Three-state model parameter identification method of ball screw feeding system

Abstract

The invention relates to a three-state model parameter identification method of a ball screw feeding system, and relates to the technical field of machining. Comprising the steps that a three-state model structure considering the gap influence caused by lead screw abrasion is constructed, and three states comprise the rigid body state under the low-frequency non-gap condition, the flexible state under the high-frequency non-gap condition and the rigid body state under the low-frequency gap condition; discretizing the models in different states, and constructing a parameter estimation model; and estimating model parameters in each state in the parameter estimation model based on a recursive maximum likelihood parameter identification method. According to the method, the influence of the lead screw gap and friction on the model precision and the identification process is considered at the same time, so that the three-state model provided by the method can more accurately represent the dynamic characteristics of the lead screw system, and the provided parameter identification method has higher identification precision.

Description

Technical Field

[0001] The invention relates to the technical field of mechanical processing, and in particular to a three-state model parameter identification method for a ball screw feed system. Background Art

[0002] Reference 1 "Y.Maeda, K.Harata, M.Iwasaki, A friction model-based frequency response analysis for frictional servo systems, IEEE Transactions on Industrial Informatics, 2018, 14: 5146–5155." discloses a flexible body model parameter identification method considering the effects of phase lag and nonlinear friction. This method considers the phase lag effect and uses the LuGre friction model for friction compensation, and uses the sine frequency sweep method to accurately identify the flexible body model parameters. However, this method does not consider the effect of the gap caused by the wear of the lead screw. The existence of the gap causes the frequency component to change during the frequency sweep commutation process, and the frequency sweep method fails.

[0003] Reference 2 "CYLee, SHHwang, E.Nam, BKMin, Identification of mass and sliding friction parameters of machine tool feed drive using recursive leastsquares method, 2020, 109: 2831-2844." discloses a rigid body model parameter identification method based on recursive least squares method. In order to solve the problem of difficult identification of friction nonlinearity in the low-speed section, this method artificially divides the screw speed into low-speed and high-speed sections, linearly transforms the low-speed section model, and performs parameter identification based on the linearized model. However, this method requires artificial division of high and low speed areas, and the implementation steps are cumbersome. In addition, since the model structure mutation problem caused by the gap is not considered, the identification algorithm also has the risk of failure during commutation.

[0004] The typical characteristics of the above literature are: whether it is the rigid body model parameter identification or the flexible body model parameter identification, the identification is based on a single model structure, and the model structure mutation caused by the gap is not considered. In addition, there is a lack of a simpler and more effective method for friction model parameter identification. Summary of the invention

[0005] The technical problems to be solved by the present invention are:

[0006] In order to overcome the problem of difficulty in identifying model parameters of a ball screw feed servo system caused by the existence of gap, the present invention provides a recursive maximum likelihood parameter identification method of a ball screw feed system based on a three-state model.

[0007] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0008] A three-state model parameter identification method for a ball screw feed system, characterized by comprising:

[0009] S1: construct a three-state model structure considering the effect of the gap caused by the wear of the lead screw, wherein the three states include a rigid state under low-frequency non-gap, a flexible state under high-frequency non-gap, and a rigid state under low-frequency gap;

[0010] S2: discretize the models of the rigid body state under low-frequency non-gap and the rigid body state under low-frequency gap to obtain a parameter estimation model of the discrete rigid body model; discretize the model of the flexible state under high-frequency non-gap to obtain a parameter estimation model of the discrete flexible body model;

[0011] S3: Estimate the parameters in the parameter estimation model of discrete rigid body model and discrete flexible body model based on the recursive maximum likelihood parameter identification method.

[0012] A further technical solution of the present invention: S1 comprises the following steps:

[0013] Step 1: First, establish the rigid body model of the low-speed non-clearance ball screw feed system:

[0014]

[0015] in J 1 represents the total inertia of the system, B 1 is the viscous friction coefficient, F f1 is the equivalent friction of the system, K a and K t are the current amplification factor and torque amplification factor, r g is the transmission ratio, Respectively represent the position, velocity and acceleration of the motor side; According to this formula, the open-loop transfer function of the rigid body system model can be obtained as:

[0016]

[0017] where x M (s),u e (s) and F fe1 (s) is x M (t),u e (t) and F fe1(t) Transformation result in Laplace domain, s represents the Laplace operator;

[0018] Step 2: Then establish a flexible body model under high speed and no gap:

[0019]

[0020] in

[0021] They represent the position, velocity and acceleration of the load side respectively; the subscripts "M" and "L" represent the motor side and the load side respectively. Since the influence of the gap is not considered, the friction at this time can be considered to be equal to the friction in step 1, that is, F fe3 =F fe1 ; K S ,C S are the torsional stiffness and viscosity coefficient of the screw system respectively; according to this formula, the open-loop transfer function of the flexible system model can be obtained:

[0022]

[0023] B(s)=M L s 2 +(C Se +C L )s+K Se

[0024] A(s)=M M M L s 4 +[M L C M +M M C L +(M M +M L )C Se ]s 3

[0025] +[C M C L +(C M +C L )C Se +(M M +M L )K Se ]s 2 +(C M +C L )K Se s

[0026] At low speeds, the effects of viscous friction are usually negligible, which means Then the open-loop transfer function of the system can be simplified as follows:

[0027]

[0028] Based on the simplified transfer function G 2 (s), the anti-resonance frequency f of the system ares and the resonant frequency f res The calculation results are as follows:

[0029]

[0030] Step 3: Finally, establish a rigid body model under low speed gap:

[0031]

[0032] in J 2 Indicates the inertia on the motor side, B 2 is the viscous friction coefficient, F f2 is the friction force; in this process, the speed of the screw is very low, and the viscous friction term is can be ignored. According to this formula, the open-loop transfer function of the rigid body system model can be obtained as follows:

[0033]

[0034] Step 4: Combining the model structures of steps 1, 2, and 3, the following three-state model structure is summarized:

[0035]

[0036] To facilitate subsequent presentation, and State 1 for short. and Abbreviated as State 2, and Abbreviated as State 3; Corresponding to the speed of the motor side and the load side respectively;

[0037] Step 5: A composite friction model considering the gap effect is used in the three-state model, which is expressed as follows:

[0038]

[0039] Among them, F c1 ,F s1 ,v s1 They represent the Coulomb friction, static friction and Stribeck speed caused by the screw and the guide rail respectively; F c2 ,F s2 ,v s2represents the friction model parameters caused only by the screw; the time taken for the gap-crossing process is usually very short, and the friction in this process can be considered to remain constant. The composite friction model constructed above can be further simplified into the following form:

[0040]

[0041] A further technical solution of the present invention: S2 comprises the following steps:

[0042] Step 6: Use the following discrete error model to discretize the three-state model constructed in steps 1, 2, and 3:

[0043]

[0044] u(k)=u 0 (k)

[0045] Where u(k) and y(k) represent the input and output at the kth discrete time step, represents the transfer function in the discrete domain, z represents the time-shift operator, and e(k) represents the discrete error;

[0046] Step 7: Use the method in step 6 to discretize the continuous rigid body model in steps 1 and 3. The discretization method is the zero-order holder method. The discretization results are as follows:

[0047]

[0048] in is the parameter to be estimated, T s is the sampling time;

[0049] The discrete rigid body model in step 8 and step 7 can be expressed in the following linear parameter form:

[0050] y L =Φθ+e L

[0051] y L =[ω(2)ω(3)...ω(L)] T

[0052] e L =[e(2)e(3)...e(L)] T

[0053] in, and represent the time-varying positive and negative friction in State1, respectively. and denote the constant positive and negative friction in State 3, respectively. L denotes the total number of samples used in the parameter estimation process. PV(ω(k)) and NV(ω(k)) are the sign functions that identify the friction direction and are defined as follows:

[0054]

[0055] where ω c is the angular velocity noise caused by the quantization process; after the parameter θ is identified, the identification results of the model parameters involved in steps 1 and 3 can be expressed as:

[0056]

[0057] Step 9: Use the method in step 6 to discretize the continuous flexible body model in step 2. The discretization results are as follows:

[0058]

[0059] Among them, θ 1 ,θ 2 ,...,θ 6 is the parameter to be estimated;

[0060] Step 10: The discrete flexible body model in step 9 can be expressed in the same linear parameter form as in step 8, but with different y L ,e L ,θ,Φ:

[0061] y L =[ω(4)ω(5)...ω(L)] T

[0062] e L =[e(4)e(5)...e(L)] T

[0063] θ=[θ 1 θ 2 θ 3 θ 4 θ 5 θ 6 θ 7 θ 8 ] T

[0064]

[0065] A=[A u A ω ]

[0066]

[0067] FP (k)=-PV(k-1)-PV(k-2)-PV(k-3),k>3

[0068] F N (k)=-NV(k-1)-NV(k-2)-NV(k-3),k>3

[0069] After the parameters θ are identified, the parameter model in the discrete domain in step 9 is converted into a transfer function in the continuous domain using the zero-pole matching method:

[0070]

[0071] The mathematical relationship between the model parameters in step 2 and the model parameters of the transfer function in the continuous domain can be expressed as:

[0072]

[0073] A further technical solution of the present invention: S3 comprises the following steps:

[0074] Step 11. Considering the three-state model established in step 4, given L sets of independent measurement results u(k) and ω(k) and parameter θ, the following joint conditional probability distribution equation can be obtained:

[0075] State 1 and State 3:

[0076]

[0077] State 2:

[0078]

[0079] Step 12: According to different model structures, the discrete models in steps 8 and 10 can be expressed as follows:

[0080] State 1 and State 3:

[0081] ω(k)=θ(1)ω(k-1)+θ(2)u(k-1)-θ(3)PV(k-1)

[0082] -θ(4)NV(k-1)+e(k)

[0083] State 2:

[0084] ω(k)=θ(1)u(k-1)+θ(2)u(k-2)+θ(3)u(k-3)

[0085] -θ(4)ω(k-1)-θ(5)ω(k-2)-θ(6)ω(k-3)

[0086] -θ(7)(PV(k-1)+PV(k-2)+PV(k-3))

[0087] -θ(8)(NV(k-1)+NV(k-2)+NV(k-3))+e(k)

[0088] Step 13: Substitute the discrete model in step 12 into step 11, and the result will become:

[0089]

[0090] Where K 1 and K 2 is a constant, σ e is the standard deviation, and its value varies according to the state; in order to speed up the step 11 through the joint conditional probability distribution P(y L |u L-1 ,θ) to solve the value of parameter θ, and L |u L-1 ,θ) to find the log-likelihood function:

[0091]

[0092] Therefore, the process of solving the parameter θ can be regarded as solving lnP(y L |u L-1 ,θ) is the maximum value of lnP(y L |u L-1 ,θ) about The partial differential result of can be expressed as:

[0093]

[0094] Step 14: Construct the following cost equation:

[0095]

[0096] The maximum likelihood parameter estimation result of e(k) is The result is as follows:

[0097]

[0098] in

[0099] Step 15: Based on the analysis of steps 11 to 14, the recursive maximum likelihood parameter estimation result for the three-state model design can be expressed as:

[0100]

[0101] Where I is a 4th-order identity matrix for State 1 and State 3, and an 8th-order identity matrix for State 2. After θ is identified, the last n groups of θ are used as the initial value for iteration, and the iteration termination condition is designed as:

[0102] θ N+1 -θ N ≤∈

[0103] where θ N Represents the result of the Nth iteration, ∈ is a specified sufficiently small vector.

[0104] A computer system, characterized in that it comprises: one or more processors, and a computer-readable storage medium for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors implement the above-mentioned method.

[0105] A computer-readable storage medium, characterized in that it stores computer-executable instructions, which are used to implement the above method when executed.

[0106] A computer program product, characterized by comprising computer executable instructions, wherein the instructions are used to implement the above method when executed.

[0107] The beneficial effects of the present invention are:

[0108] The present invention provides a three-state model parameter identification method for a ball screw feed system. First, the clearance effect caused by screw wear is considered, and a three-state model structure that reflects the dynamic characteristics of the screw system is established, including a rigid state under low-frequency non-clearance, a flexible state under high-frequency non-clearance, and a rigid state under low-frequency clearance; then a state identification method is designed according to the difference between the load side position and the motor side position, and excitation signals are designed respectively; finally, an iterative parameter estimation method based on recursive maximum likelihood is proposed to identify the model parameters under each state. The present invention simultaneously considers the influence of screw clearance and friction on the model accuracy and identification process, so that the three-state model proposed by the method can more accurately characterize the dynamic characteristics of the screw system, and the proposed parameter identification method has higher identification accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0109] The drawings are only for the purpose of illustrating particular embodiments and are not to be considered limiting of the present invention. Like reference symbols denote like components throughout the drawings.

[0110] Figure 1 It is a flow chart of the method of the present invention.

[0111] Figure 2 is an excitation signal diagram used in the embodiment of the method of the present invention.

[0112] Figure 3 It is the State 1 model parameter identification result in the embodiment of the method of the present invention.

[0113] Figure 4 It is the Bode diagram of the State 2 model in the embodiment of the method of the present invention.

[0114] Figure 5 It is the modal knocking result in the embodiment of the method of the present invention.

[0115] Figure 6 is a cross-power spectrum diagram of the acceleration signal in the embodiment of the method of the present invention.

[0116] Figure 7 It is the dynamic characteristic response result of a reciprocating motion process in the embodiment of the method of the present invention.

[0117] Figure 8 It is the fitting result of the composite friction model in the embodiment of the method of the present invention.

[0118] Fig. 9 It is a three-state model representation diagram of the present invention taking into account the gap effect. DETAILED DESCRIPTION

[0119] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0120] The present invention provides a three-state model parameter identification method for a ball screw feed system. First, a three-state model structure considering the influence of clearance is designed, namely, a rigid body model and a flexible body model under non-clearance, and a rigid body model under clearance to characterize the dynamic characteristics of the ball screw feed servo system. Then, the models under different states are discretized to construct a parameter estimation model. Finally, a parameter identification algorithm based on recursive maximum likelihood is proposed to estimate the model parameters under each state, and combined with parameter iterative estimation, the accuracy of parameter estimation is improved. The present invention takes into account the influence of the existence of clearance on the model structure and the effectiveness of parameter identification, so that the model and parameter identification method proposed in the method of the present invention have more accurate dynamic accuracy and identification effect.

[0121] like Figure 1 As shown, the following steps are included:

[0122] Constructing a three-state model structure that considers the effect of the gap caused by the wear of the lead screw, wherein the three states include a rigid state under low-frequency non-gap, a flexible state under high-frequency non-gap, and a rigid state under low-frequency gap;

[0123] Discretize the models under different states and construct parameter estimation models;

[0124] The parameter identification method based on recursive maximum likelihood is used to estimate the model parameters under each state in the parameter estimation model.

[0125] The above steps are expanded as follows:

[0126] Step 1: First, establish the rigid body model of the low-speed non-clearance ball screw feed system:

[0127]

[0128] in J 1 represents the total inertia of the system, B 1 is the viscous friction coefficient, F f1 is the equivalent friction of the system, K a and K t are the current amplification factor and torque amplification factor, r g is the transmission ratio, Respectively represent the position, velocity and acceleration of the motor side. According to this formula, the open-loop transfer function of the rigid body system model can be obtained as:

[0129]

[0130] where x M (s),u e (s) and F fe1 (s) is x M (t),u e (t) and F fe1 (t) Transformation result in Laplace domain, s represents the Laplace operator.

[0131] Step 2: Then establish a flexible body model under high speed and no gap:

[0132]

[0133] in

[0134] The subscripts "M" and "L" represent the motor side and the load side, respectively. Since the influence of the gap is not considered, the friction at this time can be considered to be equal to the friction in step 1, that is, F fe3 =F fe1 . KS ,C S are the torsional stiffness and viscosity coefficient of the screw system respectively. According to this formula, the open-loop transfer function of the flexible system model can be obtained:

[0135]

[0136] B(s)=M L s 2 +(C Se +C L )s+K Se

[0137] A(s)=M M M L s 4 +[M L C M +M M C L +(M M +M L )C Se ]s 3 +[C M C L +(C M +C L )C Se +(M M +M L )K Se ]s 2 +(C M +C L )K Se s

[0138] At low speeds, the effects of viscous friction are usually negligible, which means Then the open-loop transfer function of the system can be simplified as follows:

[0139]

[0140] Based on the simplified transfer function G 2 (s), the anti-resonance frequency f of the system ares and the resonant frequency f res The calculation results are as follows:

[0141]

[0142] Step 3: Finally, establish a rigid body model under low speed gap:

[0143]

[0144] in J 2 Indicates the inertia on the motor side, B2 is the viscous friction coefficient, F f2 is the friction force. In this process, the speed of the screw is very low, and the viscous friction term is can be ignored. According to this formula, the open-loop transfer function of the rigid body system model can be obtained as follows:

[0145]

[0146] Step 4: Combining the model structures of steps 1, 2, and 3, the following three-state model structure is summarized:

[0147]

[0148] To facilitate subsequent presentation, And x L ≠0 is abbreviated as State 1. and Abbreviated as State 2, and Abbreviated as State 3. Corresponding to the speed of the motor side and the load side respectively.

[0149] Step 5: A composite friction model considering the gap effect is used in the three-state model, such as Fig. 9 As shown, it means as follows:

[0150]

[0151] Among them, F c1 ,F s1 ,v s1 They represent the Coulomb friction, static friction and Stribeck speed caused by the screw and the guide rail respectively. c2 ,F s2 ,v s2 Represents the friction model parameters caused only by the screw. The time taken for the gap-crossing process is usually very short, and the friction in this process can be considered to remain constant. The composite friction model constructed above can be further simplified into the following form:

[0152]

[0153] Step 6: Use the following discrete error model to discretize the three-state model constructed in steps 1, 2, and 3:

[0154]

[0155] u(k)=u 0 (k)

[0156] Where u(k) and y(k) represent the input and output at the kth discrete time step, represents the transfer function in the discrete domain, z represents the time-shift operator, and e(k) represents the discrete error.

[0157] Step 7: Use the method in step 6 to discretize the continuous rigid body model in steps 1 and 3. The discretization method is the zero-order holder method. The discretization results are as follows:

[0158]

[0159] in is the parameter to be estimated, T s is the sampling time.

[0160] The discrete rigid body model in step 8 and step 7 can be expressed in the following linear parameter form:

[0161] y L =Φθ+e L

[0162] y L =[ω(2)ω(3)...ω(L)] T

[0163] e L =[e(2)e(3)...e(L)] T

[0164] in, and represent the time-varying positive and negative friction in State1, respectively. and denote the constant positive and negative friction in State 3, respectively. L denotes the total number of samples used in the parameter estimation process. PV(ω(k)) and NV(ω(k)) are the sign functions that identify the friction direction and are defined as follows:

[0165]

[0166] where ω c is the angular velocity noise caused by the quantization process. After the parameters θ are identified, the identification results of the model parameters involved in steps 1 and 3 can be expressed as:

[0167] State 1

[0168] Step 9: Use the method in step 6 to discretize the continuous flexible body model in step 2. The discretization results are as follows:

[0169]

[0170] Among them, θ 1 ,θ 2 ,...,θ 6 is the parameter to be estimated.

[0171] Step 10: The discrete flexible body model in step 9 can be expressed in the same linear parameter form as in step 8, but with different y L ,e L ,θ,Φ:

[0172] y L =[ω(4)ω(5)...ω(L)] T

[0173] e L =[e(4)e(5)...e(L)] T

[0174] θ=[θ 1 θ 2 θ 3 θ 4 θ 5 θ 6 θ 7 θ 8 ] T

[0175]

[0176] A=[A u A ω ]

[0177]

[0178] F P (k)=-PV(k-1)-PV(k-2)-PV(k-3),k>3

[0179] F N (k)=-NV(k-1)-NV(k-2)-NV(k-3),k>3

[0180] After the parameters θ are identified, the parameter model in the discrete domain in step 9 is converted into a transfer function in the continuous domain using the zero-pole matching method:

[0181]

[0182] The mathematical relationship between the model parameters in step 2 and the model parameters of the transfer function in the continuous domain can be expressed as:

[0183]

[0184] Step 11. Considering the three-state model established in step 4, given L sets of independent measurement results u(k) and ω(k) and parameter θ, the following joint conditional probability distribution equation can be obtained:

[0185] State 1 and State 3:

[0186]

[0187] State 2:

[0188]

[0189] Step 12: According to different model structures, the discrete models in steps 8 and 10 can be expressed as follows:

[0190] State 1 and State 3:

[0191] ω(k)=θ(1)ω(k-1)+θ(2)u(k-1)-θ(3)PV(k-1)

[0192] -θ(4)NV(k-1)+e(k)

[0193] State 2:

[0194] ω(k)=θ(1)u(k-1)+θ(2)u(k-2)+θ(3)u(k-3)

[0195] -θ(4)ω(k-1)-θ(5)ω(k-2)-θ(6)ω(k-3)

[0196] -θ(7)(PV(k-1)+PV(k-2)+PV(k-3))

[0197] -θ(8)(NV(k-1)+NV(k-2)+NV(k-3))+e(k)

[0198] Step 13: Substitute the discrete model in step 12 into step 11, and the result will become:

[0199]

[0200] Where K 1 and K 2 is a constant, σ e is the standard deviation, and its value varies according to the state. In order to speed up the step 11 through the joint conditional probability distribution P(y L |u L-1 ,θ) to solve the value of parameter θ, and L |u L-1 ,θ) to find the log-likelihood function:

[0201]

[0202] Therefore, the process of solving the parameter θ can be regarded as solving lnP(y L |u L-1 ,θ) is the maximum value of lnP(y L |u L-1 ,θ) about The partial differential result of can be expressed as:

[0203]

[0204] Step 14: Construct the following cost equation:

[0205]

[0206] The maximum likelihood parameter estimation result of e(k) is The result is as follows:

[0207]

[0208] in

[0209] Step 15: Based on the analysis of steps 11 to 14, the recursive maximum likelihood parameter estimation result for the three-state model design can be expressed as:

[0210]

[0211] Where I is a 4th-order identity matrix for State 1 and State 3, and an 8th-order identity matrix for State 2. After θ is identified, the last n groups of θ are used as the initial value for iteration, and the iteration termination condition is designed as:

[0212] θ N+1 -θ N ≤∈

[0213] where θ N Represents the result of the Nth iteration, ∈ is a specified sufficiently small vector.

[0214] It can be seen that this example can more accurately characterize the dynamic characteristics of the system and perform accurate parameter identification because the influence of the gap on the model structure and parameter identification process is taken into account.

[0215] The method proposed in the present invention is tested on an open five-axis CNC machining platform. The sampling interval T of the control board s Set to 0.0005s. Design three different states respectively. Figure 2The excitation signal shown. The actual positions of the motor side and the load side are obtained by feedback from the incremental encoder and the grating ruler respectively. The parameter identification algorithm in the present invention is implemented by programming in Matlab / Simulink2021a.

[0216] Figure 3 The model parameters in State 1 obtained by using the method of the present invention, recursive least squares identification and recursive least squares identification with a variable forgetting factor, it can be seen that the method of the present invention has a faster estimation convergence speed; Figure 4 The Bode diagram of the model in State 2 obtained by using the method of the present invention, the frequency sweep method and the variable forgetting factor recursive least squares identification, combined with Figure 5 The modal tap results and Figure 6 The results of the cross power spectrum density analysis of the acceleration signal during uniform acceleration show that the method of the present invention has a more accurate identification accuracy for the flexible body model parameter identification. The three-state model parameter identification results are shown in Table 1. Figure 7 The dynamic characteristics description results of a reciprocating motion process using the method of the present invention, recursive least squares identification and recursive least squares method with variable forgetting factor are shown. Based on the friction parameters identified by the method of the present invention, the composite friction model proposed in this paper is obtained by least squares fitting, as shown in FIG. Figure 8 The parameter fitting results are shown in Table 2.

[0217] It can be seen that, due to the influence of the gap on the model structure and parameter identification process, this example can more accurately characterize the dynamic characteristics of the ball screw feed system with gap, and perform more accurate parameter identification based on the three-state model proposed in the method of the present invention.

[0218] Table 1 Parameter identification results of three-state model

[0219]

[0220] Table 2 Composite friction model parameters obtained by fitting

[0221]

[0222] The above description is only a specific implementation mode of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can easily think of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and these modifications or substitutions should be included in the protection scope of the present invention.

Claims

1. A three-state model parameter identification method for a ball screw feed system. It is characterized in that include: S1: construct a three-state model structure considering the effect of the gap caused by the wear of the lead screw, wherein the three states include a rigid state under low-frequency non-gap, a flexible state under high-frequency non-gap, and a rigid state under low-frequency gap; S2: discretize the models of the rigid body state under low-frequency non-gap and the rigid body state under low-frequency gap to obtain a parameter estimation model of the discrete rigid body model; discretize the model of the flexible state under high-frequency non-gap to obtain a parameter estimation model of the discrete flexible body model; S3: Estimate the parameters in the parameter estimation model of discrete rigid body model and discrete flexible body model based on the recursive maximum likelihood parameter identification method.

2. According to the three-state model parameter identification method of the ball screw feed system according to claim 1, It is characterized in that S1 includes the following steps: Step 1: First, establish the rigid body model of the low-speed non-clearance ball screw feed system: in J 1 represents the total inertia of the system, B 1 is the viscous friction coefficient, F f1 is the equivalent friction of the system, K a and K t are the current amplification factor and torque amplification factor, r g is the transmission ratio, x M (t) represent the position, velocity and acceleration of the motor side respectively; according to this formula, the open-loop transfer function of the rigid body system model can be obtained as follows: where x M (s),u e (s) and F fe1 (s) is x M (t),u e (t) and F fe1 (t) Transformation result in Laplace domain, s represents the Laplace operator; Step 2: Then establish a flexible body model under high speed and no gap: in x L (t) represents the position, velocity and acceleration of the load side respectively; the subscripts "M" and "L" represent the motor side and the load side respectively. Since the influence of the gap is not considered, the friction at this time can be considered to be equal to the friction in step 1, that is, F fe3 =F fe1 ; K S ,C S are the torsional stiffness and viscosity coefficient of the screw system respectively; according to this formula, the open-loop transfer function of the flexible system model can be obtained: B(s)=M L s 2 +(C Se +C L )s+K Se A(s)=M M M L s 4 +[M L C M +M M C L +(M M +M L )C Se ]s 3 +[C M C L +(C M +C L )C Se +(M M +M L )K Se ]s 2 +(C M +C L )K Se s At low speeds, the effects of viscous friction are usually negligible, which means Then the open-loop transfer function of the system can be simplified as follows: Based on the simplified transfer function G 2 (s), the anti-resonance frequency f of the system ares and the resonant frequency f res The calculation results are as follows: Step 3: Finally, establish a rigid body model under low speed gap: in J 2 Indicates the inertia on the motor side, B 2 is the viscous friction coefficient, F f2 is the friction force; in this process, the speed of the screw is very low, and the viscous friction term is can be ignored. According to this formula, the open-loop transfer function of the rigid body system model can be obtained as follows: Step 4: Combining the model structures of steps 1, 2, and 3, the following three-state model structure is summarized: To facilitate subsequent presentation, and State 1 for short. and State 2 for short. and Abbreviated as State 3; Corresponding to the speed of the motor side and the load side respectively; Step 5: A composite friction model considering the gap effect is used in the three-state model, which is expressed as follows: where F c1 ,F s1 ,v s1 They represent the Coulomb friction, static friction and Stribeck speed caused by the screw and the guide rail respectively; F c2 ,F s2 ,v s2 represents the friction model parameters caused only by the screw; the time taken for the gap-crossing process is usually very short, and the friction in this process can be considered to remain constant. The composite friction model constructed above can be further simplified into the following form:

3. According to the three-state model parameter identification method of a ball screw feed system as described in claim 2, It is characterized in that S2 includes the following steps: Step 6: Use the following discrete error model to discretize the three-state model constructed in steps 1, 2, and 3: u(k)=u 0 (k) Where u(k) and y(k) represent the input and output at the kth discrete time step, represents the transfer function in the discrete domain, z represents the time-shift operator, and e(k) represents the discrete error; Step 7: Use the method in step 6 to discretize the continuous rigid body model in steps 1 and 3. The discretization method is the zero-order holder method. The discretization results are as follows: in θ 2 =-e -pTs , is the parameter to be estimated, T s is the sampling time; The discrete rigid body model in step 8 and step 7 can be expressed in the following linear parameter form: y L =Φθ+e L y L =[ω(2) ω(3)...ω(L)] T And L =[e(2) e(3)...e(L)] T in, and Respectively represent State 1 Time-varying positive and negative friction, and denote the constant positive and negative friction in State 3, respectively. L denotes the total number of samples used in the parameter estimation process. PV(ω(k)) and NV(ω(k)) are the sign functions that identify the friction direction and are defined as follows: where ω c is the angular velocity noise caused by the quantization process; after the parameter θ is identified, the identification results of the model parameters involved in steps 1 and 3 can be expressed as: Step 9: Use the method in step 6 to discretize the continuous flexible body model in step 2. The discretization results are as follows: Among them, θ 1 ,θ 2 ,...,θ 6 is the parameter to be estimated; Step 10: The discrete flexible body model in step 9 can be expressed in the same linear parameter form as in step 8, but with different y L ,e L ,θ,Φ: y L =[ω(4) ω(5)...ω(L)] T And L =[e(4) e(5)...e(L)] T θ=[θ 1 i 2 i 3 i 4 i 5 i 6 i 7 i 8 ] T A=[A u A ω ] F P (k)=-PV(k-1)-PV(k-2)-PV(k-3),k>3 F N (k)=-NV(k-1)-NV(k-2)-NV(k-3),k>3 After the parameters θ are identified, the parameter model in the discrete domain in step 9 is converted into a transfer function in the continuous domain using the zero-pole matching method: The mathematical relationship between the model parameters in step 2 and the model parameters of the transfer function in the continuous domain can be expressed as:

4. According to the three-state model parameter identification method of a ball screw feed system as claimed in claim 3, It is characterized in that S3 includes the following steps: Step 11. Considering the three-state model established in step 4, given L sets of independent measurement results u(k) and ω(k) and parameter θ, the following joint conditional probability distribution equation can be obtained: State 1 and State 3: State 2: Step 12: According to different model structures, the discrete models in steps 8 and 10 can be expressed as follows: State 1 and State 3: ω(k)=θ(1)ω(k-1)+θ(2)u(k-1)-θ(3)PV(k-1)-θ(4)NV(k-1)+e(k) State 2: ω(k)=θ(1)u(k-1)+θ(2)u(k-2)+θ(3)u(k-3)-θ(4)ω(k-1)-θ(5)ω(k-2)-θ(6)ω(k -3)-θ(7)(PV(k-1)+PV(k-2)+PV(k-3))-θ(8)(NV(k-1)+NV(k-2)+NV(k-3))+e(k) Step 13: Substitute the discrete model in step 12 into step 11, and the result will become: Where K 1 and K 2 is a constant, σ e is the standard deviation, and its value varies according to the state; in order to speed up the step 11 through the joint conditional probability distribution P(y L |u L-1 ,θ) to solve the value of parameter θ, and L |u L-1 ,θ) to find the log-likelihood function: Therefore, the process of solving the parameter θ can be regarded as solving lnP(y L |u L-1 ,θ) maximum value; lnP(y L |u L-1 ,θ) about The partial differential result of can be expressed as: Step 14: Construct the following cost equation: The maximum likelihood parameter estimation result of e(k) is The result is as follows: in Step 15: Based on the analysis of steps 11 to 14, the recursive maximum likelihood parameter estimation result for the three-state model design can be expressed as: Where I is a 4th-order identity matrix for State 1 and State 3, and an 8th-order identity matrix for State 2. After θ is identified, the last n groups of θ are used as the initial value for iteration, and the iteration termination condition is designed as: i N+1 -θ N ≤e where θ N Represents the result of the Nth iteration, ∈ is a specified sufficiently small vector.

5. A computer system, Features include: One or more processors, and a computer-readable storage medium for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors are enabled to implement the method of claim 1.

6. A computer-readable storage medium, Features Computer executable instructions are stored, and when the instructions are executed, they are used to implement the method of claim 1.

7. A computer program product, Features The invention comprises computer executable instructions, which are used to implement the method of claim 1 when being executed.

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