CN115857322A - Fractional order fluid control valve system parameter identification method based on gradient iteration algorithm - Google Patents
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Abstract
The invention provides a method for identifying parameters of a fractional order fluid control valve system based on a gradient iterative algorithm, belongs to the technical field of identification of fluid control valve systems, and solves the problem of low identification precision of the parameters of the fractional order fluid control valve system. The technical scheme is as follows: a method for identifying a fractional order fluid control valve system based on a gradient iterative algorithm comprises the following steps: step 1) establishing a fractional order fluid control valve system Wiener nonlinear model; and 2) constructing an identification process of the gradient iterative algorithm. The invention has the beneficial effects that: the gradient iterative algorithm provided by the invention has higher convergence speed and higher convergence precision, and can be better suitable for modeling and parameter identification of a fractional order fluid control valve system.
Description
Technical Field
The invention relates to the technical field of fluid control valve system identification, in particular to a fractional order fluid control valve system parameter identification method based on a gradient iterative algorithm.
Background
With the rapid development of science and technology, industrial processes will inevitably put more stringent and urgent demands on the control of actual production processes. In order to meet such control requirements and achieve better control effects, accurate and effective mathematical models must be established for the actual production process. The actual production process almost involves the control of gas or liquid, so that the fluid control valve is indispensable in a control system, which is an important link constituting an industrial automation system. Fluid control valves are mechanical devices for controlling the state of fluid flow (pressure, flow, cut-off/on), and due to their nonlinear flow characteristics, modeling them has become a significant difficulty in production control. To better analyze and predict the production process, it is necessary to build an accurate system model for the fluid control valve while identifying the parameters of the built model. For this reason, researchers have proposed different identification methods, such as: random gradient algorithm, newton iterative algorithm, particle swarm algorithm and the like.
The random gradient algorithm has the problems of low convergence speed and low identification precision in parameter identification; the Newton iteration algorithm is an iteration algorithm, an inverse matrix of a Hessian matrix of an objective function needs to be solved in each step, the calculation is complex, and the occupied memory is large; although the particle swarm algorithm serving as the swarm intelligence algorithm can be well applied to different working conditions, the selection of genetic operators is troublesome sometimes, and the problem of low identification precision exists.
How to solve the above technical problems is the subject of the present invention.
Disclosure of Invention
The invention aims to provide a method for identifying parameters of a fractional order fluid control valve system based on a gradient iterative algorithm, which has higher convergence speed and higher convergence precision and can be better suitable for modeling and parameter identification of the fractional order fluid control valve system.
The invention is realized by the following measures: the method for identifying the parameters of the fractional order fluid control valve system based on the gradient iterative algorithm specifically comprises the following steps:
step 1) establishing an input and output mathematical model of a fractional order fluid control valve system.
And 2) constructing an identification process of the gradient iterative algorithm.
As a further optimization scheme of the method for identifying the parameters of the fractional order fluid control valve system based on the gradient iterative algorithm, the specific modeling step of the step 1) is as follows:
(1-1) constructing a structure of a fractional order fluid control valve system Wiener nonlinear model.
(1-2) according to the model, constructing a fractional order fluid control valve system Wiener nonlinear model expression as follows:
e(t)＝D(z)v(t), (3)
y(t)＝x(t)+e(t), (4)
the meaning of each symbol in the above formula: u (t) is the model input signal, y (t) is the model output signal, v (t) is a mean of 0 and a variance of σ 2 And white noise satisfying a Gaussian distribution, the intermediate variables u (t), x (t) and e (t) being signals immeasurable in the middle, z -1 Is the unit delay symbol: z is a radical of formula -1 y (t) = y (t-1), a (z), B (z) and D (z) are constant polynomials with the following definitions:
wherein the polynomial factor a i ，b j And d l Is the parameter to be estimated, α i ，β j And gamma l Is the fractional order of the polynomial denominator. The present invention contemplates a fractional order system, i.e., the fractional order is a multiple of the same base and is known:
(1-3) intermediate signal
And e (t) can be expressed as:
simplifying to obtain:
the invention adopts Gr unwald Letnikov (GL) definition to solve fractional order derivative, and the GL definition can be expressed as:
where Δ is the discrete fractional order difference operator, Δ α m (kh) is the alpha fractional derivative of the function m (k), which can be given as t = kh, where h is the sampling interval and k is the number of samples to compute the derivative approximation. Substituting equation (7) into equations (5) and (6), the intermediate signal after dispersion
And e (t) can be rewritten as:
the output of the nonlinear element in the model is in a polynomial form, which can be expressed as:
wherein p is i Is an unknown coefficient to be identified and the order r of the polynomial function is known. To ensure the uniqueness of the parameters, let the first modulus p of the non-linear component 1 ＝1。
(1-4) obtaining an identification model of a Wiener nonlinear model of a fractional order fluid control valve system:
in the above-mentioned formula,
is a systematic information vector, represented as:
wherein,
are respectively defined as
θ is the parameter vector of the system, expressed as: θ = [ θ = 1 T ,θ 2 T ,θ 3 T ] T ，
Wherein, theta 1 ，θ 2 ，θ 3 Are respectively defined as:
θ 2 ＝[p 2 ,p 3 ,…,p r ] T ,
the method for identifying parameters of the Wiener nonlinear model of the fractional order fluid control valve system based on the gradient iterative algorithm is further designed in that the step 2) is specifically as follows:
step 2-1) initialization, given iteration times k max Data length N;
step 2-2) using the pneumatic control signal of the valve as input data u (t) of a fractional order fluid control valve system model) Fluid flow as output data y (t) and valve plug position as intermediate signal
Step 2-3) defining a stacking output vector Y (N) according to the input and output data, and defining a stacking information matrix psi (N) as a formula (12);
step 2-4) defining a criterion function J (theta) as
Wherein,
is an estimate of the pile-up information matrix, and->
Is an estimate of the parameter vector; />
Step 2-5) intermediate variables in the information vector
Fractional derivative of an intermediate variable->
And fractional order derivative of the undetectable noise Δ α v (t) is replaced by its evaluation value>
And &>
Calculating an estimate ≥ of the information vector according to equation (14)>
Construction according to equation (15)>
Step 2-6) selecting a suitable convergence factor mu according to formula (16) k ；
Step 2-7) calculating the estimated value of the parameter vector according to the formula (17)
Step 2-8) calculating the estimated intermediate variables according to the equations (8), (18)
And the estimated noise->
The fractional derivative { (R) } of the noise and the intermediate variable estimated is calculated as defined by GL of equation (7)>
Step 2-9) judging whether the maximum iteration times are reached, if not, skipping the program to step 2-5), and if so, entering step 2-10);
and 2-10) outputting a result to finish identification.
Compared with the prior art, the invention has the beneficial effects that:
(1) The method establishes a model for identifying the parameters of the fractional order Wiener nonlinear system of the fluid control valve, takes a pneumatic control signal of the valve as input data, and identifies the parameters of the model by using a gradient iterative algorithm; it can be seen from fig. 4 that the algorithm can identify the internal parameters of the model well.
(2) Compared with a random gradient algorithm, the gradient iteration algorithm uses all data available for the system in each iteration process, updates intermediate variables and noise in each iteration process so as to obtain an estimated information vector, improves the convergence rate, can better identify a nonlinear system, has higher identification precision and obtains smaller estimation error; meanwhile, the identification method has better applicability to a fractional order fluid control valve Wiener nonlinear model.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention and not to limit the invention.
Fig. 1 is an overall flowchart of a fractional order fluid control valve Wiener nonlinear system identification method based on a gradient iterative algorithm provided by the invention.
Fig. 2 is a schematic structural diagram of the fractional order fluid control valve provided by the present invention, which mainly comprises a displacement sensor, magnetic steel, an electromagnetic linear actuator, a mushroom valve, a valve seat, and a valve body upper cover fixed on a central shaft center, wherein one side of the valve body is provided with a fluid inlet connected with an external gas supply pipeline.
Fig. 3 is a schematic diagram of a general model of an input/output system of the fractional-order fluid control valve parameter identification method based on the gradient iterative algorithm provided by the invention.
FIG. 4 is a schematic diagram of the error between the identification parameter and the true value according to the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. Of course, the specific embodiments described herein are merely illustrative of the invention and are not intended to be limiting.
Example 1
Referring to fig. 1 to 4, the present embodiment provides a technical solution of a method for identifying parameters of a fractional order fluid control valve system based on a gradient iterative algorithm, which includes the following specific steps:
step 1) establishing an input and output mathematical model of a fractional order fluid control valve system.
And 2) constructing an identification process of the gradient iterative algorithm.
As a further optimization scheme of the identification method for the fractional order fluid control valve system based on the gradient iterative algorithm provided by this embodiment, the specific modeling steps of step 1) are as follows:
(1-1) constructing a structure of a fractional order fluid control valve system Wiener nonlinear model.
(1-2) according to the model, constructing a fractional order fluid control valve system Wiener nonlinear model expression as follows:
e(t)＝D(z)v(t), (3)
y(t)＝x(t)+e(t), (4)
the meaning of each symbol in the above formula: u (t) is the model input signal, y (t) is the model output signal, v (t) is a mean of 0 and a variance of σ 2 And white noise, an intermediate variable, satisfying Gaussian distribution
x (t) and e (t) are signals which are not measurable in the middle, z -1 Is the unit delay symbol: z is a radical of -1 y (t) = y (t-1), a (z), B (z) and D (z) are constant polynomials with the following definitions:
wherein the polynomial factor a i ，b j And d l Is the parameter to be estimated, α i ，β j And gamma l Is the fractional order of the polynomial denominator. The present embodiment considers a fractional order system, i.e. the fractional order is a multiple of the same base and is known:
(1-3) intermediate signal
And e (t) can be expressed as: />
Simplifying to obtain:
this example uses the Gr ü nwald Letnikov (GL) definition to solve for fractional derivatives, which can be expressed as:
where Δ is the discrete fractional order difference operator, Δ α m (kh) is the fractional derivative of the order a of the function m (k), and it is possible to let t = kh, where h is the sampling interval and k is the number of samples to which the derivative approximation is calculated. Substituting equation (7) into equations (5) and (6), the intermediate signal after dispersion
And e (t) can be rewritten as:
the output of the nonlinear element in the model is in a polynomial form, which can be expressed as:
wherein p is i Is an unknown coefficient to be identified and the order r of the polynomial function is known. To ensure the uniqueness of the parameters, let the first modulus p of the non-linear component 1 ＝1。
(1-4) obtaining an identification model of a Wiener nonlinear model of a fractional order fluid control valve system:
in the above-mentioned formula,
is a systematic information vector, represented as:
wherein,
are respectively defined as
θ is a parameter vector of the system, expressed as: θ = [ θ = 1 T ,θ 2 T ,θ 3 T ] T ，
Wherein, theta 1 ，θ 2 ，θ 3 Are respectively defined as:
θ 2 ＝[p 2 ,p 3 ,…,p r ] T ,
preferably, the model of step 1) is a fractional Wiener nonlinear model.
Preferably, the step 2) of constructing the identification process of the gradient iterative algorithm includes the following specific steps:
step 2-1) initialization, given iteration times k max Data length N;
step 2-2) taking a pneumatic control signal of the valve as input data u (t) of a fractional order fluid control valve system model, taking fluid flow as output data y (t), and taking the position of the valve plug as an intermediate signal
Step 2-3) defining a stacking output vector Y (N) according to the input and output data, and defining a stacking information matrix psi (N) as a formula (12);
step 2-4) defining a criterion function J (theta) as
Wherein,
is an estimate of the pile-up information matrix, and->
Is an estimate of the parameter vector;
step 2-5) intermediate variables in the information vector
Fractional derivatives of intermediate variables
And fractional derivative of the undetectable noise Δ α v (t) is replaced by its evaluation value>
And &>
Calculating an estimate ≥ of the information vector according to equation (14)>
Construction according to equation (15)>
Step 2-6) selecting a suitable convergence factor mu according to the formula (16) k ；
Step 2-7) calculating the estimated value of the parameter vector according to the formula (17)
Step 2-8) calculating the estimated intermediate variables according to the equations (8), (18)
And the estimated noise->
The fractional derivative { (R) } of the noise and the intermediate variable estimated is calculated as defined by GL of equation (7)>
Step 2-9) judging whether the maximum iteration times are reached, if not, skipping the program to step 2-5), and if so, entering step 2-10);
and 2-10) outputting a result to finish identification.
The schematic of the fractional order fluid control valve system employed in this embodiment is shown in fig. 2. Wherein u (t) is a pneumatic control signal of the valve,
is the valve plug position, x (t) is the estimated fluid flow, and y (t) is the actual fluid flow.
With the above-mentioned fractional Wiener model, the following model can be established for the present embodiment:
e(t)＝(1+d 1 z -α )v(t)＝(1+0.1z -0.3 )v(t),
y(t)＝x(t)+e(t),
comparing the above model with step 1), it is possible to obtain
a 1 ＝0.2,a 2 ＝0.4,b 1 ＝0.3,b 2 ＝0.5,p 2 ＝1,d 1 ＝0.1,
For the above model, a criterion function J (θ) is determined for use in the gradient iteration algorithm, the criterion function being defined as follows:
wherein Y (N) is a pile-up output vector,
is an estimate of the pile-up information matrix, and->
Is an estimate of the parameter vector;
in order to conveniently substitute the parameters to be identified into the gradient iterative algorithm, the parameters to be identified are formed into a parameter vector θ, and the parameters to be identified are as follows:
θ＝[a 1 ,a 2 ,b 1 ,b 2 ,p 2 ,d 1 ] T ,
initializing according to step 2-1), and giving iteration times k max Data length N;
obtaining input and output data of the fractional order fluid control valve system model according to the step 2-2), and calculating the position of the valve plug
Defining a stacking output vector Y (N) and a stacking information matrix psi (N) according to the step 2-3);
obtaining a criterion function J (theta) according to the step 2-4);
calculating an estimated value of the information vector according to step 2-5)
Evaluation value for constructing accumulation information matrix>
Selecting a proper convergence factor mu according to the step 2-6) k ；
Updating the estimated value of the parameter vector according to the step 2-7)
Calculating estimated intermediate variables according to steps 2-8)
And the estimated noise->
Calculating a fractional order derivative of the estimated intermediate variable and noise ≧>
And (5) completing circulation according to the steps 2-9) and 2-10) and outputting a result.
Wherein, the convergence factor mu is set k And data length N, several considerations need to be taken into account: the too small convergence factor can cause too large identification error and fail to obtain accurate identification result; too large a convergence factor may result in a fluctuating recognition result and a non-converged recognition result. The problem of low identification precision is caused by unsatisfactory identification result due to the fact that the data length is too small; too large data length will cause a problem of large calculation amount.
The parameter identification result performed by using the fractional order fluid control valve system parameter identification method based on the gradient iterative algorithm of the present embodiment is shown in fig. 4; the identification method is high in identification precision, the estimated value of the parameter to be identified is very close to the true value, and meanwhile, the identification method is good in applicability to parameter identification of the fractional order fluid control valve model.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.
Claims (3)
1. The method for identifying the parameters of the fractional order fluid control valve system based on the gradient iterative algorithm is characterized by comprising the following steps of:
step 1) establishing an input and output mathematical model of a fractional order fluid control valve system;
and 2) constructing an identification process of the gradient iterative algorithm.
2. The gradient iterative algorithm-based fractional order fluid control valve system identification method of claim 1, wherein the step 1) comprises the steps of:
(1-1) constructing a structure of a fractional order fluid control valve system Wiener nonlinear model;
(1-2) constructing a fractional order fluid control valve system Wiener nonlinear model expression according to the Wiener nonlinear model obtained in the step (1-1) as follows:
e(t)＝D(z)v(t), (3)
y(t)＝x(t)+e(t), (4)
where u (t) is the model input signal, y (t) is the model output signal, and v (t) is a mean of 0 and a variance of σ 2 And white noise, an intermediate variable, satisfying Gaussian distribution
x (t) and e (t) are signals which are not measurable in the middle, z -1 Is the unit delay symbol: z is a radical of -1 y (t) = y (t-1), a (z), B (z) and D (z) are constant polynomials with the following definitions:
wherein the polynomial factor a i ，b j And d l Is the parameter to be estimated, α i ，β j And gamma l Is the fractional order of the polynomial denominator, the present invention considers fractional fit systems, i.e. the fractional order is a multiple of the same base and is known:
(1-3) intermediate signal
And e (t) is expressed as:
simplifying to obtain:
the invention adopts Gr unwald Letnikov (GL) definition to solve fractional derivative, wherein the GL definition is as follows:
where Δ is the discrete fractional order difference operator, Δ α m (kh) is the alpha fractional derivative of the function m (k) with t = kh, where h is the sampling interval and k is the number of samples to calculate the derivative approximation, substituting equation (7) into equations (5), (6), the intermediate signal after discretization
And e (t) rewritten as:
the output of the nonlinear element in the model is in polynomial form and is expressed as:
wherein p is i Is an unknown coefficient to be identified, and the order r of the polynomial function is known, in order to ensure the uniqueness of the parameter, let the first modulus p of the nonlinear component 1 ＝1；
(1-4) obtaining an identification model of a Wiener nonlinear model of a fractional order fluid control valve system:
in the above-mentioned formula,
is a systematic information vector, represented as:
wherein,
are respectively defined as
θ is the parameter vector of the system, expressed as: θ = [ θ = 1 T ,θ 2 T ,θ 3 T ] T ，
Wherein, theta 1 ，θ 2 ，θ 3 Are respectively defined as:
θ 2 ＝[p 2 ,p 3 ,…,p r ] T ,
3. the gradient iterative algorithm-based method for identifying parameters of a Wiener nonlinear model of a fractional order fluid control valve system according to claim 1, wherein the step 2) comprises the steps of:
step 2-1) initialization, given iteration times k max Data length N;
step 2-2) taking a pneumatic control signal of the valve as input data u (t) of a fractional order fluid control valve system model, taking fluid flow as output data y (t), and taking the position of the valve plug as an intermediate signal
Step 2-3) defining a stacking output vector Y (N) according to the input and output data, and defining a stacking information matrix psi (N) as a formula (12);
step 2-4) defining a criterion function J (theta) as
Wherein,
is an estimate of the pile-up information matrix, and->
Is an estimate of the parameter vector;
step 2-5) intermediate variables in the information vector
Fractional derivative of an intermediate variable->
And fractional derivative of the undetectable noise Δ α v (t) is replaced by its evaluation value>
And &>
Calculating an estimate ≥ of the information vector according to equation (14)>
Construction according to equation (15)>
Step 2-6) selecting a suitable convergence factor mu according to formula (16) k ；
Step 2-7) calculating the estimated value of the parameter vector according to the formula (17)
Step 2-8) calculating the estimated intermediate variables according to the equations (8), (18)
And the estimated noise->
The fractional derivative { (R) } of the noise and the intermediate variable estimated is calculated as defined by GL of equation (7)>
Step 2-9) judging whether the maximum iteration times are reached, if not, skipping the program to step 2-5), and if so, entering step 2-10);
and 2-10) outputting a result to finish identification.
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| CN115033838B (en) * | 2022-06-27 | 2024-06-25 | 南通大学 | Fractional order water tank identification method based on forgetting augmentation random gradient algorithm |
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