Maximum Likelihood Gradient Iterative Parameter Estimation Method Based on Generalized Time-Varying System Identification Model

Abstract

The present invention discloses a maximum likelihood gradient iterative parameter estimation algorithm based on a generalized time-varying system identification model. Due to the influence of factors such as disturbances, the model parameters of a motor speed control system are difficult to accurately estimate. DC motor control systems are characterized by randomness and the influence of disturbances. Furthermore, measuring the internal parameters of the motor during operation is extremely difficult. Furthermore, in actual operation, due to factors such as measurement noise, the system is contaminated by colored noise, which significantly affects the algorithm's identification accuracy. To improve the accuracy of motor parameter estimation, the present invention, based on a gradient search algorithm, transforms the system parameter identification problem into a probability density function extremum problem based on the maximum likelihood principle, and utilizes the maximum likelihood principle to directly process system noise to improve the algorithm's identification accuracy. The present invention includes the steps of constructing an identification model of a generalized time-varying system affected by colored noise, constructing a maximum likelihood gradient iterative parameter estimation algorithm flow, and constructing a maximum likelihood gradient iterative parameter estimation algorithm. The present method is simple, reliable, and has high identification accuracy, and can be applied to parameter estimation in DC motor control systems.

Description

Technical Field

[0001] The invention relates to a maximum likelihood gradient iterative parameter estimation algorithm based on a generalized time-varying system identification model. Background Art

[0002] With the continuous development of low-carbon lifestyles, electric vehicles are developing particularly rapidly. As a key driving device in electric vehicles, the electric motor is a mechanical device that directly converts the electrical energy stored in the power battery into mechanical energy. It does not require the gearbox or other traditional fuel vehicle structures, resulting in a simple and reliable structure, high efficiency, and zero emissions. During operation, electric motors are subject to vibration, load changes, and other factors, causing significant changes in their control system parameters. Traditional identification algorithms do not have the ability to quickly track these time-varying parameters. Furthermore, the presence of unmeasurable variables in their control systems reduces the estimation accuracy of the identification algorithms. By considering the factors that affect the changes in system parameters, analyzing the disturbances, and utilizing a generalized time-varying system model to construct a mathematical model of the electric motor, accurate parameter estimation of the motor system is achieved.

[0003] A generalized time-varying system affected by a disturbance has its parameters changing with the disturbance amount. It is a typical time-varying parameter system and is widely present in chemical industry and practical production processes. The identification model of a generalized time-varying system has a wide range of applications and can describe many time-varying systems. It has received widespread attention in the field of system identification. The generalized time-varying system has good versatility and generalization, and has a good descriptive effect on various systems. The present invention uses the maximum likelihood gradient iterative parameter estimation algorithm to perform parameter identification on a separately excited DC motor speed control system based on the generalized time-varying system identification model. Summary of the Invention

[0004] The present invention aims to estimate the model parameters of the speed regulation system of a separately excited DC motor by using a maximum likelihood gradient iterative parameter estimation algorithm based on a generalized time-varying system identification model.

[0005] The technical solution of the present invention is:

[0006] 1) Construct an identification model based on a generalized time-varying system. The specific steps are as follows:

[0007] Step 1: The generalized time-varying system model expression is as follows:

[0008]

[0009]

[0010] The meaning of each symbol in the above formula: u(t) and y(t) are the input and output of the system respectively, a i (t s) and b i (t s ) is the time-varying parameter of the system, w(t) is the colored noise, and v(t) is a zero-mean noise with a variance of σ 2 And the white noise satisfies Gaussian distribution.

[0011] Step 2: According to the characteristics of time-varying parameters of generalized time-varying systems, the time-varying parameters are expressed as

[0012]

[0013]

[0014] where a i j and b i j is the coefficient of the parameter, ξ i (t) is the disturbance of the system.

[0015] Step 3: Construct the relationship between the sub-output variables y1(t) and w(t) of the generalized time-varying system model as follows:

[0016] y1(t s )=y(t s )-β T (t s )θ,

[0017] w(t s )=y(t s )-α T (t s )Ξψ(t s ).

[0018] Step 4: The two sub-identification models of the generalized time-varying system are obtained as follows:

[0019] y1(t)=α T (t s )Ξψ(t s )+v(t s ),

[0020] β T (t s )θ+v(t s ).

[0021] Step 5: Obtain two maximum likelihood criterion functions:

[0022]

[0023]

[0024] The noise v(t s ) can be expressed as

[0025]

[0026] 2) Construct the maximum likelihood gradient iterative parameter estimation algorithm process:

[0027] Step 1: Start the recognition algorithm;

[0028] The second step is to set k = 0 and set the initial values ​​of the relevant intermediate variables;

[0029] Step 3: Collect the armature voltage, output angular velocity and excitation current data of the separately excited DC motor as the input and output data of the model and the measurable disturbance data, and perform data preprocessing;

[0030] Step 4: Construct information vector α(t s ) and the measurable disturbance vector ψ(t);

[0031] Step 5: Calculation

[0032] Step 6: Construction and

[0033] Step 7: Calculate step length and

[0034] Step 8: Update the coefficient matrix and parameter vector

[0035] Step 9: Calculation

[0036] Step 10: If k=k+1 and repeat steps 6 to 9. Otherwise, get the parameter estimate and

[0037] Step 11: End the process.

[0038] The definitions of the variables are as follows:

[0039] Define input u(t), output y(t), disturbance ρ i (t);

[0040] Define w(t) as the intermediate variable of colored noise, v(t) is a variable with a mean of zero and a variance of σ 2 And white noise that satisfies Gaussian distribution;

[0041] Define Ξ as the coefficient matrix and θ as the parameter vector;

[0042] definition is the filtered system output, is the system output after filtering;

[0043] definition is the estimated value of the coefficient matrix Ξ at the kth iteration; is the estimated value of the coefficient vector θ at the kth iteration;

[0044] 3) According to the maximum likelihood gradient iterative parameter estimation algorithm process, construct its algorithm:

[0045]

[0046]

[0047]

[0048]

[0049]

[0050]

[0051]

[0052]

[0053]

[0054] α(t s )=[-y(t s -1),-y(t s -2),···,-y(t s -n a ),u(t s -1),u(t s -2),···,u(t s -n b )] T , (10)

[0055] ψ(t s )=[1,ξ1(t s ),ξ2(t s ),···,ξ p-1 (t s )] T , (11)

[0056]

[0057]

[0058]

[0059]

[0060] The specific steps of the above algorithm are:

[0061] 1. Start the identification algorithm, set k = 0, data length is l, and set the initial value: p0=10 6 , where p0 is a very large value, set ε = 10 -3 .

[0062] 2. Obtain the armature voltage data of the separately excited DC motor as input data, the motor output angular velocity data as output data, and the excitation current data as measurable disturbance data, and perform data filtering.

[0063] 3. Calculate α(t s ) and ψ(t);

[0064] 4. Calculate using equations (8) and (9) and

[0065] 5. Construct through equations (12) and (13) and

[0066] 6. Calculate using equations (3) and (5) and

[0067] 7. Estimated by refreshing the iterations of formula (2) and formula (4)

[0068] 8. Calculate the noise estimation sequence through formula (14)

[0069] 9. k increases by 1 and repeats steps 5 to 9; otherwise, proceed to step 11;

[0070] 10. Obtain coefficient matrix estimates and parameter vector estimates

[0071] 11. End identification;

[0072] The definitions of the variables are as follows:

[0073] Define input u(t), output o(t), disturbance ρ i (t);

[0074] Define ψ(t) as the measurable disturbance vector consisting of the disturbance quantity;

[0075] Define Ξ as the coefficient matrix;

[0076] Define θ as a parameter vector;

[0077] definition is the estimated value of Ξ at the kth iteration; is the estimated value of θ at the kth iteration;

[0078] definition is the noise estimate;

[0079] definition Represents two iteration steps.

[0080] The invention is simple and reliable, has high estimation accuracy, and can be applied to parameter estimation of a generalized time-varying identification model of a separately excited DC motor. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] The present invention will be further described below with reference to the accompanying drawings and examples.

[0082] Figure 1 It is a flowchart of the maximum likelihood gradient iterative parameter estimation algorithm of the system.

[0083] Figure 2 The following is a schematic diagram of a specific example of the method of the present invention. A large amount of armature voltage data of a DC motor is collected as input data, output angular velocity as output data, and excitation current as disturbance. After data preprocessing, the parameter estimation algorithm is used to run the result as follows: Figure 2 As shown, where δ is the parameter estimation error.

Claims

1. A maximum likelihood gradient iterative parameter estimation method based on a generalized time-varying system identification model, comprising the following steps: (1) Construct an identification model based on a generalized time-varying system. The specific steps are as follows: Step 1: The generalized time-varying system model expression is as follows: The meaning of each symbol in the above formula: u(t) and y(t) are the input and output of the system respectively, a i (t s ) and b i (t s ) is the time-varying parameter of the system, w(t) is the colored noise, and v(t) is a zero-mean noise with a variance of σ 2 And white noise that satisfies Gaussian distribution; Step 2: According to the characteristics of time-varying parameters of generalized time-varying systems, the time-varying parameters are expressed as where a i j and b i j is the coefficient of the parameter, ξ i (t) is the disturbance of the system; Step 3: Construct the relationship between the sub-output variables y1(t) and w(t) of the generalized time-varying system model as follows: w(t s )=y(t s )-α T (t s )Ξψ(t s ) Step 4: The two sub-identification models of the generalized time-varying system are obtained as follows: y1(t)=α T (t s )Ξψ(t s )+v(t s ), Step 5: Obtain two maximum likelihood criterion functions: The noise v(t s ) can be expressed as (2) Constructing the data filtering accelerated gradient search parameter estimation algorithm process: Step 1: Start the recognition algorithm; The second step is to set k = 0 and set the initial values ​​of the relevant intermediate variables; Step 3: Collect the armature voltage, output angular velocity and excitation current data of the separately excited DC motor as the input and output data of the model and the measurable disturbance data, and perform data preprocessing; Step 4: Construct information vector α(t s ) and the measurable disturbance vector ψ(t); Step 5: Calculation Step 6: Construction and Step 7: Calculate step length and Step 8: Update the coefficient matrix and parameter vector Step 9: Calculation Step 10: If And repeat steps 5 to 9; otherwise, get the parameter estimate and Step 11: End the process; The definitions of the variables are as follows: Define input u(t), output y(t), disturbance ρ i (t); Define w(t) as the intermediate variable of colored noise, v(t) is a variable with a mean of zero and a variance of σ 2 And white noise that satisfies Gaussian distribution; Define Ξ as the coefficient matrix, is the parameter vector; definition is the filtered system output, is the system output after filtering; definition is the estimated value of the coefficient matrix Ξ at the kth iteration; is the coefficient vector The estimated value of the kth iteration; (3) Based on the maximum likelihood gradient iterative parameter estimation algorithm, a maximum likelihood gradient iterative parameter estimation algorithm is constructed.

2. The maximum likelihood gradient iterative parameter estimation method based on a generalized time-varying system according to claim 1, wherein: The maximum likelihood gradient iterative parameter estimation algorithm described in step (3) is: α(t s )=[-y(t s -1),-y(t s -2),···,-y(t s -n a ),u(t s -1),u(t s -2),···,u(t s -n b )] T ,(10) ψ(t s )=[1,ξ1(t s ),ξ2(t s ),···,ξ p-1 (t s )] T , (11) The specific steps of the above algorithm are: 1) Start the identification algorithm, set k = 0, data length is l, and set the initial value: p0=10 6 , where p0 is a very large value, set ε = 10 -3 ; 2) obtaining armature voltage data of a separately excited DC motor as input data, motor output angular velocity data as output data, and excitation current data as measurable disturbance data, and performing data filtering; 3) Calculate α(t s ) and ψ(t); 4) Calculate by equations (8) and (9) and 5) Constructed by equations (12) and (13) and 6) Calculate by formula (3) and (5) and 7) Estimated by refreshing the iterations of formula (2) and formula (4) 8) Calculate the noise estimation sequence through formula (14) 9) k increases by 1 and repeats steps 5 to 9; otherwise, proceed to step 11; 10) Obtain coefficient matrix estimation and parameter vector estimates 11) End identification; The definitions of the variables are as follows: Define input u(t), output o(t), disturbance ρ i (t); Define ψ(t) as the measurable disturbance vector consisting of the disturbance quantity; Define Ξ as the coefficient matrix; definition is the parameter vector; definition is the estimated value of Ξ at the kth iteration; For the kth iteration estimated value of; definition is the noise estimate; definition Represents two iteration steps.

Images