CN113128083A - Actuator optimal arrangement method for vibration control of hydraulic arc steel gate - Google Patents
Actuator optimal arrangement method for vibration control of hydraulic arc steel gate Download PDFInfo
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Abstract
The invention discloses an optimal arrangement method of actuators for vibration control of a hydraulic radial steel gate, which comprises the following specific steps of: considering the structural characteristics of the arc-shaped steel gate, establishing a simplified model capable of reflecting the dynamic characteristics of the prototype arc-shaped steel gate; constructing a control equation for the active control of the arc steel gate according to the simplified model; establishing an optimized arrangement model of the number and the positions of the actuators by applying an LOR algorithm; and solving the optimization model and determining an optimal arrangement scheme of the actuators. The method provided by the invention can reduce the blindness of the arrangement of the actuator in the active control of the flow-induced vibration of the radial steel gate, improve the performance of an active control system and ensure the safe operation of the radial steel gate.
Description
Technical Field
The invention belongs to the technical field of hydraulic engineering, and relates to an optimal arrangement method of an actuator for vibration control of a hydraulic radial steel gate.
Background
The vibration problem of hydraulic arc steel gate is the subject of being focused on in the hydraulic engineering field, and because of the diversity of load, the vibration form of arc steel gate also has the diversity, and the vibration mechanism is complicated. At present, in engineering practice, the problem of resonance of the gate is generally solved by optimizing hydraulic conditions and structural dynamic characteristics of the gate so that a low-frequency region of the radial gate avoids a high-energy region of pulsating water pressure, but the method is not effective for all types of vibration, such as parameter vibration and self-excited vibration existing in a certain form, and the vibration is difficult to be reduced by the method. And for the radial steel gate which is already in service, the hydraulic boundary and the structural dynamic characteristic of the gate are difficult to change.
At present, an active control technology for applying an actuator to an arc-shaped steel gate is gradually applied to vibration control of the arc-shaped steel gate, and is a hot research problem of arc-shaped steel gate vibration reduction research. The principle of active control is that on the basis of gate vibration response feedback, an optimal active control force is determined through an active control algorithm in a controller, then an instruction is sent to an actuator, the actuator applies the active control force to a gate, and characteristic parameters (mass, damping and rigidity) of a structure are actively adjusted to adapt to external dynamic load, so that the purpose of suppressing vibration is achieved. To the active control system of arc steel gate, the actuator is the mechanism of exerting of active control power, and the optimal arrangement of the quantity and the position of actuator has important influence to active control, reaches under the prerequisite of anticipating the control effect, should arrange as few as possible actuator, makes to tie the gate structure succinct more, and improper actuator is arranged and will directly influence arc steel gate active control system's performance.
At present, research on the active control technology of the flow-induced vibration of the radial steel gate is still in the theoretical research and numerical simulation stages, especially the arrangement position and the arrangement quantity of the actuators on the radial gate are still blind, and an effective and reasonable actuator arrangement method is not provided.
Disclosure of Invention
The invention aims to provide an optimal arrangement method of actuators for vibration control of a hydraulic radial steel gate, which has the characteristics of reducing the blindness of the arrangement of the actuators in the active control of flow-induced vibration of the radial steel gate, improving the performance of an active control system and ensuring the safe operation of the radial steel gate.
The technical scheme adopted by the invention is that the optimal arrangement method of the actuators for controlling the vibration of the hydraulic radial steel gate is implemented according to the following steps:
step 1, establishing a simplified model reflecting dynamic characteristics of the arc-shaped steel gate according to the structural characteristics of the arc-shaped steel gate;
step 2, constructing a control equation of the active control of the arc steel gate according to the simplified model;
step 3, establishing an optimal arrangement model of the number and the positions of the actuators;
and 4, solving the optimization model and determining an optimal arrangement scheme of the actuators.
The invention is also characterized in that:
the step 1 is implemented according to the following steps:
step 1.1, analyzing the dynamic characteristics of the arc-shaped steel gate by using finite element software, selecting proper units for simulating different components according to the structural characteristics of the gate, and obtaining the natural vibration frequency and the vibration mode of the gate;
step 1.2, considering the influence of a panel, distributing the mass of the panel on a main cross beam, neglecting the influence of curvature of a curved beam, replacing the curved beam with a straight beam, building a space frame simplified model of the arc steel gate through structural simplification, and analyzing the dynamic characteristics of the simplified model by adopting a dynamic stiffness method to obtain the natural vibration frequency and the vibration mode of the simplified model;
and 1.3, comparing the dynamic characteristics of the arc-shaped steel gate and the simplified model thereof, adjusting the simplified model by using the principle that the two are close to each other, and finally establishing the simplified model reflecting the dynamic characteristics of the arc-shaped steel gate.
The step 2 is implemented according to the following steps:
step 2.1, establishing a second-order dynamic differential equation for actively controlling the flow-induced vibration of the radial steel gate:
wherein M, C and K are the mass matrix, damping matrix and damping matrix of the simplified model, respectivelyA stiffness matrix, wherein the damping adopts Rayleigh damping; when the finite element characteristic matrixes M, C and K are formed, the shape function is an accurate shape function which meets the component free vibration differential equation;
and x (t) are acceleration, velocity and displacement vectors, respectively; f (t) is the excitation load, DsThe action position matrix of the excitation load; u (t) is the control force vector applied by the actuator, BsIs a matrix of positions of the actuators;
step 2.2, deducing a first-order state equation of the active control of the flow-induced vibration of the radial steel gate according to the formula (1):
in the formula (I), the compound is shown in the specification,
i is an identity matrix and is a matrix of the identity,
step 3 is specifically implemented according to the following steps:
step 3.1, establishing an objective function:
the quadratic performance index J of the LQR algorithm is adopted as a target function of the actuator optimization arrangement problem:
in the formula (I), the compound is shown in the specification,
and R is a weight matrix of the state vector Z (t) and the control force vector U (t), and alpha and beta are undetermined parameters.
According to the optimal control principle of the LQR algorithm, the corresponding optimal control force U (t) is as follows:
U(t)＝-GZ(t) (4)
wherein G ═ R-1BTP is an optimal feedback gain matrix, and is determined by the following formula:
-PA-ATP+PBR-1BTP-Q＝0 (5)
step 3.2, determining constraint conditions:
the constraints require that equation of state (2) be satisfied, and the position matrix B is determined from the structural positions of the actuator arrangementssValue range of
3.3, establishing an optimized layout model:
determining a position matrix B that minimizes the performance index J under the constraint of the equation of statesEstablishing an optimized mathematical model:
in the formula (I), the compound is shown in the specification,
is BsThe value range of (a).
Step 4 is specifically implemented according to the following steps:
step 4.1, determining the members of the arc-shaped steel gate arrangement actuators and the arrangement quantity according to the vibration characteristics of the arc-shaped steel gate;
4.2, selecting the performance index J as a fitness function, solving an optimization model by adopting a genetic algorithm, and determining the arrangement position of the actuator;
4.3, carrying out minimization design on the feedback gain matrix G;
and 4.4, determining an optimal arrangement scheme of the actuators.
The invention has the beneficial effects that: the optimal arrangement method of the actuators for the vibration control of the hydraulic radial steel gate can reduce the blindness of the arrangement of the actuators in the flow-induced vibration active control of the radial steel gate, improve the performance of an active control system and ensure the safe operation of the radial steel gate.
Drawings
FIG. 1 is a flow chart of an optimal arrangement method of an actuator for controlling the vibration of a hydraulic radial steel gate, which is disclosed by the invention;
FIG. 2 is a simplified model diagram of a certain radial steel gate in the optimized arrangement method of the actuator for controlling the vibration of the hydraulic radial steel gate according to the present invention;
FIG. 3 is a time course curve of shock excitation load borne by a certain radial steel gate in the actuator optimal arrangement method for vibration control of the hydraulic radial steel gate;
FIG. 4 is an actuator layout diagram of a certain radial steel gate in the actuator optimal layout method for vibration control of the hydraulic radial steel gate.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
The invention relates to an actuator optimal arrangement method for vibration control of a hydraulic radial steel gate, which is implemented according to the following steps as shown in figure 1:
step 1, establishing a simplified model capable of reflecting dynamic characteristics of the arc-shaped steel gate according to the structural characteristics of the arc-shaped steel gate, and specifically implementing the steps as follows:
step 1.1, analyzing the dynamic characteristics of the arc-shaped steel gate by using finite element software, selecting proper units for simulating different components according to the structural characteristics of the gate, wherein if a panel adopts shell unit simulation, a main beam, a secondary beam and a connecting rod piece adopt beam unit simulation, and a hinge adopts three-dimensional solid unit simulation to obtain the natural vibration frequency and the vibration mode of the gate;
step 1.2, considering the influence of a panel, distributing the mass of the panel on a main cross beam, neglecting the influence of curvature of a curved beam, replacing the curved beam with a straight beam, establishing a simplified model of the arc-shaped steel gate, and analyzing the dynamic characteristics of the simplified model by adopting a dynamic stiffness method to obtain the natural vibration frequency and the vibration mode of the simplified model;
step 1.3, comparing the dynamic characteristics of the arc steel gate and the simplified model thereof, adjusting the parameters of the simplified model by using the principle that the arc steel gate and the simplified model are close to each other, determining the mass distribution proportion of the panel and the size of each component, and finally establishing the simplified model capable of reflecting the dynamic characteristics of the prototype gate;
as shown in fig. 2, through the above steps, a simplified model of a certain arc-shaped steel gate is established;
step 2, constructing a control equation of the active control of the arc steel gate, and specifically implementing the following steps:
step 2.1, establishing a second-order dynamic differential equation for actively controlling the flow-induced vibration of the radial steel gate:
in the formula, M, C and K are respectively a mass matrix, a damping matrix and a rigidity matrix of the simplified model, and Rayleigh damping is adopted for damping; when the finite element characteristic matrixes M, C and K are formed, the shape functions are accurate shape functions which satisfy the component free vibration differential equation, and the values of the characteristic matrixes M, C and K can be determined as long as the structure is given;
and x (t) are acceleration, velocity and displacement vectors, respectively; f (t) is the excitation load, DsThe action position matrix of the excitation load; u (t) is the control force vector applied by the actuator, BsIs a matrix of positions of the actuators;
step 2.2, deducing a first-order state equation of the active control of the flow-induced vibration of the radial steel gate according to the formula (1):
in the formula (I), the compound is shown in the specification,
i is an identity matrix and is a matrix of the identity,
step 3, establishing an optimal arrangement model of the number and the positions of the actuators, and specifically implementing the following steps:
step 3.1, establishing an objective function:
the quadratic performance index J of the LQR algorithm is adopted as a target function of the actuator optimization arrangement problem:
in the formula (I), the compound is shown in the specification,
r ═ β I is a weight matrix of the state vector z (t) and the control force vector u (t), respectively, α and β are undetermined parameters, the values of which are determined by a trial algorithm;
according to the optimal control principle of the LQR algorithm, the corresponding optimal control force U (t) is as follows:
U(t)＝-GZ(t) (4)
wherein G ═ R-1BTP is an optimal feedback gain matrix, and is determined by the following formula:
-PA-ATP+PBR-1BTP-Q＝0 (5)
step 3.2, determining constraint conditions:
the constraints require that equation of state (2) be satisfied, and the position matrix B is determined from the structural positions of the actuator arrangementssValue range of
3.3, establishing an optimized layout model:
determining a position matrix B that minimizes the performance index J under the constraint of the equation of states(including double information of the number and the positions of the actuators), establishing an optimized mathematical model:
in the formula (I), the compound is shown in the specification,
is BsThe value range of (a);
step 4, solving the optimization model, and specifically implementing the following steps:
step 4.1, determining which members are provided with the actuators and the number of the actuators according to the vibration characteristics of the arc-shaped steel gate: the support arms are weak components of the arc-shaped steel gate and are key components for leading safety, so that 1 actuator needs to be arranged on each support arm, the main beam is fixedly connected with the panel, instability is not easy to occur, control is not needed, and the structural chord is not needed to be controlled, so that the problem of optimizing the arrangement of the number and the positions of the actuators is simplified into the problem of optimizing the number and the positions of the fixed actuators;
4.2, selecting the performance index J as a fitness function, solving an optimization model by adopting a genetic algorithm, and determining the arrangement position of the actuator;
4.3, carrying out minimization design on the feedback gain matrix G;
and 4.4, determining an optimal arrangement scheme of the actuators.
The specific working principle of the invention is as follows:
in the method of the invention: the method comprises the following steps that step 1 is used for establishing a simplified model of the radial steel gate, so that a control equation for active control of the radial steel gate is established, the simplified model can correctly reflect the dynamic characteristics of the radial steel gate, a centralized mass method is usually adopted when the simplified model of the radial steel gate is established in the past, the radial steel gate is simplified into the simplified model with the centralized mass by the centralized mass method, modal loss is easily caused, the dynamic characteristics of the gate cannot be fully reflected, and the contribution of all components of the gate to the dynamic characteristics is fully considered by the method in step 1;
in the method, the step 2 is used for constructing a control equation for actively controlling the arc steel gate, the control equation comprises a second-order dynamic differential equation and a first-order state equation, when a finite element characteristic matrix M, C and K are formed, the traditional method of taking a low-order polynomial as a shape function is abandoned, the adopted shape function is an accurate shape function meeting the free vibration differential equation of the rod piece, the rod piece only needs to be divided into a few units, and the calculation precision and the calculation efficiency can be improved;
in the method of the invention: step 3 is used for establishing an optimal arrangement model of the actuators in the active control of the flow-induced vibration of the radial steel gate, the optimization model is established by adopting related parameters of a linear quadratic form optimal control algorithm LQR, a quadratic form performance index J defined by the LQR algorithm has clear physical significance, is simpler in mathematical processing, is easy to form closed-loop optimal control and is often used as a target function of the problem of the active control optimal control, and therefore, the performance index J of the LQR algorithm is used as the target function of the optimal arrangement of the actuators;
in the method of the invention: and 4, solving an optimization model, namely determining the arrangement members of the actuators and the arrangement number of the actuators on the members according to the vibration characteristics of the arc steel gate, simplifying the problem of optimizing the arrangement of the number and the positions of the actuators into the problem of optimizing the positions by fixing the number of the actuators, and reducing the solving difficulty.
Aiming at a certain simplified model of the radial steel gate shown in fig. 2, the excitation load shown in fig. 3 is applied, the method provided by the invention is applied to determine the optimal arrangement scheme of the actuator for controlling the vibration of the radial steel gate, as shown in fig. 4, the actuator is arranged on 4 support arms, the distance between the actuator and a hinge is 0.55 times of the length of the support arm, the contrast values of the maximum acceleration, the maximum speed and the maximum displacement of the support arms before and after the arrangement mode of the actuator as shown in fig. 4 are shown in table 1, and as can be seen from table 1, the actuator arrangement scheme determined by the optimal arrangement method of the actuator provided by the invention can effectively reduce the dynamic response of the gate, and has obvious vibration reduction effect.
TABLE 1
| Vibration response quantity | Before active control | After active control |
| Acceleration (m/s)2) | 1.57 | 0.64 |
| Speed (m/s) | 0.41 | 0.21 |
| Displacement (m) | 0.0052 | 0.0023 |
The optimal arrangement method of the actuators for controlling the vibration of the radial steel gate is suitable for different types of actuators (traditional actuators and intelligent material actuators) and different types of radial gate vibration modes (such as forced vibration, parameter vibration and the like).
Claims (5)
1. An optimal arrangement method of actuators for vibration control of a hydraulic radial steel gate is characterized by comprising the following steps:
step 1, establishing a simplified model reflecting dynamic characteristics of the arc-shaped steel gate according to the structural characteristics of the arc-shaped steel gate;
step 2, constructing a control equation of the active control of the arc steel gate according to the simplified model;
step 3, establishing an optimal arrangement model of the number and the positions of the actuators;
and 4, solving the optimization model and determining an optimal arrangement scheme of the actuators.
2. The optimal arrangement method of the actuators for controlling the vibration of the hydraulic radial steel gate as claimed in claim 1, wherein the step 1 is implemented by the following steps:
step 1.1, analyzing the dynamic characteristics of the arc-shaped steel gate by using finite element software, selecting proper units for simulating different components according to the structural characteristics of the gate, and obtaining the natural vibration frequency and the vibration mode of the gate;
step 1.2, considering the influence of a panel, distributing the mass of the panel on a main cross beam, neglecting the influence of curvature of a curved beam, replacing the curved beam with a straight beam, building a space frame simplified model of the arc steel gate through structural simplification, and analyzing the dynamic characteristics of the simplified model by adopting a dynamic stiffness method to obtain the natural vibration frequency and the vibration mode of the simplified model;
and 1.3, comparing the dynamic characteristics of the arc-shaped steel gate and the simplified model thereof, adjusting the simplified model by using the principle that the two are close to each other, and finally establishing the simplified model reflecting the dynamic characteristics of the arc-shaped steel gate.
3. The optimal arrangement method of the actuators for controlling the vibration of the hydraulic radial steel gate as claimed in claim 1, wherein the step 2 is implemented by the following steps:
step 2.1, establishing a second-order dynamic differential equation for actively controlling the flow-induced vibration of the radial steel gate:
wherein M, C and K are the mass matrix, damping matrix and stiffness matrix of the simplified model, damping respectivelyAdopting Rayleigh damping; when the finite element characteristic matrixes M, C and K are formed, the shape function is an accurate shape function which meets the component free vibration differential equation;
and x (t) are acceleration, velocity and displacement vectors, respectively; f (t) is the excitation load, DsThe action position matrix of the excitation load; u (t) is the control force vector applied by the actuator, BsIs a matrix of positions of the actuators;
step 2.2, deducing a first-order state equation of the active control of the flow-induced vibration of the radial steel gate according to the formula (1):
in the formula (I), the compound is shown in the specification,
i is an identity matrix and is a matrix of the identity,
4. the optimal arrangement method of the actuators for controlling the vibration of the hydraulic radial steel gate as claimed in claim 1, wherein the step 3 is implemented by the following steps:
step 3.1, establishing an objective function:
the quadratic performance index J of the LQR algorithm is adopted as a target function of the actuator optimization arrangement problem:
in the formula (I), the compound is shown in the specification,
and R is a weight matrix of the state vector Z (t) and the control force vector U (t), and alpha and beta are undetermined parameters.
According to the optimal control principle of the LQR algorithm, the corresponding optimal control force U (t) is as follows:
U(t)＝-GZ(t) (4)
wherein G ═ R-1BTP is an optimal feedback gain matrix, and is determined by the following formula:
-PA-ATP+PBR-1BTP-Q＝0 (5)
step 3.2, determining constraint conditions:
the constraints require that equation of state (2) be satisfied, and the position matrix B is determined from the structural positions of the actuator arrangementssValue range of
3.3, establishing an optimized layout model:
determining a position matrix B that minimizes the performance index J under the constraint of the equation of statesEstablishing an optimized mathematical model:
in the formula (I), the compound is shown in the specification,
is BsThe value range of (a).
5. The optimal arrangement method of the actuators for controlling the vibration of the hydraulic radial steel gate as claimed in claim 4, wherein the step 4 is implemented by the following steps:
step 4.1, determining the members of the arc-shaped steel gate arrangement actuators and the arrangement quantity according to the vibration characteristics of the arc-shaped steel gate;
4.2, selecting the performance index J as a fitness function, solving an optimization model by adopting a genetic algorithm, and determining the arrangement position of the actuator;
4.3, carrying out minimization design on the feedback gain matrix G;
and 4.4, determining an optimal arrangement scheme of the actuators.
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