1. A nuclear power device pipeline system vibration damping and noise reduction method based on fractional order PID control is characterized by comprising the following steps:

step 1: establishing a vibration model of a typical piping system, comprising the sub-steps of:

step 1.1: the control equation to be satisfied when the particle system moves is,

where m is the mass matrix of the system, c is the damping matrix of the system, k is the stiffness matrix of the system, u is the displacement of the particles, and p (t) is the force imparted to the particles;

step 1.2: further obtaining the power equation of the typical pipeline system of the nuclear power plant as follows,

wherein α is a mass matrix of the piping system, β is a damping matrix of the piping system, δ is a stiffness matrix of the piping system, r is a displacement of the liquid in the piping, and f (t) is a force to which the liquid is subjected;

step 1.3: define the state vector x ═ r, dr/dt ] T, yield

The observation equation of the system is thus obtained as,

where N is an index matrix of dimensions N x q, each column containing only one non-zero entry that marks a particular degree of freedom to be monitored by the accelerometer;

step 1.4: the forces f (t) are decomposed, assuming that the matrix P, Q has the following relationship,

further obtaining a dynamic equation of a typical pipeline system of the nuclear power plant,

wherein the content of the first and second substances,

C＝-N^Tα^-1(βP+δQ)

D_e＝N^Tα^-1R

D_c＝N^Tα^-1S

step 1.5: introducing process noise omega and observation noise v into the formula in the step 1.4, and constructing a state space expression of the system by using the formula as follows:

y＝Cx+D_ef_e+D_cf_c+Hw+v

wherein the covariance matrix of the process noise omega and the observation noise v is defined as,

E(ww^T)＝Q_n,E(vv^T)＝R_n

if u is defined^T＝[f_e ^T,f_c ^T]^T、B＝[B_e,B_c]、D＝[D_e,D_c]Then the state space expression of the system can be expressed as,

y＝Cx+Du+Hw+v

kalman filtering provides the system with an optimal estimate of the state vector x, expressed in state space,

where the filter gain matrix L is the optimal solution to minimize the steady state error covariance P,

step 2: and introducing fractional order PID output feedback control and fractional order PID state feedback control. The method for constructing the mathematical model of the fractional order PID output feedback control and the fractional order PID state feedback control based on the system comprises the following substeps:

step 2.1: for a fractional order PID output feedback control scheme, the control force is controlled by a linear combination of the channel signals, i.e.

It is assumed that,

Z₁(t)＝∫ydt

according to the Oustaloup filter of the prior art,

substituting the control rule of the fractional order PID output feedback controller into the pipeline system model formula in the step 1.4, and deducing the state space expression of the system as follows:

wherein

Step 2.2: the control rule of the fractional order PID state feedback controller is substituted into a pipeline system model formula, the state space expression of the system can be deduced as,

wherein the content of the first and second substances,

step 2.3: optimizing calculation by adopting particle swarm algorithm

The speed and position updating formula of the particle swarm algorithm is as follows:

where ω is the inertial weight, the magnitude of which directly affects the convergence of the particle swarm algorithm, C₁Is the weight coefficient of the individual optimum value of the particle tracking, representing the weight of the experience of the particle tracking playing a role in the motion, C₂The weight coefficient is the optimal value of the particle tracking group and represents the weight of social experience in motion;

substituting the control rule formula (14) of fractional order PID output feedback control into the formula (25) to construct an objective function,

the objective function of the fractional order PID state feedback controller is constructed in the same way,

2. the method for reducing vibration and noise of the nuclear power plant pipeline system based on the fractional order PID control as claimed in claim 1, wherein in the step 2.1,

3. the method for reducing vibration and noise of the nuclear power plant pipeline system based on the fractional order PID control as claimed in claim 1, wherein in the step 2.1,

Background

Vibration control is an important branch in the field of vibration engineering and can be divided into passive control and active control. The passive control does not need external energy, so the device has simple structure, good vibration damping effect and reliability in many occasions, and has been widely applied. However, with the development of scientific technology and the increasing requirements of people on vibration environment, products and structural vibration characteristics, passive control is difficult to meet the requirements, so that active control strategies are more introduced into the vibration and noise reduction process.

The active vibration control means that a certain control strategy is applied according to a detected vibration signal in the vibration control process, and the actuator is driven to exert certain influence on a control target through real-time calculation so as to achieve the purpose of suppressing or eliminating vibration. The method is approved by the current mechanical engineering by virtue of the characteristics of good effect, strong adaptability, comprehensive multidisciplinary, good control effect and strong adaptability. The Weichen and the like provide an active control strategy considering the deformation of a pipeline structure, a complex pipeline system model is established on the basis of a continuous beam model, a system dynamic equation is transformed into a generalized coordinate through a mode, and an active controller is designed aiming at the generalized coordinate so as to reduce the vibration of each part of the pipeline in each direction.

The active control based on the fractional order is a hotspot of research on control directions in recent years, and compared with the traditional active control, the active control based on the fractional order introduces order parameters on the basis of the active control, so that the control range of the controller is wider, and the control method is more flexible. According to Chenyandong et al, fractional order PID control is utilized to realize vibration damping control of a complex vehicle suspension system, a 1/4 vehicle two-degree-of-freedom nonlinear suspension mathematical model is established, then a fractional order calculus theory is combined, and a fractional order PID controller is designed.

Through retrieval, aiming at a complex and high-latitude system of a typical pipeline system of a nuclear power plant, the method of adopting a fractional order PID controller to realize the control of the vibration of the nuclear power plant is not used in the field at present.

Disclosure of Invention

The technical problem solved by the invention is as follows: aiming at the defects of the existing method, the invention provides a vibration reduction method adopting fractional order PID output feedback control and fractional order PID state feedback control on a typical pipeline system of a nuclear power plant.

The technical scheme of the invention is as follows: a nuclear power plant pipeline system vibration damping and noise reduction method based on fractional order PID control comprises the following steps:

step 1: establishing a vibration model of a typical piping system, comprising the sub-steps of:

step 1.1: the control equation to be satisfied when the particle system moves is,

where m is the mass matrix of the system, c is the damping matrix of the system, k is the stiffness matrix of the system, u is the displacement of the particles, and p (t) is the force imparted to the particles;

step 1.2: further obtaining the power equation of the typical pipeline system of the nuclear power plant as follows,

wherein α is a mass matrix of the piping system, β is a damping matrix of the piping system, δ is a stiffness matrix of the piping system, r is a displacement of the liquid in the piping, and f (t) is a force to which the liquid is subjected;

step 1.3: define the state vector x ═ r, dr/dt ] T, yield

The observation equation of the system is thus obtained as,

where N is an index matrix of dimensions N x q, each column containing only one non-zero entry that marks a particular degree of freedom to be monitored by the accelerometer;

step 1.4: the forces f (t) are decomposed, assuming that the matrix P, Q has the following relationship,

further obtaining a dynamic equation of a typical pipeline system of the nuclear power plant,

wherein the content of the first and second substances,

C＝-N^Tα^-1(βP+δQ)

D_e＝N^Tα^-1R

D_c＝N^Tα^-1S

step 1.5: introducing process noise omega and observation noise v into the formula in the step 1.4, and constructing a state space expression of the system by using the formula as follows:

y＝Cx+D_ef_e+D_cf_c+Hw+v

wherein the covariance matrix of the process noise omega and the observation noise v is defined as,

E(ww^T)＝Q_n,E(vv^T)＝R_n

if u is defined^T＝[f_e ^T,f_c ^T]^T、B＝[B_e,B_c]、D＝[D_e,D_c]Then the state space expression of the system can be expressed as,

y＝Cx+Du+Hw+v

kalman filtering provides the system with an optimal estimate of the state vector x, expressed in state space,

where the filter gain matrix L is the optimal solution to minimize the steady state error covariance P,

step 2: and introducing fractional order PID output feedback control and fractional order PID state feedback control. The method for constructing the mathematical model of the fractional order PID output feedback control and the fractional order PID state feedback control based on the system comprises the following substeps:

step 2.1: for a fractional order PID output feedback control scheme, the control force is controlled by a linear combination of the channel signals, i.e.

It is assumed that,

Z₁(t)＝∫ydt

according to the Oustaloup filter of the prior art,

substituting the control rule of the fractional order PID output feedback controller into the pipeline system model formula in the step 1.4, and deducing the state space expression of the system as follows:

wherein

Step 2.2: the control rule of the fractional order PID state feedback controller is substituted into a pipeline system model formula, the state space expression of the system can be deduced as,

wherein the content of the first and second substances,

step 2.3: optimizing calculation by adopting particle swarm algorithm

The speed and position updating formula of the particle swarm algorithm is as follows:

where ω is the inertial weight, the magnitude of which directly affects the convergence of the particle swarm algorithm, C₁Is the weight coefficient of the individual optimum value of the particle tracking, representing the weight of the experience of the particle tracking playing a role in the motion, C₂The weight coefficient is the optimal value of the particle tracking group and represents the weight of social experience in motion;

substituting the control rule formula (14) of fractional order PID output feedback control into the formula (25) to construct an objective function,

the objective function of the fractional order PID state feedback controller is constructed in the same way,

the further technical scheme of the invention is as follows: a nuclear power plant pipeline system vibration damping and noise reduction method based on fractional order PID control, in step 2.1,

the further technical scheme of the invention is as follows: a nuclear power plant pipeline system vibration damping and noise reduction method based on fractional order PID control, in step 2.1,

effects of the invention

The invention has the technical effects that: compared with the prior art, the invention has the following beneficial effects:

(1) the mathematical model of the typical pipeline system of the nuclear power plant established by the power equation can better describe the actual system condition.

(2) The particle swarm optimization algorithm can be used for quickly finding out controller parameters which enable the system vibration suppression effect to be optimal, namely proportional gain Kp, integral gain Ki, differential gain Kd, integral order lambda and differential order mu.

(3) Compared with open-loop and closed-loop control methods, the method has the advantage that the suppression of the vibration of the typical pipeline system of the nuclear power plant can be effectively realized by introducing the fractional-order PID controller.

(4) The vibration signal energy can be reduced by 9% on the basis of open loop after the fractional order PID output feedback controller is introduced. The vibration signal energy can be reduced by 35% on the open loop basis at most after the fractional order PID state feedback controller is introduced.

Drawings

FIG. 1 is a flow chart of a design of a fractional order PID controller

FIG. 2 is a flow chart of a particle swarm optimization algorithm

FIG. 3 sensor distribution location

FIG. 4 open-loop, closed-loop and fractional order PID output feedback signal energy comparison

FIG. 5 open-loop, closed-loop and fractional order PID state feedback signal energy comparison

Sensor number 62 closed loop output and fractional order PID output feedback control output

Sensor number 722 sensor closed loop output and fractional order PID output feedback control output

Comparison of closed-loop and fractional PID output feedback control output probability density for sensor number 82 FIG.

Comparison of sensor number 922 closed loop with fractional PID output feedback control output probability density

Closed-loop output and fractional PID state feedback control output of sensor number 1010

Sensor number 1123 closed loop output and fractional order PID state feedback control output

Comparison of output probability density for closed-loop and fractional PID state feedback control for sensor No. 1210

Output probability density comparison of sensor 1323 closed loop and fractional order PID state feedback control

Detailed Description

In the description of the present invention, it is to be understood that the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "clockwise", "counterclockwise", and the like, indicate orientations and positional relationships based on those shown in the drawings, and are used only for convenience of description and simplicity of description, and do not indicate or imply that the device or element being referred to must have a particular orientation, be constructed and operated in a particular orientation, and thus, should not be considered as limiting the present invention.

Referring to fig. 1-13, the invention provides a damping method adopting fractional order PID output feedback control and fractional order PID state feedback control on a typical pipeline system of a nuclear power plant aiming at the defects of the existing method, and the method adds two order parameters lambda and mu on the basis of the traditional integer order PID control parameters, so that a controller can be more accurately matched with a system model.

The technical scheme of the scheme is as follows: firstly, according to a kinetic equation, a mathematical model of a typical pipeline system of the nuclear power plant is constructed, and a state space expression of the mathematical model is deduced. And then, vibration reduction is carried out on the system by introducing fractional order PID output feedback control and fractional order PID state feedback control, and a control parameter proportional matrix Kp, an integral matrix Ki, a differential matrix Kd, an integral order lambda and a differential order mu of the fractional order PID output feedback control and the fractional order PID state feedback control are obtained by minimizing a quadratic objective function through a particle swarm algorithm.

Step 1: a vibration model of a typical piping system is established. And according to a kinetic equation, constructing a mathematical model of the typical pipeline system of the nuclear power plant, and deducing a state space expression of the mathematical model.

Step 1.1: the dynamic equation is the basis for structural dynamic analysis, and the control equation, namely the dynamic equation, which is required to be satisfied when the particle system moves is known as,

where m is the mass matrix of the system, c is the damping matrix of the system, k is the stiffness matrix of the system, u is the displacement of the particles, and p (t) is the force imparted to the particles.

Using equation (1), the power equation for constructing a typical piping system for a nuclear power plant is,

where α is the mass matrix of the piping system, β is the damping matrix of the piping system, δ is the stiffness matrix of the piping system, r is the displacement of the liquid in the piping, and f (t) is the force to which the liquid is subjected.

Assuming that the state vector x ═ r, dr/dt ] T, one can derive,

since the sensor herein employs an accelerometer, the system's observation equation is,

where N is an index matrix of dimensions N x q, each column contains only one non-zero entry that marks a particular degree of freedom to be monitored by the accelerometer.

The force f (t) is decomposed,

wherein f is_e(t) is nodal excitation force, f_c(t) is the output feedback control force of the actuator for suppressing the undesirable vibration. R represents v degrees of freedom excited by external node force, and the ith external force acts on the qth of the finite element model_iThe degree of freedom, which is such that only one entry per column of the matrix R is 1 and the rest are 0. S represents m degrees of freedom of control force for restraining undesirable vibration by an actuator, and j external force acts on q th degree of freedom of the finite element model_jAnd (4) degree of freedom.

Matrix P, Q is assumed, so that it has the following relationship,

substituting equations (5) and (6) into equations (3) and (4) can obtain the kinetic equation of the typical pipeline system of the nuclear power plant,

wherein the content of the first and second substances,

C＝-N^Tα^-1(βP+δQ)

D_e＝N^Tα^-1R

D_c＝N^Tα^-1S

aiming at a fractional order PID state feedback controller, a Kalman filter is introduced into a model, so that a state estimation value is obtained. Introducing process noise omega and observation noise nu into the formula (7), and constructing a state space expression of the system according to the process noise omega and the observation noise nu,

wherein the covariance matrix of the process noise omega and the observation noise v is defined as,

E(ww^T)＝Q_n,E(vv^T)＝R_n (10)

if u is defined^T＝[f_e ^T,f_c ^T]^T、B＝[B_e,B_c]、D＝[D_e,D_c]Then the state space table of the systemThe expression may be expressed as a number of,

kalman filtering provides the system with an optimal estimate of the state vector x, expressed in state space,

where the filter gain matrix L is the optimal solution to minimize the steady state error covariance P,

step 2: and introducing fractional order PID output feedback control and fractional order PID state feedback control. And constructing a mathematical model of fractional order PID output feedback control and fractional order PID state feedback control based on the system. And (3) minimizing a quadratic objective function by a particle swarm algorithm to find optimal values of a proportional gain Kp, an integral gain Ki, a differential gain Kd, an integral order lambda and a differential order mu.

Step 2.1: for a fractional order PID output feedback control scheme, the control force is controlled by a linear combination of the channel signals, i.e.

It is assumed that,

Z₁(t)＝∫ydt (15)

according to the Oustaloup filter of the prior art,

substituting a control rule formula (17) of a fractional order PID output feedback controller into a pipeline system model formula (7) can deduce a state space expression of the system as follows:

wherein

Step 2.2: in the same way, the control rule of the fractional order PID state feedback controller is substituted into the pipeline system model formula (12), the state space expression of the system can be deduced as,

wherein the content of the first and second substances,

step 2.3: optimizing calculation by adopting particle swarm algorithm

The speed and position updating formula of the particle swarm algorithm is as follows:

where ω is the inertial weight, the magnitude of which directly affects the convergence of the particle swarm algorithm, C₁Is the weight coefficient of the individual optimum value of the particle tracking, representing the weight of the experience of the particle tracking playing a role in the motion, C₂The weight coefficient is the optimal value of the particle tracking group and represents the weight of social experience in motion.

Substituting the control rule formula (14) of fractional order PID output feedback control into the formula (25) to construct an objective function,

the objective function of the fractional order PID state feedback controller is constructed in the same way,

the first term of the integrand in the objective function represents the error value of the system, the second term of the integrand represents the consumption of control energy in the control process, and the optimal control law of the minimum error can be obtained by using smaller control energy by solving the minimum value of the objective function, so that the optimal control of the typical pipeline system vibration of the nuclear power device is realized.

When the particle swarm optimization is adopted for optimization calculation, firstly, initial values are set for parameters, the iteration times, the particle number, the particle speed, the particle position range and the particle speed range are set, then the fitness is obtained by taking the formulas (21) and (22) as the objective function of the particle swarm optimization fractional order PI output feedback controller, the particle speed and the position are updated by the formula (20), and the optimal proportional gain K is obtained_pIntegral gain K_iDifferential gain K_dIntegral order λ and differential order μ. The obtained optimal parameters are brought into a fractional order PID controller, and control force is applied to a passive object, namely a typical pipeline system of a nuclear power device through the optimal parameters, so that the vibration of the pipeline system is actively inhibited.

The working flow of the invention is described in detail below by referring to the accompanying drawings and examples.

FIG. 1 shows a general flow chart of fractional order PID controller design, which is roughly divided into four parts, firstly establishing a typical pipeline system model of a nuclear power plant, then designing a fractional order PID output feedback controller, and then realizing proportional gain K in the controller by utilizing a particle swarm optimization algorithm_pIntegral gain K_iDifferential gain K_dAnd the optimization calculation of the integral order lambda and the differential order mu preferably brings the found optimal parameters into the system to form a controller to realize the vibration suppression of the typical pipeline system of the nuclear power plant. The specific working flow of the invention is as follows.

Step 1: and (3) constructing a mathematical model of a typical pipeline of the process system according to a given formula, and preparing for introducing fractional PID output feedback control and fractional PID state feedback control. Initializing the values of a mass matrix alpha, a rigidity matrix delta and a damping matrix beta.

Step 2: designing a fractional order PID output feedback controller and a fractional order PID state feedback controller according to the formulas (21) and (22), taking a system quadratic form objective function as an objective function of a particle swarm optimization algorithm, and obtaining a proportional gain K by minimizing the objective function value_pIntegral gain K_iDifferential gain K_dThe integral order lambda and the differential order mu are brought into the pipeline system to realize the optimal control of the vibration of the pipeline system. Fig. 2 shows a particle swarm algorithm flow chart.

Example (c): and (3) simulating and realizing the suppression of system vibration by using MATLAB software. In simulation results, a mass matrix alpha, a damping matrix beta and a rigidity matrix delta in a typical pipeline system of the nuclear power plant are given. The matrix A, B is obtained by equation (8)_e、B_c、C、D_e、D_cWherein A is 888 × 888 dimensional matrix, B_e、B_cIs 888 in function2-dimensional matrix, C is 25 × 888-dimensional matrix, D_e、D_cA 25 x 2 dimensional matrix.

The vibration was monitored by selecting 25 sensors, the distribution of which is shown in fig. 3. The time taken was 0.001s, and 10000 samples were collected in total, i.e., 10s total elapsed time. The fractional order PI feedback control parameters are optimized by using a PSO algorithm, and the parameters of the PSO algorithm are shown in a table 1.

TABLE 1 particle swarm optimization Algorithm parameters

Obtaining a proportional gain K after optimization_pIntegral gain K_iDifferential gain K_dIntegral order λ and differential order μ. The integral order of the fractional order PID output feedback control is lambda-1.4229492217092, and the differential order is mu-0.949286374771172. The integral order of the fractional order PID state feedback control is λ 0.196020000000000, and the differential order is μ 1.995281229802501.

And 4, step 4: and (3) carrying out MATLAB simulation to bring the found optimal parameters into a fractional order PID output feedback controller and a fractional order PID state feedback controller to realize the suppression of the vibration of the typical pipeline system of the nuclear power plant.

Fig. 3 shows the positions of 25 sensors selected during the experimental simulation.

Fig. 4 calculates the signal energy values of the positions of 25 sensors adopting open-loop, closed-loop and fractional order PID output feedback control strategies, and the suppression effect of the fractional order PID output feedback control on the vibration of the pipeline system is obviously superior to that of the other two control strategies through comparison.

Fig. 5 calculates signal energy values of positions of 25 sensors using open-loop, closed-loop and fractional order PID state feedback control strategies, respectively, and the suppression effect of fractional order PID state feedback control on the vibration of the pipeline system is obviously superior to that of other two control strategies through comparison.

FIG. 6 shows the amplitude values of the closed-loop output of the No. 2 sensor and the output of the fractional PID output feedback control, and the comparison shows that the output amplitude after the fractional PID output feedback control is adopted is obviously lower than the output amplitude of the closed-loop control.

Fig. 7 shows the amplitude values of the closed-loop output of sensor No. 22 and the output of fractional PID output feedback control, and by comparison, it can be found that the output amplitude after the fractional PID output feedback control is adopted is significantly lower than the output amplitude of the closed-loop control.

Fig. 8 and 9 show the probability density functions of the vibration amplitudes after the sensors No. 2 and No. 22 are located and closed-loop control and fractional order PID output feedback control are adopted, and it can be seen that the probability density of the vibration amplitudes is more concentrated near 0 after the fractional order PID output feedback controller is adopted.

Fig. 10 shows the amplitude values of the closed-loop output of the sensor No. 10 and the output of the fractional PID state feedback control, and by comparison, it can be found that the output amplitude after the fractional PID state feedback control is adopted is obviously lower than the output amplitude of the closed-loop control.

Fig. 11 shows the amplitude values of the closed-loop output of sensor number 23 and the output of the fractional PID state feedback control, and by comparison, it can be found that the output amplitude after the fractional PID state feedback control is adopted is significantly lower than the output amplitude of the closed-loop control.

Fig. 12 and 13 show the probability density functions of the vibration amplitude after the sensor No. 10 and the sensor No. 23 are positioned by adopting closed-loop control and fractional order PID state feedback control, and it can be seen that the probability density of the vibration amplitude is more concentrated near 0 after the fractional order PID state feedback controller is adopted.

The invention adopts the fractional order PID output feedback and the fractional order PID state feedback method to reduce the typical pipeline system vibration of the nuclear power device. A mathematical model of a typical pipeline system of the nuclear power plant is deduced through a kinetic equation, and parameters of optimal fractional order PID output feedback control and fractional order PID state feedback control are obtained by minimizing a quadratic form objective function through a particle swarm algorithm. Compared with the prior art, the vibration reduction algorithm has superiority and effectiveness.