Numerical control machine tool iterative learning error compensation control method based on stable inverse model

Abstract

The invention relates to a numerical control machine tool iterative learning error compensation control method based on a stable inverse model, which realizes stable inversion of a system by regarding an unstable part as non-causal operation and generating control input based on infinite preview. According to the method, the stability of the system can be ensured, rapid convergence can be realized, and meanwhile, a high-precision control effect is kept. Through the innovative technical scheme, the problems of stability, precision and efficiency during processing of a non-minimum phase system in the prior art are effectively solved, and a comprehensive and efficient solution is provided for error compensation control of the numerical control machine tool. The modular design of the numerical control machine tool iterative learning error compensation control system based on the stable inverse model enables the system to have good flexibility and expandability. And different modules can be adjusted or replaced according to specific application requirements. And the related method provided by the invention is applied, so that the method also has the beneficial effects of the related method.

Description

Technical Field

[0001] The present invention relates to the technical field related to machine tool intelligent control, and in particular to an iterative learning error compensation control method for numerically controlled machine tools based on a stable inverse model. Background Art

[0002] The motion precision control of CNC machine tools is a complex problem, which is currently mainly achieved through methods such as feedback control and feedforward compensation. In terms of feedback control, traditional PID control is difficult to meet high-precision requirements due to hysteresis. In terms of feedforward compensation, model-based compensation methods require accurate system models, which are difficult to implement in practical applications. Therefore, iterative learning control (ILC), as a method that can use historical data for error compensation, has been widely used in the precision control of CNC machine tools.

[0003] In the prior art, the most similar implementation solutions are mainly:

[0004] 1. Error compensation method based on adaptive iterative learning (201911349193.0). This method regards the CNC machine tool as a nonlinear system and designs an adaptive ILC algorithm. However, it overcomplicates the problem because the CNC motion platform is actually very linear.

[0005] 2. Iterative learning feedforward control method for machine tool feed system (201910977406.8). This method uses a PD-type ILC controller, but the convergence speed is slow and multiple iterations are required to achieve better results.

[0006] 3. Model-based iterative learning error compensation control system for CNC machine tools (202410105019.6). This method uses the system model for ILC design and can achieve fast convergence. However, if the system is a non-minimum phase system, this method will fail.

[0007] 4. CNC machine tool control system based on iterative trajectory shaping and control compensation (202410105099.5). This method combines trajectory shaping and control compensation, and designs an iterative learning controller based on the inverse of the model, which can more comprehensively reduce system vibration and improve accuracy. However, if the system is a non-minimum phase system, this method will also fail.

[0008] It is worth noting that non-minimum phase systems are common in CNC machine tools, for example, they often appear in systems with flexible connections or large time delays. This makes Schemes 3 and 4 likely to face serious limitations in practical applications.

[0009] For motion platforms with dynamic characteristics close to linear, such as CNC machine tools, the ILC design based on model inversion is still the most effective. However, the existence of unstable zeros in non-minimum phase systems will convert the inverse model into unstable poles, resulting in unbounded control input. In discrete systems, unstable zeros mainly come from: (1) the non-co-location arrangement of actuators and sensors; (2) the zero-order hold effect during the sampling process. Therefore, not all systems in industrial control systems are non-minimum phase systems, but they are still inevitable in specific situations.

[0010] The existing technology has the following main shortcomings in the error compensation control of CNC machine tools:

[0011] 1. Poor adaptability to non-minimum phase systems: Patents No. 202410105019.6 and 202410105099.5 use model-based iterative learning control methods. These methods fail when faced with non-minimum phase systems. The reason is that the inverse model of the non-minimum phase system is unstable, and the direct use of such an inverse model will lead to an unstable control system. Non-minimum phase systems are more common in CNC machine tools, for example, they often appear in systems with flexible connections or large time delays. This situation is particularly common in high-speed, high-precision CNC machine tools, such as large machine tools with insufficient rigidity or precision micro-machine tools.

[0012] 2. System stability problem: When dealing with non-minimum phase systems, existing technologies often have difficulty ensuring system stability. This is because the zero point of the non-minimum phase system is in the right half plane, and the pole of its inverse system will also be in the right half plane, resulting in system instability. This instability will seriously affect the control effect and may even cause the system to diverge, which is manifested in the actual processing process as a decrease in workpiece accuracy or increased machine tool vibration.

[0013] 3. Contradiction between convergence speed and stability: For example, Patent No. 201910977406.8 uses a PD-type iterative learning controller. Although it can ensure stability, the convergence speed is slow and multiple iterations are required to achieve the ideal control effect. Some fast convergence methods (such as Patent No. 202410105019.6) can quickly reduce errors, but it is difficult to ensure stability when facing non-minimum phase systems. How to achieve fast convergence while ensuring stability has become a difficult problem.

[0014] 4. Disadvantages of the approximate inversion method: The approximate model inversion method based on ZPETC or ZMETC (such as the research of Dai L et al.) will produce phase and amplitude errors in certain frequency bands because it is not an accurate model inversion result. This approximation will significantly affect the control effect, especially when dealing with non-minimum phase systems. In CNC machining with high precision requirements, these errors may cause the machining accuracy to fail to meet the standard.

[0015] The root cause of these shortcomings is that the existing technology lacks an effective stable inverse model method when dealing with non-minimum phase systems. The characteristics of non-minimum phase systems make it impossible to directly apply traditional model inversion methods, while existing alternative methods are difficult to achieve a good balance between stability, convergence speed and accuracy. Therefore, how to effectively deal with non-minimum phase systems and achieve stable, fast and high-precision error compensation control has become a key challenge in the field of CNC machine tool control. Summary of the invention

[0016] The purpose of the present invention is to solve at least one of the deficiencies of the prior art and to provide an iterative learning error compensation control method for a CNC machine tool based on a stable inverse model.

[0017] In order to achieve the above object, the present invention adopts the following technical solutions:

[0018] Specifically, an iterative learning error compensation control method for a CNC machine tool based on a stable inverse model is proposed, which acts on a feed drive system of a CNC machine tool. The method includes the following steps:

[0019] Step 110: Obtain the expected trajectory r d , and initialize a pre-established control model, wherein the control model is an iterative learning error compensation control model for CNC machine tools based on a stable inverse model;

[0020] The control model includes a real-time module and an offline module. The offline module includes a storage unit and an iterative learning inversion calculation module ILC. The real-time module includes an error calculation unit and a PID control unit. The offline module stores the control compensation amount u required for the j-1 iteration through the storage unit. j-1 and the feedback control error e j-1 The u is calculated by iterative learning inversion calculation module j , the real-time module passes the expected trajectory r d , feedback control error e j and u j Calculate the actual position y j ;

[0021] Step 120: configure the 0th iteration condition, that is, set the first control compensation u0 = 0, and change the desired trajectory r d inputting the control model;

[0022] Step 130: Execute the trajectory tracking control task and obtain the desired trajectory r in real time. d The actual position y of the motor end j The feedback control error e j ;

[0023] Step 140, determining whether the maximum value of the difference between two feedback control errors is less than a preset threshold value δ, if yes, go to step 160, if no, go to step 150;

[0024] Step 150: Let j = j + 1, and control the error e according to the feedback j And the control compensation u j The control compensation u required for the j+1th iteration is calculated by the offline module j+1 , return to step 130 and continue to perform the trajectory tracking control task;

[0025] Step 160, j=j+1; u j+1 =u j ; Continue to execute the trajectory tracking control task until the processing task is completed.

[0026] Further, specifically, according to the feedback control error e j And the control compensation u j The control compensation u required for the j+1th iteration is calculated by the offline module j+1 ,include,

[0027] u j+1 =L q (u j +L e e j ) (1)

[0028] Where L e is the learning filter, L e is a robust filter, and the error is constructed for this purpose.

[0029] e j =r d -y j

[0030] In addition, based on the principle of model iterative learning control method, it is necessary to find a j to y j Mathematical model H, so that L e =H -1 , the transfer function in the discrete domain is expressed in state space as follows: C P (A C ,B C ,C C ,D C ), P M (A m ,B m ,C m ,0), from which we can get the state space expression of H(A,B,C,D), where the input and output relationship is expressed as follows:

[0031] x[k+1]=Ax[k]+Bu j [k]

[0032] y j [k] = Cx[k]

[0033] in C=[0C m ], D = 0, but D is a zero matrix, not full rank, so for the input y j [k] Perform n-step delay processing to achieve process, at this time there is,

[0034] C ′ =CA n ,

[0035] D ′ =CA n-1 B;

[0036] Thus, a non-zero D matrix can be obtained, and then the following two different situations are processed;

[0037] Case 1: When the controlled object P M (z) is the case of the minimum phase system, and the error compensation can be directly calculated by the inverse model, with the input being e j , the output is Δu j , let Δu in formula (1) j =L e e j , then there is,

[0038] x[k+1]=(AB(C ′ B) -1 C′A)x[k]+BD′ -1 e j [k]

[0039] Δu j [k] = D ′-1 C′x[k]+D ′-1 e i [k+n]

[0040] Case 2: When the controlled object P M (z) is a non-minimum phase system, and x[k] is expressed as Where T contains (AB(C ′ B) -1 C′A) such that

[0041]

[0042] Thus there is

[0043]

[0044] where |λ(A s )|<1, and |λ(A u )|>1, that is, A s Contains all stable poles, A u Including unstable poles, the stable state solution is as follows:

[0045] x s [k+1]=A s x s [k]+B s e j [k],x[-∞]=0,

[0046] Solving forward in time, the steady state solution is as follows:

[0047] x u [k+1]=A u x u [k]+B u e j [k],x[+∞]=0,

[0048] Solving backward in time, finally, the ILC feedforward control command compensation can be obtained as:

[0049] Δu j [k] = C s x s [k]+C u x u [k]+De j [k],

[0050] Finally, the actual error compensation amount for the next iteration can be obtained

[0051] u j+1 [k] = L q {u j [k]+Δu j [k]},

[0052] Where k is the kth sampling point of the signal sequence, L q is a low pass filter.

[0053] Further, specifically, the n-step delay process includes:

[0054] Do 1 step delay,

[0055] y j [k+1]=CAx[k]+CBu[k],

[0056] At this time, if CB < σ, σ is a sufficiently small number, then do n steps of delay

[0057] y j [k+n]=CA n x[k]+CA n-1 Bu[k],

[0058] Until CA n-1 B≥σ.

[0059] Further, specifically, the value of σ is set to σ = 1 × 10 -5 .

[0060] Further, specifically, L q It is a fifth-order Butterworth low-pass filter with a cutoff frequency of 110Hz.

[0061] Further, specifically, the preset threshold δ is δ=10 -6 mm.

[0062] The present invention also proposes an iterative learning error compensation control system for a CNC machine tool based on a stable inverse model, comprising:

[0063] The real-time module includes an error calculation unit and a PID control unit, which is used to calculate the desired trajectory r d , feedback control error e j and u j Calculate the actual position y j

[0064] The offline module includes a storage unit and an iterative learning inversion calculation module ILC, which is used to store the control compensation amount u required for the j-1th iteration stored in the storage unit. j-1 and the feedback control error e j-1 The u is calculated by iterative learning inversion calculation module j ;

[0065] The CNC machine tool feed drive system includes a motor, a coupling, a ball screw mechanism and a platform mechanism.

[0066] The beneficial effects of the present invention are:

[0067] The present invention proposes an iterative learning error compensation control method for CNC machine tools based on a stable inverse model. By treating the unstable part as a non-causal operation and generating control input based on infinite preview, the stable inversion of the system is achieved. This method can not only ensure the stability of the system, but also achieve rapid convergence while maintaining a high-precision control effect. It has the following advantages:

[0068] 1. Effectively solve the stability problem of non-minimum phase systems:

[0069] The present invention uses non-causal time domain inversion technology to decompose the system state into stable and unstable parts, and uses non-causal operations to process unstable poles. This method can effectively solve the inversion instability problem of non-minimum phase systems and overcome the limitations of existing technologies in processing such systems.

[0070] 2. Achieve a balance between fast convergence and stability:

[0071] Compared with the method using PD-type iterative learning controller, the present invention achieves faster convergence speed by combining iterative learning controller and non-causal time domain inversion technology while ensuring system stability, which solves the contradiction between convergence speed and stability in the prior art.

[0072] 3. Improve control accuracy:

[0073] The present invention avoids the phase and amplitude errors caused by approximate inversion methods (such as ZPETC or ZMETC) through an accurate stable inverse model, which significantly improves the control accuracy, especially when dealing with non-minimum phase systems.

[0074] 4. Flexibility and scalability:

[0075] The modular design of the present invention makes the system have good flexibility and scalability. Different modules can be adjusted or replaced according to specific application requirements.

[0076] Wide range of applications:

[0077] Since the present invention can effectively handle non-minimum phase systems, it is applicable to a wider range of CNC machine tool types, including high-speed, high-precision CNC machine tools, and systems with flexible connections or larger time delays.

[0078] In general, the present invention effectively solves the stability, accuracy and efficiency problems of the prior art when dealing with non-minimum phase systems through innovative technical solutions, and provides a comprehensive and efficient solution for error compensation control of CNC machine tools. BRIEF DESCRIPTION OF THE DRAWINGS

[0079] The above and other features of the present disclosure will become more apparent by describing in detail the embodiments shown in the accompanying drawings. The same reference numerals in the accompanying drawings of the present disclosure represent the same or similar elements. Obviously, the accompanying drawings described below are only some embodiments of the present disclosure. For those skilled in the art, other accompanying drawings can be obtained based on these accompanying drawings without creative work. In the accompanying drawings:

[0080] Figure 1 It is a schematic diagram of the iterative learning error compensation control method for CNC machine tools based on a stable inverse model involved in the present invention;

[0081] Figure 2 It is a structural principle block diagram of the CNC machine tool feed drive module including a motor drive submodule and a ball screw feed submodule;

[0082] Figure 3 It is a logic principle block diagram of the present invention;

[0083] Figure 4 is a flow chart of the iterative learning process in the present invention;

[0084] Figure 5 is a hardware schematic diagram for implementing the method;

[0085] Figure 6 The simulation curve diagram is shown when the experimental input is a circular trajectory command of two axes;

[0086] Figure 7 The figure shows the error convergence results of the X-axis and Z-axis under the ILC based on non-causal inversion in the experiment;

[0087] Figure 8 The figure shows the schematic diagram of the dual-axis error results of the 10th iteration convergence in the experiment;

[0088] Fig. 9 (a) is a schematic diagram of the ballbar measurement results of the XZ platform circular test when the method is applied. Fig. 9 (b) is a schematic diagram of the ballbar measurement results of the XZ platform circular test under the control method (inverse ZPETC frequency domain approximate model). DETAILED DESCRIPTION

[0089] The following will be combined with the embodiments and drawings to clearly and completely describe the concept, specific structure and technical effects of the present invention, so as to fully understand the purpose, scheme and effect of the present invention. It should be noted that the embodiments in this application and the features in the embodiments can be combined with each other without conflict. The same reference numerals used throughout the drawings indicate the same or similar parts.

[0090] Example 1, reference Figure 1 , Figure 2 , Figure 3 as well as Figure 4 The present invention proposes an iterative learning error compensation control method for a CNC machine tool based on a stable inverse model, which acts on a feed drive system of a CNC machine tool. The method includes the following steps:

[0091] Step 110: Obtain the expected trajectory r d , and initialize a pre-established control model, wherein the control model is an iterative learning error compensation control model for CNC machine tools based on a stable inverse model;

[0092] The control model includes a real-time module and an offline module. The offline module includes a storage unit and an iterative learning inversion calculation module ILC. The real-time module includes an error calculation unit and a PID control unit. The offline module stores the control compensation amount u required for the j-1 iteration through the storage unit. j-1 and the feedback control error e j-1 The u is calculated by iterative learning inversion calculation module j , the real-time module passes the expected trajectory r d , feedback control error e j and u j Calculate the actual position y j ;

[0093] Step 120: configure the 0th iteration condition, that is, set the first control compensation u0 = 0, and change the desired trajectory r d inputting the control model;

[0094] Step 130: Execute the trajectory tracking control task and obtain the desired trajectory r in real time. d The actual position y of the motor end j The feedback control error e j ;

[0095] Step 140, determining whether the maximum value of the difference between two feedback control errors is less than a preset threshold value δ, if yes, go to step 160, if no, go to step 150;

[0096] Step 150: Let j = j + 1, and control the error e according to the feedback j And the control compensation u j The control compensation u required for the j+1th iteration is calculated by the offline module j+1 , return to step 130 and continue to perform the trajectory tracking control task;

[0097] Step 160, j=j+1; u j+1 =u j ; Continue to execute the trajectory tracking control task until the processing task is completed.

[0098] In this embodiment 1, in general, Figure 4 , follow these steps to understand this method:

[0099] Step 1: Initialization, use the identification method to obtain the transfer function P M Model, design a PID controller C that makes the system stable P. Thus, the matrix parameters required for offline calculation of the inversion model in the offline module can be further obtained. If the system is a minimum phase system, the model inverse calculation matrix is ​​designed according to the method of case 1, otherwise, the stable model inverse calculation matrix is ​​designed according to the method of case 2. In addition, the system starts to receive the desired trajectory command r after interpolation and velocity planning. d ;

[0100] Step 2: Configure the 0th iteration condition and set the first control compensation amount to u0=0;

[0101] Step 3: Reshape the input quantity r in the trajectory j and control compensation u j Input and controller C P Under the action, the trajectory tracking control task is performed and the desired trajectory r is obtained in real time d The actual position y of the motor end j The feedback control error e j ;

[0102] Step 4: If the maximum value of the difference between the two iteration errors on the platform is less than the given value, we take δ = 10 -6 mm indicates that the iteration has converged and goes to step 6 to end the iterative learning; otherwise, it goes to step 5;

[0103] Step 5: Let j = j + 1, according to the error e j and u j , we can use the offline module calculated by step 1 to calculate the inverse result of the model, and finally get the control compensation u required for the j+1th iteration j+1 , return to step 3 and continue to perform the trajectory tracking task;

[0104] Step 6: j = j + 1; u j+1 =u j ; Continue to execute the tracking task until the processing task is completed;

[0105] Step 7: End.

[0106] As a preferred embodiment 2 of the present invention, the present invention is further described below in conjunction with the accompanying drawings and embodiments:

[0107] Figure 2 The schematic diagram of the CNC machine tool feed drive system shown in the figure shows that the rotary motor drives the ball screw to achieve the linear motion of the platform. According to Patent No. 202410105099.5, Figure 3 P M (z) is a fourth-order model. According to the simplified diagram, the transfer function based on the input and output relationship is as follows:

[0108]

[0109] Where P M (z) represents the transfer function from position command to motor position output, and q1, q2, q3, ... q8 are the system parameters to be identified.

[0110] Based on the transfer function, the above coefficients can be obtained through conventional system parameter identification methods. For example, under open-loop conditions, a set of excitation signals containing multiple frequency components is input, the output results are observed, and finally the least squares method is used to calculate the parameters.

[0111] Figure 1 The CNC machine tool iterative learning error compensation control system based on the stable inverse model proposed by the present invention includes: an offline module, a real-time module and a CNC machine tool feed drive system, the offline module includes a storage unit and an iterative learning inversion calculation module; the real-time module includes an error calculation unit and a PID control unit; the CNC machine tool feed drive system includes a motor, a coupling, a ball screw mechanism and a platform mechanism, Figure 2 The motor shown has a rotary encoder mounted on the end to detect the actual position of the motor. j is the iteration number currently being executed.

[0112] The error calculation unit in the real-time module needs to calculate the deviation in real time, such as the deviation between the expected trajectory and the platform position, the deviation between the trajectory command input and the actual position, j =r j -y j , where y j The actual position of the motor encoder position obtained by the proportional conversion module; the PID control unit is in e j Through the controller C P Output control quantity, the purpose is to suppress e j The size of the control compensation u in the offline module j After combination, it is used as u input into the CNC machine tool feed drive system. Figure 2 As shown;

[0113] The storage unit in the offline module is mainly used to store historical data, such as error e j-1 , control compensation amount u j-1 Based on the above data, the iterative learning inversion calculation module uses the iterative learning method based on the inversion model to calculate the control compensation u of the jth iteration offline (non-real time) j ,u j Injected into the output of the PID control unit and combined with its output.

[0114] The iterative learning method using the stable model inverse involves

[0115] u j+1 =L q(u j +L e e j )

[0116] That is, according to the result of the previous iteration, calculate the next control compensation u j+1 , L in the above formula e is the learning filter, L e is a robust filter, where L q Generally designed as a low-pass filter, L e This is achieved using the model inversion method, and the error is constructed for this purpose.

[0117] e j =r d -y j

[0118] In addition, based on the principle of model iterative learning control method, it is necessary to find a j to y j Mathematical model H, so that L e =H -1 It is not difficult if the system transfer function is known, such as: C P (z),P M (z), but the result of the expression of the transfer function in the frequency domain can only be designed as an approximate model inverse based on the frequency domain method, and the accurate model inverse cannot be obtained, which leads to poor control error. For this reason, the time domain state space method is used instead. The transfer function in the discrete domain is written as a state space expression as follows: C P (A C ,B C ,C C ,D C ), P M (A m ,B m ,C m ,0), where A C ,B C ,C C ,D C are the matrices under the state space equation corresponding to the controller C_P transfer function. In control science, these matrices can be obtained if C_P is known. From this, the state space expression H(A, B, C, D) can be obtained. A m ,B m ,C m ,0 is the matrix under the state space equation corresponding to the transfer function of the control object P_M (generally the system is suitable, so the D term is D m =0), these matrices can be obtained by knowing P_M in control science, which can express the input and output relationship:

[0119] x[k+1]=Ax[k]+Buj [k]

[0120] y j [k] = Cx[k]

[0121] in C=[0C m ], and D = 0. However, D is a zero matrix and is not full rank, so for the input y j [k] Do the following 1, 2, 3...step delay processing to help achieve process, for example, to do a 1-step delay,

[0122] y j [k+1]=CAx[k]+CBu[k]

[0123] At this time, if CB<σ(σ is a sufficiently small number, let σ=1×10 -5 , if it is too small, it will introduce numerical calculation errors), and then do n steps of delay

[0124] y j [k+n]=CA n x[k]+CA n-1 Bu[k]

[0125] Until CA n-1 B≥σ, then

[0126] C ′ =CA n

[0127] D ′ =CA n-1 B

[0128] In this way, a non-zero D matrix can be obtained, and then the following two different situations are processed.

[0129] (1) When the controlled object P M (z) is the case of the minimum phase system, and the error compensation can be directly calculated by the inverse model, with the input being e j , the output is Δu j , let Δu in the previous formula (1) j =L e e j

[0130] x[k+1]=(AB(C ′ B) -1 C′A)x[k]+BD′ -1 e j [k]

[0131] Δu j [k] = D ′-1C′x[k]+D ′-1 e j [k+n]

[0132] (2) However, when the controlled object P M (z) is the case of a non-minimum phase system. The unstable zeros will become poles of the system after the model inversion, resulting in the matrix (AB(C ′ B) -1 C′A) characteristic root is outside the unit circle. If the calculation is done in a causal way, the result will be divergent / no solution, and the system will eventually be unstable. To this end, the present invention uses a non-causal calculation method to process the inverse unstable poles of the model (the unstable zeros of the original model). It is not difficult to find the transformation matrix T mathematically. The state in the first case can be decomposed into stable and unstable parts through state transformation, for example: Where T contains (AB(C ′ B) -1 C′A) such that

[0133]

[0134] thereby

[0135]

[0136] where |λ(A s )|<1, and |λ(A u )|>1, in other words, A s Contains all stable poles, A u Contains unstable poles. The stable state solution is as follows:

[0137] x s [k+1]=A s x s [k]+B s e j [k],x[-∞]=0

[0138] Solving forward in time, the steady state solution is as follows:

[0139] x u [k+1]=A u x u [k]+B u e j [k],x[+∞]=0

[0140] Solve backward in time. Finally, the ILC feedforward control command compensation can be obtained as:

[0141] Δu j [k] = C s xs [k]+C u x u [k]+De j [k]

[0142] Finally, the actual error compensation amount for the next iteration can be obtained

[0143] u j+1 [k] = L q {u j [k]+Δu j [k]}

[0144] Where k is the kth sampling point of the signal sequence, L q It is designed as a fifth-order Butterworth low-pass filter with a cutoff frequency of 110Hz in order to remove high-frequency noise introduced during the signal measurement process. The Butterworth filter is chosen to ensure a maximally flat passband and good stability. The cutoff frequency is chosen based on the bandwidth of the system and the desired smoothing effect on the learning trajectory. In order to eliminate the phase delay introduced by the causal filter, the filtered signal is reversed in time and passed through the filter again.

[0145] In addition, X u Represents the unstable part of the original system X. s Represents the stable part of the original system X, which is similar to the decoupling operation.

[0146] When carrying out specific applications,

[0147] Implementation 1: System situation

[0148] This method is implemented on an XZ-axis CNC lathe motion platform. The transfer function of the dual-axis platform is obtained by system identification as follows:

[0149]

[0150] The dual-axis motion system is controlled by a discrete-time PD controller, which is expressed as:

[0151]

[0152] Where T = 1 / f is the sampling period, K p and K d are proportional and differential gains, T f is the filter time constant. The controller parameters are adjusted according to the identified model, with the goal of achieving a balance between tracking performance and robustness. The final parameter value is: K on the X axis p =169,K d =2.01,T f=1.01×10 -5 ,K of Z axis p =221,K d =3.21,T f =1.05×10 -5 .

[0153] Implementation 2: Actual Results

[0154] In order to verify the effectiveness of the model-based iterative trajectory shaping and control compensation numerical control and yellowing control method designed in this invention, the trajectory tracking experiment was carried out on the actual XZ platform. The hardware configuration Figure 5 As shown in the figure, the controller is implemented in the NI Compact RIO real-time hardware platform. Through the FPGA wiring board of the platform, an efficient real-time module can be realized. The error data after collection is calculated with a sampling time of 1KHz. j , and compensation data u j , transmitted to the upper PC machine via Ethernet, MATLAB matrix calculation is run in the PC, and the next iteration control compensation u is obtained after calculation according to the method of the present invention. j+1 , and then transmitted to NI Compact RIO via Ethernet to control the CNC dual-axis platform in real time.

[0155] Figure 6 The input for the experiment is a circular trajectory command for both axes with a radius of 50 mm, so the trajectory commands for both axes are circular trajectory commands controlled by acceleration and deceleration.

[0156] Figure 7 The error convergence results of the X-axis and Z-axis under the ILC based on non-causal inversion are shown. Although there are NMP zeros in the X-axis model, its convergence behavior is similar to that of the Z-axis, and both achieve convergence within 3 iterations.

[0157] Figure 8 The dual-axis error result converged in the 10th iteration

[0158] Fig. 9 (a) is the ballbar measurement result of the XZ platform circular test under this method, Fig. 9 (b) is the ballbar measurement results of the XZ platform circular test under the control method (ZPETC frequency domain approximate model inversion), the results are 8.0μm and 8.9μm respectively, showing that this method can, on the one hand, stabilize the calculation results through a non-causal calculation method, and on the other hand, this method is an accurate model inversion calculation method, which can further improve the trajectory tracking accuracy.

[0159] Embodiment 3, the present invention also proposes an iterative learning error compensation control system for CNC machine tools based on a stable inverse model, comprising:

[0160] The real-time module includes an error calculation unit and a PID control unit, which is used to calculate the desired trajectory r d , feedback control error e j and u j Calculate the actual position y j

[0161] The offline module includes a storage unit and an iterative learning inversion calculation module ILC, which is used to store the control compensation amount u required for the j-1th iteration stored in the storage unit. j-1 and the feedback control error e j-1 The u is calculated by iterative learning inversion calculation module j ;

[0162] The CNC machine tool feed drive system includes a motor, a coupling, a ball screw mechanism and a platform mechanism.

[0163] In addition, each functional module in each embodiment of the present invention may be integrated into one processing module, or each module may exist physically separately, or two or more modules may be integrated into one module. The above-mentioned integrated module may be implemented in the form of hardware or in the form of software functional modules.

[0164] If the integrated module is implemented in the form of a software function module and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the present invention implements all or part of the processes in the above-mentioned embodiment method, and can also be completed by instructing the relevant hardware through a computer program. The computer program can be stored in a computer-readable storage medium, and the computer program can implement the steps of the above-mentioned various method embodiments when executed by the processor. Among them, the computer program includes computer program code, and the computer program code can be in source code form, object code form, executable file or some intermediate form. The computer-readable medium may include: any entity or system that can carry the computer program code, recording medium, U disk, mobile hard disk, disk, optical disk, computer memory, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), electrical carrier signal, telecommunication signal and software distribution medium, etc.

[0165] Although the description of the present invention has been quite detailed and specifically describes several described embodiments, it is not intended to be limited to any of these details or embodiments or any particular embodiment, but should be regarded as providing a broad possible interpretation of these claims in view of the prior art by reference to the appended claims, thereby effectively covering the intended scope of the present invention. In addition, the above description of the present invention is based on the embodiments foreseeable by the inventor, and its purpose is to provide a useful description, and those non-substantial changes to the present invention that have not yet been foreseen may still represent equivalent changes to the present invention.

[0166] The above is only a preferred embodiment of the present invention. The present invention is not limited to the above implementation. As long as the technical effect of the present invention is achieved by the same means, it should belong to the protection scope of the present invention. Within the protection scope of the present invention, its technical scheme and / or implementation method can have various modifications and changes.

Claims

1. An iterative learning error compensation control method for CNC machine tools based on a stable inverse model, characterized in that: Acting on a CNC machine tool feed drive system, the method comprises the following: Step 110: Obtain the expected trajectory r d , and initialize a pre-established control model, wherein the control model is an iterative learning error compensation control model for CNC machine tools based on a stable inverse model; The control model includes a real-time module and an offline module. The offline module includes a storage unit and an iterative learning inversion calculation module ILC. The real-time module includes an error calculation unit and a PID control unit. The offline module stores the control compensation amount u required for the j-1 iteration in the storage unit. j-1 and the feedback control error e j-1 The u is calculated by iterative learning inversion calculation module j , the real-time module passes the expected trajectory r d , feedback control error e j and u j Calculate the actual position y j ; Step 120: configure the 0th iteration condition, that is, set the first control compensation u0 = 0, and change the desired trajectory r d inputting the control model; Step 130: Execute the trajectory tracking control task and obtain the desired trajectory r in real time. d The actual position y of the motor end j The feedback control error e j ; Step 140, determining whether the maximum value of the difference between two feedback control errors is less than a preset threshold value δ, if yes, go to step 160, if no, go to step 150; Step 150: Let j = j + 1, and control the error e according to the feedback j And the control compensation u j The control compensation u required for the j+1th iteration is calculated by the offline module j+1 , return to step 130 and continue to perform the trajectory tracking control task; Step 160, j=j+1; u j+1 =u j ; Continue to execute the trajectory tracking control task until the processing task is completed.

2. The iterative learning error compensation control method for CNC machine tools based on a stable inverse model according to claim 1 is characterized in that: Specifically, according to the feedback control error e j And the control compensation u j The control compensation u required for the j+1th iteration is calculated by the offline module j+1 ,include, the j+1 =L q (the j +L e and j ) (1) Where L e is the learning filter, L e is a robust filter, for which the error is constructed, e j =r d -y j In addition, based on the principle of model iterative learning control method, it is necessary to find a j to y j Mathematical model H, so that L e =H -1 , the transfer function in the discrete domain is expressed in state space as follows: C P (A C ,B C ,C C ,D C ), P M (A m ,B m ,C m ,0), from which we can get the state space expression of H(A,B,C,D), where the input and output relationship is expressed as follows: x[k+1]=Ax[k]+Bu j [k] y j [k]=Cx[k] in C=[0C m ], D = 0, but D is a zero matrix, not full rank, so for the input y j [k] Perform n-step delay processing to achieve process, at this time there is, C ′ =CA n , D ′ =CA n-1 B; Thus, a non-zero D matrix can be obtained, and then the following two different situations are processed; Case 1: When the controlled object P M (z) is the case of the minimum phase system, and the error compensation can be directly calculated by the inverse model, with the input being e j , the output is Δu j , let Δu in formula (1) j =L e e j , then there is, x[k+1]=(A-B(C ′ B) -1 C′A)x[k]+BD′ -1 e j [k] Δu j [k]=D ′-1 C′x[k]+D ′-1 and j [f+n] Case 2: When the controlled object P M (z) is a non-minimum phase system, and x[k] is expressed as Where T contains (AB(C ′ B) -1 C′A) such that Thus there is where |λ(A s )|<1, and |λ(A u )|>1, that is, A s Contains all stable poles, A u Including unstable poles, the stable state solution is as follows: x s [k+1]=A s x s [k]+B s e j [k],x[-∞]=0, Solving forward in time, the steady state solution is as follows: x u [k+1]=A u x u [k]+B u e j [k],x[+∞]=0, Solving backward in time, the ILC feedforward control command compensation can be obtained as: Δu j [k]=C s x s [k]+C u x u [k]+Of j [k], Finally, the actual error compensation amount for the next iteration can be obtained at j+1 [k]=L q {at j [k]+Δu j [k]}, Where k is the kth sampling point of the signal sequence, L q is a low pass filter.

3. The iterative learning error compensation control method for CNC machine tools based on a stable inverse model according to claim 2 is characterized in that: Specifically, the n-step delay process includes: Do 1 step delay, y j [k+1]=CAx[k]+CBu[k], At this time, if CB < σ, σ is a sufficiently small number, then do n steps of delay y j [k+n]=CA n x[k]+CA n-1 Book[k], Until CA n-1 B≥σ.

4. The iterative learning error compensation control method for CNC machine tools based on a stable inverse model according to claim 3 is characterized in that: Specifically, the value of σ is set to σ = 1 × 10 -5 .

5. The iterative learning error compensation control method for CNC machine tools based on a stable inverse model according to claim 2, characterized in that: Specifically, L q It is a fifth-order Butterworth low-pass filter with a cutoff frequency of 110Hz.

6. The method for iterative learning error compensation control of CNC machine tools based on a stable inverse model according to claim 5, characterized in that: Specifically, the preset threshold δ is δ=10 -6 mm.

7. Iterative learning error compensation control system for CNC machine tools based on stable inverse model, characterized in that: include: The real-time module includes an error calculation unit and a PID control unit, which is used to calculate the desired trajectory r d , feedback control error e j and u j Calculate the actual position y j The offline module includes a storage unit and an iterative learning inversion calculation module ILC, which is used to store the control compensation amount u required for the j-1th iteration stored in the storage unit. j-1 and the feedback control error e j-1 The u is calculated by iterative learning inversion calculation module j ; The CNC machine tool feed drive system includes a motor, a coupling, a ball screw mechanism and a platform mechanism.

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