CN114337427B - Rotary inertia identification method of recursive least square method with forgetting factor - Google Patents
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Abstract
The invention discloses a rotational inertia identification method of a recursive least square method with forgetting factors. The method comprises the following steps: writing an asynchronous motor motion equation into a recursive least square form, and determining output variables, parameters to be identified and an observation matrix; defining observed quantity length, forgetting factors, an initialization covariance matrix and identification parameters; calculating a gain matrix at the current moment; calculating covariance of the current moment; updating the parameter estimation value; updating the objective function value; and comparing the calculated objective function value with a preset objective function value, continuously updating, and finally calculating to obtain the motor moment of inertia information. The invention introduces a rotary inertia identification method with forgetting factors by a recursive least square method, and improves the system control performance of the motor under the conditions of load rotary inertia change and the like.
Description
Technical Field
The invention relates to the technical field of motor moment of inertia identification, in particular to a moment of inertia identification method of a recursive least square method with forgetting factors.
Background
In a modern high-performance alternating current motor speed regulation control system, vector control technology has been widely applied to high-performance control of various alternating current motors by virtue of the advantages of excellent performance, simple and reliable method and the like. The key to the implementation of the vector control technology is that decoupling is performed on the premise that accurate flux linkage estimation is performed, and the accuracy of flux linkage estimation depends greatly on motor parameters, so that the identification of the motor parameters plays an important fundamental role in the vector control technology. In addition to being limited by the accuracy of the identification of the motor parameters, is also affected by the load characteristics. In the characteristics of torque, moment of inertia and the like of a load, the moment of inertia has a great influence on the dynamic performance of motor operation. In a small ac motor control system, the moment of inertia of the load is typically several times or even tens of times that of the motor rotor, so that the variation of the moment of inertia of the load can have a significant effect on the mechanical characteristics of the system. For example, in multi-axis robots widely used in industrial control, moment of inertia of a motor load may change when an object is transferred, and if the moment of inertia cannot be identified in real time, dynamic performance of a system may be affected. Therefore, on-line identification of the total rotational inertia of the AC motor control system is an effective means of improving the performance of the control system.
The least square method is a common and most basic identification method, the thought is to select a state variable and an observed variable of a model, calculate the square sum of errors between the observed value and an actual value, adjust model parameters to enable the square sum to be minimum, and the model parameters at the moment can be considered to be equal to the actual system parameters. The method is widely applied, can be used for dynamic and static systems, is applicable to both off-line identification and on-line identification, and has the characteristics of unbiased identification result, consistency, effectiveness and the like. Based on the common least square method, recursive least square methods, weighted least square methods and the like are widely applied, wherein the recursive least square method solves the defects of complex calculation and occupation of the memory of a processor of the common least square method by avoiding repeated matrix calculation and matrix inversion. In the field of motor parameter identification, a motor model is generally simplified and equivalent to a linear model directly related to motor parameters, and then online identification is performed by using a recursive least square method. However, the recursive least square method encounters a problem of parameter saturation when applied to time-varying parameter identification. Because the time-varying parameter identification is performed online, new observation data are continuously obtained, and the new data and the old data have the same weight in the identification process, the new data identification result is influenced by the old data along with the identification, so that larger deviation is generated.
Disclosure of Invention
The invention aims to provide a rotary inertia identification method of a recursive least square method with forgetting factors, so as to improve the system control performance of a motor under the conditions of load rotary inertia change and the like.
The technical solution for realizing the purpose of the invention is as follows: a rotational inertia identification method of a recursive least square method with forgetting factors comprises the following steps:
step 1, establishing a recursive least square model of an asynchronous motor, determining an output quantity y, a parameter theta to be identified and an observation matrix
Step 2, defining observed quantity length, forgetting factor, initializing covariance matrix P (0) and parameter theta (0) to be identified;
Step 3, calculating a gain matrix K (t) at the current moment;
Step 4, calculating the covariance P (t) of the current moment;
step 5, updating the parameter estimation value
Step 6, updating the objective function value J t (theta);
And 7, comparing the objective function value J t (theta) with a preset objective function value J set (), if J t(θ)＞Jset (), t=t+1 and returning to the step 3, otherwise, outputting the motor moment of inertia information.
Compared with the prior art, the invention has the remarkable advantages that: (1) The forgetting factor is introduced, so that the weight occupied by old data can be reduced, when the parameter to be identified is suddenly changed, a new value can be identified at a faster response speed, the smaller the forgetting factor is, the smaller the weight occupied by the old data is, the faster the response speed is, and the problem of parameter saturation is effectively solved; (2) By adopting the rotational inertia identification method of the recursive least square method with forgetting factors, the system control performance of the motor under the conditions of load rotational inertia change and the like is improved.
Drawings
Fig. 1 is a flowchart of a method for identifying moment of inertia by a recursive least square method with forgetting factors in the present invention.
FIG. 2 is a system block diagram of a method for identifying moment of inertia with a forgetting factor by a recursive least square method in the present invention.
Detailed Description
Referring to fig. 1, the rotational inertia identification method of the recursive least square method with forgetting factors of the invention comprises the following steps:
step 1, establishing a recursive least square model of an asynchronous motor, determining an output quantity y, a parameter theta to be identified and an observation matrix
Step 2, defining observed quantity length, forgetting factor, initializing covariance matrix P (0) and parameter theta (0) to be identified;
Step 3, calculating a gain matrix K (t) at the current moment;
Step 4, calculating the covariance P (t) of the current moment;
step 5, updating the parameter estimation value
Step 6, updating the objective function value J t (theta);
And 7, comparing the objective function value J t (theta) with a preset objective function value J set (), if J t(θ)＞Jset (), t=t+1 and returning to the step 3, otherwise, outputting the motor moment of inertia information.
Further, a recursive least square model of the asynchronous motor is built in the step 1, and the output quantity y, the parameter theta to be identified and the observation matrix are determinedThe method comprises the following steps:
Step 1.1, constructing a system regression equation, specifically:
y(i)＝θ1u1(i)+θ2u2(i)+…+θnun(i)i＝1,2,3,…,m (32)
Where u 1(i),u2(i),…,un (i) is the system input observed at time t i and y (i) is the system output observed at time t i; θ= { θ 1,θ2,...,θn } is the parameter array to be identified, i.e. the regression coefficient; n is the system order;
Step 1.2, converting into a matrix form, specifically:
Y＝[y(1) y(2) … y(m)]T (33)
θ＝[θ1 θ2 … θn]T (34)
e＝[e1 e2 … em]T (36)
There are measurement equations:
Y＝Φθ+e (37)
Wherein Y is a system output matrix, phi is a system input matrix, theta is a parameter matrix to be identified, and e is a residual error;
Step 1.3, establishing errors in an objective function mode to obtain
Where J is an objective function, also called a cost function;
step 1.4, selecting a group of estimated values of θ The objective function J is minimized, so that J is derived from θ, let the derivative value be 0, and there are:
Obtaining:
I.e. the least squares estimation formula.
Further, the defining observed quantity length, forgetting factor, initializing covariance matrix P (0) and parameter θ (0) to be identified in step2 are specifically as follows:
step 2.1, discretizing an estimation formula, and describing the estimation formula in a form of a differential equation:
Where y (k) is an output sample value at the kth time of the system, u (k) is an input sample value at the kth time of the system, and k is the kth time; a 1...an,b0...bn is a parameter to be identified.
Step 2.2, introducing a shift operator:
A(Z-1)y(k)＝B(Z-1)u(k) (42)
In the method, in the process of the invention, All are coefficient matrixes, Z -x represents lag x sampling periods, u is the number of output quantities, and v is the number of input quantities;
The rewriting is as follows:
wherein e (k) is a generalized error, specifically:
e(k)＝A(Z-1)y(k)-B(Z-1)u(k) (44)
Step 2.3, introducing a discrete vector and a matrix, wherein the method comprises the following steps of:
Y＝[y(n+1)y(n+2)…y(n+N)]T (45)
e＝[e(n+1) e(n+2) … e(n+N)]T (46)
θ＝[a1 a2 … an b0 b1 … bn]T (47)
Wherein Y is a system output matrix, phi is a system input matrix, theta is a parameter matrix to be identified, e is a residual error, N is a system order, and N is an nth moment;
the matrix is arranged into a Y=phiθ+e form to obtain:
step 2.4, preparing j=e T e into a completely flat mode, and obtaining a differential form least square estimation formula:
Wherein Y is the system output matrix, phi is the system input matrix, phi T is the transpose of the system input matrix, Is an identification result matrix, and e is a residual error;
Step 2.5, adding an observation time, wherein the observed input quantity is u (n+n+1), the output quantity is y (n+n+1), and the method comprises the following steps:
θ＝[a1 a2 … an b0 b1 … bn]T (51)
e＝[e(n+1) e(n+2) … e(n+N+1)]T (52)
Phi (N) is increased by one line Y (N) is increased by one Y (n+N+1), and has:
For the observation matrix at the next moment:
Step 2.6, obtaining a parameter estimation matrix, which specifically comprises the following steps:
Step 2.7, introducing matrix inversion theory, including:
In the method, in the process of the invention, Is to find/>The obtained covariance matrix is usually initialized to be a diagonal matrix, and the values are 1e 4-1 e10; k (N) is a correction matrix;
y (n+n+1) is a new output observation; Is an estimate/> And outputting the estimated value of the (n+1) th time obtained after the calculation.
Equation (26) -equation (28) is a recursive least squares method identification equation.
Step 2.8, introducing forgetting factors, which are specifically as follows:
Wherein lambda is a forgetting factor, lambda is more than 0 and less than or equal to 1, and lambda is more than or equal to 0.9 and less than or equal to 0.99; λ=1, the degradation is a normal recursive least squares method. The initial covariance matrix is set to The forgetting factor is set to λ=0.98.
Further, the calculating the gain matrix K (N) at the current moment is specifically as follows:
Further, the calculating the covariance P (N) of the current time in step 4 is specifically as follows:
Wherein E is a unit diagonal array.
Further, the parameter estimation value is updated in the step 5The method comprises the following steps:
Further, the updated objective function value J t (θ) in step 6 is specifically as follows:
the mechanical equation of the asynchronous motor is as follows:
Where J is the system moment of inertia, ω r is the motor rotor mechanical angular velocity, T e is the motor output electromagnetic torque, T L is the load torque, and B is the damping coefficient.
Neglecting damping torque and discretizing to obtain:
where T is a sampling period, and is set to 1 μs.
Ignoring the load variation term, let y=Φθ have:
finally, the rotational inertia of the system can be identified by the output electromagnetic torque and the mechanical angular speed of the rotor of the asynchronous motor.
In summary, the invention adopts the asynchronous motor moment of inertia identification method based on forgetting factor recursive least square method, and improves the system control performance of the motor under the condition of load moment of inertia change and the like.
Claims (6)
1. A rotational inertia identification method of a recursive least square method with forgetting factors is characterized by comprising the following steps:
step 1, establishing a recursive least square model of an asynchronous motor, determining an output quantity y, a parameter theta to be identified and an observation matrix
Step 2, defining observed quantity length, forgetting factor, initializing covariance matrix P (0) and parameter theta (0) to be identified;
Step 3, calculating a gain matrix K (t) at the current moment;
Step 4, calculating the covariance P (t) of the current moment;
step 5, updating the parameter estimation value
Step 6, updating the objective function value J t (theta);
Step 7, comparing the objective function value J t (theta) with a preset objective function value J set (), if J t(θ)＞Jset (), t=t+1 and returning to step 3, otherwise, outputting the motor moment of inertia information;
The defining observed quantity length, forgetting factor, initializing covariance matrix P (0) and parameter θ (0) to be identified in step 2 is as follows:
step 2.1, discretizing an estimation formula, and describing the estimation formula in a form of a differential equation:
Where y (k) is an output sample value at the kth time of the system, u (k) is an input sample value at the kth time of the system, and k is the kth time; a 1...an,b0…bn is a parameter to be identified;
step 2.2, introducing a shift operator:
A(Z-1)y(k)＝B(Z-1)u(k) (11)
In the method, in the process of the invention, All are coefficient matrixes, Z -x represents lag x sampling periods, u is the number of output quantities, and v is the number of input quantities;
The rewriting is as follows:
wherein e (k) is a generalized error, specifically:
e(k)＝A(Z-1)y(k)-B(Z-1)u(k) (13)
Step 2.3, introducing a discrete vector and a matrix, wherein the method comprises the following steps of:
Y＝[y(n+1) y(n+2) … y(n+N)]T (14)
e＝[e(n+1) e(n+2) … e(n+N)]T (15)
θ＝[a1 a2 … an b0 b1 … bn]T (16)
Wherein Y is a system output matrix, phi is a system input matrix, theta is a parameter matrix to be identified, e is a residual error, N is a system order, and N is an nth moment;
the matrix is arranged into a Y=phiθ+e form to obtain:
step 2.4, preparing j=e T e into a completely flat mode, and obtaining a differential form least square estimation formula:
Wherein Y is the system output matrix, phi is the system input matrix, phi T is the transpose of the system input matrix, Is an identification result matrix, and e is a residual error;
Step 2.5, adding an observation time, wherein the observed input quantity is u (n+n+1), the output quantity is y (n+n+1), and the method comprises the following steps:
θ＝[a1 a2 … an b0 b1 …bn]T (20)
e＝[e(n+1) e(n+2) … e(n+N+1)]T (21)
Phi (N) is increased by one line Y (N) is increased by one Y (n+N+1), and has:
For the observation matrix at the next moment:
Step 2.6, obtaining a parameter estimation matrix, which specifically comprises the following steps:
Step 2.7, introducing matrix inversion theory, including:
wherein P (N) = [ phi T(N)Φ(N)]-1 ] is the solution The obtained covariance matrix is usually initialized to be a diagonal matrix, and the values are 1e 4-1 e10; k (N) is a correction matrix;
y (n+n+1) is a new output observation; Is an estimate/> The output estimated value of the (n+1) th time obtained after the calculation;
Equation (26) -equation (28), i.e., recursive least squares method identification equation;
Step 2.8, introducing forgetting factors, which are specifically as follows:
Wherein lambda is a forgetting factor and is more than or equal to 0.9 and less than or equal to 0.99.
2. The method for identifying the moment of inertia by a recursive least square method with forgetting factors as set forth in claim 1, wherein the step1 of establishing a recursive least square model of an asynchronous motor determines an output y, a parameter θ to be identified and an observation matrixThe method comprises the following steps:
Step 1.1, constructing a system regression equation, specifically:
y(i)＝θ1u1(i)+θ2u2(i)+…+θnun(i) i＝1,2,3,…,m (1)
Where u 1(i),u2(i),…,un (i) is the system input observed at time t i and y (i) is the system output observed at time t i; θ= { θ 1,θ2,...,θn } is the parameter array to be identified, i.e. the regression coefficient; n is the system order;
Step 1.2, converting into a matrix form, specifically:
Y＝[y(1) y(2) … y(m)]T (2)
θ＝[θ1 θ2 … θn]T (3)
e＝[e1 e2 … em]T (5)
There are measurement equations:
Y＝Φθ+e (6)
Wherein Y is a system output matrix, phi is a system input matrix, theta is a parameter matrix to be identified, and e is a residual error;
Step 1.3, establishing errors in an objective function mode to obtain
Where J is an objective function, also called a cost function;
step 1.4, selecting a group of estimated values of θ The objective function J is minimized, so that J is derived from θ, let the derivative value be 0, and there are:
Obtaining:
I.e. the least squares estimation formula.
3. The method for identifying the moment of inertia by using the recursive least square method with forgetting factors according to claim 1, wherein the calculating the gain matrix K (N) at the current time in the step 3 is specifically as follows:
4. the method for identifying the moment of inertia by using the recursive least square method with forgetting factors according to claim 1, wherein the calculating the covariance P (N) at the current time in the step 4 is as follows:
Wherein E is a unit diagonal array.
5. The method for identifying moment of inertia by recursive least square with forgetting factor as recited in claim 1, wherein the updating the parameter estimation value in step 5 is characterized byThe method comprises the following steps:
6. The method for identifying the moment of inertia by the recursive least square method with forgetting factors according to claim 1, wherein the updated objective function value J t (θ) in step 6 is specifically as follows:
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| CN106452247A (en) * | 2016-12-12 | 2017-02-22 | 广东工业大学 | Method and device for identifying rotational inertia of permanent magnet synchronous motors |
| CN107124132A (en) * | 2017-05-22 | 2017-09-01 | 珠海格力节能环保制冷技术研究中心有限公司 | A kind of method for identification of rotational inertia and identifier |
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| CN109586645A (en) * | 2018-11-27 | 2019-04-05 | 中国地质大学（武汉） | A kind of permanent magnet synchronous motor inertia recognition methods and equipment |
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|---|---|---|---|---|
| CN106452247A (en) * | 2016-12-12 | 2017-02-22 | 广东工业大学 | Method and device for identifying rotational inertia of permanent magnet synchronous motors |
| CN107124132A (en) * | 2017-05-22 | 2017-09-01 | 珠海格力节能环保制冷技术研究中心有限公司 | A kind of method for identification of rotational inertia and identifier |
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