the root mean square difference between the voltages u (k) at a given current instant is minimized. When the ANFIS inverse model is trained, it is used in a closed loop control system. At this time, the feedback control force f, which is originally one of the inputs of the ANFIS inverse model, calculated by the WOA-LQG controller d (i.e., ideal control force) replacement, the displacement, velocity, and voltage at the previous time used to train the ANFIS inverse model are replaced with the corresponding actual values in the closed-loop control system.
In the present embodiment, in steps S5 and S6, the forward model of the magnetorheological damper adopts a phenomenon model. The membership functions for each input and output in ANFIS are triangular membership functions.
In the present embodiment, the displacement, the velocity and the voltage in the input parameters when the ANFIS inverse model is trained are respectively obtained by the following signals: generating the displacement of training data by adopting a width-limited white noise signal with the amplitude of-1 m to 1m and the frequency of 0 to 9 Hz; the speed signal is obtained by differentiating the displacement signal; the control voltage is generated by a width-limited white noise signal with the amplitude of 0-10V and the frequency of 0-6 Hz. The method comprises the steps of performing signal processing on displacement input and voltage input by adopting a data filter design module, wherein the response type is band-pass, and the design method is Butterworth.
Particularly, in the embodiment, the semi-active control system is designed by using a method combining a gray prediction system with a whale optimization algorithm, an LQG controller and an ANFIS inverse model of a magnetorheological damper, and the method is suitable for vibration semi-active prediction control of the building structure based on the magnetorheological damper. The method not only can achieve an ideal structure vibration reduction control effect, but also can widely popularize the application of the LQG design method and the grey prediction system in structure semi-active control, and obtain considerable social and economic benefits.
Next, the present embodiment takes a specific object as an example to more specifically describe and verify the above process. The damping object of the embodiment of the invention is a shear frame structure of five floors, and the applied dynamic excitation is 1940El-Centro wave with 2.5 times acceleration peak. 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:
fig. 1 is a block diagram of the structural semi-active predictive control based on the magnetorheological damper in the embodiment. It consists of these two parts. The working principle is as follows: firstly, a gray prediction system is connected with the output end of an acceleration sensor, so that the acceleration sensor can correct lagged acceleration response in real time and output a predicted value of the acceleration. And then, calculating the full-state response of the building structure according to the predicted value of the acceleration response by using a Kalman filter observer in the LQG. Then, based on the full-state response, the ideal control force of the control system is calculated using the LQG. And performing band-constrained multi-objective optimization on the LQG by adopting WOA. And finally, establishing a reverse model of the magnetorheological damper through ANFIS, so that the ideal control force is converted into a control signal of the damper. It should be noted that in practice the forward model of the magnetorheological damper has not only the control signal but also the displacement and velocity of the damper (see fig. 5). The input of the ANFIS inverse model in the closed-loop control system is not only the ideal control force at the current time in fig. 1, but also the displacement, velocity and voltage value at the previous time. Before being used in a closed-loop control system, the inverse model needs to be trained in advance, and a training schematic diagram of the inverse model is shown in FIG. 5.
In the MR damper building structure system, the total number of the structural floors is 5, and the input of the Kalman filter observer is 5 acceleration responses. Therefore, 5 corresponding equal-dimensional innovation GM (1, 1) models need to be established to predict the acceleration. Taking the acceleration of the first layer as an example, fig. 2 is a design flow chart of the acceleration response gray prediction system of the layer according to the embodiment of the present invention.
Fig. 3 is a flowchart of an LQG optimization design algorithm based on whale optimization algorithm according to an embodiment of the present invention. FIG. 4 is a graph of the convergence of the whale optimization algorithm of an embodiment of the present invention. The optimization specific steps can be detailed as follows:
step 1: making Kalman filtersQ e ＝0.0001,R e ＝10 -7 ×I 5×5 ；
Step 2: an optimization objective function is determined as follows:
Obj＝β×J 1 +(α-β)×J 2 +(1-α)×J 3
wherein,
wherein x is i (t)、x di (t) and
respectively the relative displacement, the interlayer displacement and the absolute acceleration of the ith layer under control. x is the number of unc 、x d,unc And x a,unc The maximum relative displacement, the maximum interlayer displacement and the maximum absolute acceleration when the control is not carried out are respectively. J. the design is a square 1 、J 2 And J 3 Is a single objective function that minimizes the maximum relative displacement, the maximum interlayer displacement, and the maximum absolute acceleration, respectively, and α and β are weight coefficients reflecting relative importance, equal to 0.5 and 0.4, respectively. In the whale optimization algorithm, the multi-objective function is used as a fitness function f.
Step 3: determining the structures of weighting matrixes Q and R, the quantity of parameters to be optimized in the matrixes and the value range through deduction calculation according to the attributes and the control targets of the controlled objects;
let the control target of LQG be
Wherein i is 1,2, 3; q. q.s 1 、q 2 、r 1 、r 2 And r 3 Respectively, the maximum relative displacement x max Maximum absolute acceleration
And a feedback control force f d1 、f d2 And f d3 The weighting coefficient of (2). Through derivation calculation, the weighting matrix for obtaining the optimal feedback gain G is respectively:
where subscripted C, K and M represent the corresponding elements of the damping, stiffness and mass matrices of the structure, respectively. q. q.s 1 、q 2 、r 1 、r 2 And r 3 Parameters to be optimized of the weighting matrix are debugged, and the value ranges of the parameters are selected as follows:
q 1 ,q 2 ∈[10 -2 ,10 6 ],r 1 ,r 2 ,r 3 ∈[10 -6 ,10 3 ]
step 4: algorithm initialization: randomly generating position information X ═ X of whale individual 1 ,…,X N ]As initial parameters to be optimized, and initializing algorithm parameters (including population size N, iteration number T) max Objective function weighting coefficients, etc.); wherein, let N equal 30, T max ＝100。
Step 5: calculating the fitness of the population: calculating the optimal feedback gain G, the control force and the fitness function value f (X) of each individual in turn i ) Wherein if the control force exceeds the maximum range of the magnetorheological damper, let f (X) i ) 1. Then finding out an individual position with the optimal fitness value as an optimal position X;
step 6: and (3) iterative calculation: if j is<T max Update a, k 1 A, C, D, l, and the like, and the specific definition is shown below;
step 7: when the probability p is less than 0.5, a shrink wrapping mechanism is adopted, specifically:
if | A | ≧ 1(A ═ 2 × a × k 1 A, where a ∈ [0,2 ]],k 1 ∈[0,1]) Within the current populationRandomly determining individual position X of whale i,rand And updating the location of the individual using the following formula:
wherein,
if | A | <1, the location of the individual is updated using the following equation:
wherein,
wherein X leader The 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:
X i k+1 ＝D×e bl cos(2πl)+X leader
wherein D ═ X leader -X i k |，b＝1，l＝(a 2 -1)×rand+1，a 2 ∈[-2，-1]. After each individual completes the position update, whether the position exceeds the value range needs to be judged, otherwise, the calculation of the controller may be disabled.
Step 8: after each individual completes position updating, judging whether the position exceeds a preset value range, if the updated parameter is larger than an upper limit value, taking the upper limit value, and if the parameter is smaller than a lower limit value, taking the lower limit value;
step 9: calculating the updated population fitness, and replacing the optimal whale position in the original population with the optimal whale position in the new population if the fitness of the optimal whale individual in the new population is better than that of the optimal whale individual in the original population; otherwise, keeping the position of the optimal whale in the original population unchanged;
step 10: record this moment mostThe position and fitness of the optimal whale individual. If j > T max Step11 is executed; otherwise, until the condition is satisfied, j equals j +1, and steps S36 to S310 are repeated.
Step 11: and outputting optimal individual positions, namely optimal parameters of the weighting matrixes Q and R, and solving the ideal control force.
FIG. 5 is a schematic diagram of a four-input-single-output ANFIS inverse model training of the magnetorheological damper according to the embodiment of the invention. Firstly, generating displacement by adopting a width-limited white noise signal with the amplitude of-1 m to 1m and the frequency of 0Hz to 9 Hz; the speed signal is obtained by differentiating the displacement signal; the control voltage is generated by a width-limited white noise signal with the amplitude of 0-10V and the frequency of 0-6 Hz. Aiming at the two kinds of width-limited white noise signals, a data filter design module is adopted to process the signals, wherein the response type is band-pass, and the design method is Butterworth. The data acquisition time is 10s, the acquisition frequency is 1000Hz, and finally 10000 pairs of training data are generated. Then, the obtained displacement x (k), velocity
And the control voltage u (k) is used as the input of the forward model, so that the damping force f (k) is calculated. Wherein, a phenomenon model is adopted as a forward model of the magnetorheological damper. Then, adding x (k),
f (k) and the control voltage u (k-1) at the previous moment are used as input data in the process of training ANFIS, so that the ANFIS finally outputs an accurate predicted voltage
Training the target to predict the voltage
The root mean square deviation from the given actual voltage u (k) is minimized. And when the training is finished, obtaining a final reverse model of the magnetorheological damper. The ANFIS has 3 membership functions for each input and output, all being triangular membership functions.
FIG. 6 is a time chart of predicted voltage and target voltage for ANFIS training data in accordance with an embodiment of the present invention. FIG. 7 is a time-course plot of predicted damping force and target damping force for ANFIS training data in accordance with an embodiment of the present invention. As can be seen, the time-course graphs of the predicted voltage and the target voltage are in good agreement. The time-course graphs of the predicted damping force and the target damping force are also very consistent, and the fact that the target damping force can be accurately tracked according to the predicted damping force obtained by the reverse model is shown.
FIG. 8 is a graph comparing time-course response of top-level displacement with control (no dead time) and without control according to an embodiment of the present invention. FIG. 9 is a graph comparing time course response of displacement between top layers with control (no dead time) and without control according to the embodiment of the present invention. FIG. 10 is a graph comparing time course response of top layer acceleration with and without control according to an embodiment of the present invention. Therefore, the semi-active optimal control can effectively reduce three responses of the top layer of the structure.
Fig. 11 is a comparison graph of the response peaks of all floors according to the embodiment of the present invention. It can be seen that although the optimization target is the maximum displacement, the peak value of the interlayer displacement and the acceleration, the semi-active optimal control of the invention can effectively reduce all the response peak values of all the floors.
FIG. 12 is a response graph of top level displacement time course in the prediction control according to the embodiment of the present invention. Fig. 13 is a response diagram of the top acceleration time course in the prediction control according to the embodiment of the present invention. The time lag of the control system is 100ms, and the semi-active optimal predictive control can still effectively inhibit the seismic response of the structure when the time lag factor is considered.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and so forth) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The foregoing is directed to preferred embodiments of the present invention, other and further embodiments of the invention may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow. However, any simple modification, equivalent change and modification of the above embodiments according to the technical essence of the present invention will still fall within the protection scope of the technical solution of the present invention.
Claims (6)
1. The semi-active optimal predictive control method of the structure is characterized in that a gray prediction system is introduced to predict the input of an LQG controller, then an optimal design is carried out on parameters of the LQG controller by utilizing a whale optimization algorithm, and finally semi-active predictive control of the structure is realized by combining an adaptive neural fuzzy inference system; the method specifically comprises the following steps:
step S1: connecting a gray prediction system to the output end of the acceleration sensor, so that the gray prediction system corrects the delayed acceleration response in real time and outputs a predicted value of the acceleration response;
step S2: calculating the full-state response of the building structure, namely the displacement and the speed of all floors according to the predicted value of the acceleration response by using a Kalman filter observer of the controller LQG;
step S3: utilizing a whale optimization algorithm to carry out constrained multi-objective optimization design on the controller LQG, and optimizing the feedback gain of the LQG;
step S4: calculating the ideal control force of the control system by using the controller LQG optimized in the step S3 based on the full-state response;
step S5: training an ANFIS reverse model based on the forward model of the magnetorheological damper, so that the ideal control force obtained in the step S4 is converted into a control signal of the magnetorheological damper;
step S6: the control signal is used as the input of a forward model of the magnetorheological damper, and the damping force required by structural damping is calculated by utilizing the forward model of the magnetorheological damper;
step S1 specifically includes the following steps:
step S11: generating the original sequence of numbers: setting the model dimension of the gray prediction system as m, and aiming at the ith floor, acquiring the acceleration x of the current moment i (n) and acceleration x at m-1 moments before it i (n-1)，x i (n-2)，…x i (n-m +1), generating a raw data sequence:
in the formula,
is the ith layer acceleration data sequence of m-dimensional discrete sampling, and n is the current sampling moment;
step S12: the raw data is preprocessed as follows:
in the formula (d) i Is the maximum value of the absolute value of the acceleration of the ith floor;
step S13: performing accumulation operation on the preprocessed data to generate
Wherein AGO represents an accumulation operation;
step S14: generating a sequence of adjacent mean numbers:
step S15: gray modeling was performed and the following whitening equation was solved:
in the formula, parameter A gi And B gi Are respectively as
The development coefficient vector and the gray action vector of (1);
step S16: and (4) accumulating and subtracting to generate a predicted value of the step r:
in the formula, IAGO represents the subtraction operation;
step S17: and (3) reducing the data to obtain a final predicted value of the step r:
step S18: judging whether k is equal to m, if so, ending the process, otherwise, making k equal to k +1, updating the sequence by the concept of equal dimension innovation and adopting the following formula, and returning to the step S12:
in step S11, the grey prediction system adopts an equal-dimensional innovation model, and original data in the model are updated in real time; the acceleration at the oldest moment is continuously eliminated while the acceleration at the newest moment is supplemented in each sampling; if the first digit of the generated original digit sequence is equal to 0, then the collection is carried out again until a non-0 value is collected;
step S3 specifically includes the following steps:
step S31: determining a weighting matrix Q of a Kalman filter observer in a controller LQG e And R e ；
Step S32: an optimization objective function is determined as follows:
Obj＝β×J 1 +(α-β)×J 2 +(1-α)×J 3 ；
wherein,
in the formula, Obj is also a fitness function in the following whale optimization algorithm; x is the number of i (t)、x di (t) and
the relative displacement, the interlayer displacement and the absolute acceleration of the ith layer are controlled respectively; x is a radical of a fluorine atom unc 、x d,unc And
the maximum relative displacement, the maximum interlayer displacement and the maximum absolute acceleration when the control is not carried out are respectively obtained; j. the design is a square 1 、J 2 And J 3 Is a single objective function that minimizes maximum relative displacement, maximum interlayer displacement, and maximum absolute acceleration, respectively, and α and β are weight coefficients reflecting relative importance;
step S33: determining the structures of weighting matrixes Q and R of optimal feedback gains of the LQG controller according to the attributes and the control targets of the controlled objects, and determining the number and the value range of parameters to be optimized in the matrixes;
step S34: randomly generating position information X ═ X of whale individual 1 ,...,X N ]Initializing the population size N and the number of iterations T max ；
Step S35: calculating the optimal feedback gain G, feedback control force and fitness function value f (X) of each individual of the LQG controller i ) (ii) a Then finding out an individual position with the optimal fitness value as an optimal position X; let j equal to 1, and proceed to step S36;
step S36: performing iterative calculation to make j equal to j +1, updating a and k 1 、A、C、D、l；
Step S37: 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 range i,rand And updating the location of the individual using the following formula:
in the formula, A ═ 2a ═ k 1 A, where a ∈ [0,2 ]]，k 1 ∈[0,1]，
C＝2×k 2 ，k 2 ∈[0,1]；
If | A | <1, the location of the individual is updated using the following equation:
in the formula (I), wherein,
wherein X leader The 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:
wherein D ═ X leader -X i k |，b＝1,l＝(a 2 -1)×rand+1,a 2 ∈[-2,-1]；
Step S38: after each individual completes position updating, judging whether the position exceeds a preset value range, if the updated parameter is larger than an upper limit value, taking the upper limit value, and if the parameter is smaller than a lower limit value, taking the lower limit value;
step S39: calculating the updated population fitness, and replacing the optimal whale position in the original population with the optimal whale position in the new population if the fitness of the optimal whale individual in the new population is better than that of the optimal whale individual in the original population; otherwise, keeping the position of the optimal whale in the original population unchanged;
step S310: recording the position and fitness of the optimal whale individual at the moment; if j is<T max Returning to step S36, otherwise, proceeding to step S311;
step S311: and outputting the optimal individual positions, namely the optimal parameters of the weighting matrixes Q and R.
2. The method according to claim 1, wherein in step S35, if the feedback control force exceeds the maximum measurement range of the magnetorheological damper, the fitness function value f (X) is adjusted so that the feedback control force is the ideal control force in the semi-active closed-loop control system i )＝1。
3. The method according to claim 1, wherein the step S4 specifically includes the following steps:
step S41: the predicted acceleration value output from the gray prediction system and the ideal control force output from the LQG controller in step S1 are input to the Kalman filter observer of the LQG controller, based on the Q set in S31 e And R e The filter observer is made to output an estimated value of the full-state response z (t)
Wherein the Kalman filter observer is represented as:
in the formula, K e Is the gain of the Kalman filter observer, represented by Q e And R e Jointly determining;
is a measurement output consisting of n layers of acceleration,
is an estimate of Y (t); A. b and C are system equation of state matrices, f d (t) is a feedback control force, i.e. said desired control force;
step S42: let the control targets of LQG be:
in the formula, q 1 、q 2 And r i Respectively, the maximum relative displacement x max Maximum absolute acceleration
And feedback control component force f di N is the number of control forces, T is the sampling period; the core of the control is that the optimal feedback controller is obtained, so that the performance index J reaches the minimum value, and the performance index J is rewritten as follows:
wherein Q is a state variable
R is the feedback control force f d Wherein the parameters of the weighting matrices Q and R are determined optimally in step S3, f d Is composed of N f di Forming a diagonal matrix;
step S43: according to the optimal control law, the feedback control force of the controller is obtained as follows:
where G is the optimal feedback gain and P is found by the following Riccati equation:
-PA-A T P+PBR -1 B T P-Q＝0
wherein A and B are state equation matrixes of the controlled system and are determined by structural parameters.
4. According to claim1, the method for controlling semi-active optimal prediction of a structure is characterized in that in step S5: in the training of ANFIS reverse model, the displacement x (k), speed at the current time
The damping force f (k) output by the forward model of the magnetorheological damper and the voltage u (k-1) at the previous moment serve as input, so that the predictive voltage is output
The training objective is to make the predicted voltage
And the voltage u (k) at the given current instant is minimized; when the ANFIS inverse model is trained, it is used in a closed loop control system, at which time the damping force, originally one of the inputs to the ANFIS inverse model, is calculated by the WOA-LQG controller as the feedback control force f d Instead, the displacement, velocity and voltage at the previous time used in the previous ANFIS inverse model training are replaced by the corresponding actual values in the closed-loop control system.
5. The method for semi-active optimal predictive control of a structure of claim 1, wherein in steps S5 and S6, the forward model of the magnetorheological damper is a phenomenon model.
6. The method as claimed in claim 4, wherein the displacement, velocity and voltage of the input parameters during the training of the ANFIS inverse model are obtained from the following signals: generating the displacement of training data by adopting a width-limited white noise signal with the amplitude of-1 m to 1m and the frequency of 0 to 9 Hz; the speed signal is obtained by differentiating the displacement signal; the control voltage is generated by a width-limited white noise signal with the amplitude of 0-10V and the frequency of 0-6 Hz.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201911198626.7A CN110865541B (en) | 2019-11-29 | 2019-11-29 | Structure semi-active optimal prediction control method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201911198626.7A CN110865541B (en) | 2019-11-29 | 2019-11-29 | Structure semi-active optimal prediction control method |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN110865541A CN110865541A (en) | 2020-03-06 |
| CN110865541B true CN110865541B (en) | 2022-09-13 |
Family
ID=69656868
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201911198626.7A Active CN110865541B (en) | 2019-11-29 | 2019-11-29 | Structure semi-active optimal prediction control method |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN110865541B (en) |
Families Citing this family (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112650056B (en) * | 2020-10-14 | 2022-04-01 | 中国海洋大学 | Method, device and equipment for determining vibration reduction control law of ocean platform and storage medium |
| CN112776551B (en) * | 2021-01-28 | 2022-10-25 | 西安交通大学 | Semi-active control method and system for magneto-rheological suspension based on motion pattern |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2005091091A2 (en) * | 2004-03-16 | 2005-09-29 | Modelway S.R.L. | A method and system for controlling semiactive suspensions, for example for vehicles, and corresponding structure and computer-program product |
| CN109725537A (en) * | 2019-01-24 | 2019-05-07 | 闽江学院 | A kind of improved linear optimal semi-active control method |
-
2019
- 2019-11-29 CN CN201911198626.7A patent/CN110865541B/en active Active
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2005091091A2 (en) * | 2004-03-16 | 2005-09-29 | Modelway S.R.L. | A method and system for controlling semiactive suspensions, for example for vehicles, and corresponding structure and computer-program product |
| CN109725537A (en) * | 2019-01-24 | 2019-05-07 | 闽江学院 | A kind of improved linear optimal semi-active control method |
Non-Patent Citations (2)
| Title |
|---|
| 基于地震波灰色预测的结构振动最优控制研究;毕光辉等;《兰州交通大学学报》;20060330;第25卷(第01期);正文第1-5章 * |
| 基于帝国竞争算法和LQG的磁流变阻尼器-建筑结构系统的振动控制;林秀芳等;《振动与冲击》;20180315;第37卷(第05期);正文第1-3章 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN110865541A (en) | 2020-03-06 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN109725537B (en) | Improved linear optimal semi-active control method | |
| CN106125574B (en) | Piezoelectric ceramics mini positioning platform modeling method based on DPI model | |
| CN110865541B (en) | Structure semi-active optimal prediction control method | |
| CN110909859A (en) | Bionic robot fish motion control method and system based on antagonistic structured control | |
| CN107608209A (en) | The feedforward of piezoelectric ceramic actuator and closed loop composite control method, system | |
| CN108008627A (en) | A kind of reinforcement learning adaptive PID control method of parallel optimization | |
| CN110110380B (en) | Piezoelectric actuator hysteresis nonlinear modeling method and application | |
| Chen et al. | Grey Signal Predictor and Evolved Control for Practical Nonlinear Mechanical Systems. | |
| CN109507891B (en) | Semi-active fuzzy control method | |
| CN110824928A (en) | Improved semi-active H infinity robust control method | |
| CN115327927A (en) | Reward function and vibration suppression reinforcement learning algorithm adopting same | |
| CN115167102A (en) | Reinforced learning self-adaptive PID control method based on parallel dominant motion evaluation | |
| CN102566426A (en) | Fractional order parameter adjustment controller algorithm of PI<alpha>D<beta> controller | |
| CN102393645A (en) | Control method of high-speed electro-hydraulic proportional governing system | |
| Fujinaka et al. | Stabilization of double inverted pendulum with self-tuning neuro-PID | |
| CN114330119A (en) | Deep learning-based pumped storage unit adjusting system identification method | |
| Tsokanas et al. | Robust model predictive control for dynamics compensation in real-time hybrid simulation | |
| CN115972216B (en) | Parallel robot forward motion solving method, control method, equipment and storage medium | |
| CN107367929A (en) | Update method, storage medium and the terminal device of Q value matrixs | |
| CN116880191A (en) | Intelligent control method of process industrial production system based on time sequence prediction | |
| CN116341376A (en) | Space thermal ion nuclear power control method based on DDPG deep reinforcement learning algorithm | |
| Al-Ali et al. | Investigation of Optimal Controllers on Dynamics Performance of Nonlinear Active Suspension Systems with Actuator Saturation | |
| CN113255208B (en) | Neural network model predictive control method for series elastic actuator of robot | |
| CN114995106A (en) | PID self-tuning method, device and equipment based on improved wavelet neural network | |
| CN113485099B (en) | Online learning control method of nonlinear discrete time system |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant | ||
| TR01 | Transfer of patent right | ||
| TR01 | Transfer of patent right |
Effective date of registration: 20240115 Address after: 230000 floor 1, building 2, phase I, e-commerce Park, Jinggang Road, Shushan Economic Development Zone, Hefei City, Anhui Province Patentee after: Dragon totem Technology (Hefei) Co.,Ltd. Address before: 200 xiyuangong Road, Shangjie Town, Minhou County, Fuzhou City, Fujian Province Patentee before: MINJIANG University |