Iterative learning error compensation control method for numerical control machine tool based on stable inverse model

Abstract

The present application relates to a stable inverse model-based iterative learning error compensation control method for numerical control machine tools, which realizes the stable inversion of the system by regarding the unstable part as a non-causal operation and generating control input based on infinite preview. This method not only ensures the stability of the system, but also realizes fast convergence while maintaining high-precision control effect. Through the innovative technical solution, the present application effectively solves the stability, precision and efficiency problems of the prior art when dealing with non-minimum phase systems, providing a comprehensive and efficient solution for numerical control machine tool error compensation control. The modular design of the stable inverse model-based iterative learning error compensation control system for numerical control machine tools proposed by the present application makes the system have good flexibility and scalability. Different modules can be adjusted or replaced according to specific application requirements. And because it applies the related methods proposed in the present application, it also has the beneficial effects of the related methods.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of intelligent control of machine tools, and particularly relates to a numerical control machine tool iterative learning error compensation control method based on a stable inverse model. BACKGROUND

[0002] Numerical control machine tool motion precision control is a complex problem, and at present, it is mainly realized through feedback control and feedforward compensation methods. 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 actual applications. Therefore, as a method that can use historical data for error compensation, iterative learning control (ILC) is widely used in numerical control machine tool precision control.

[0003] In the prior art, the closest implementation schemes mainly include:

[0004] 1. Error compensation method based on adaptive iterative learning (201911349193.0). This method regards the numerical control machine tool as a nonlinear system and designs an adaptive ILC algorithm. However, this method complicates the problem too much because the numerical control motion platform actually has high linearity.

[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 good results.

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

[0007] 4. Numerical control 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 model, which can more comprehensively reduce system vibration and improve precision. 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 numerical control machine tools, such as those with flexible connections or large time delays. This makes schemes 3 and 4 face serious limitations in actual applications.

[0009] For motion platforms with near-linear dynamic characteristics, 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, leading to unbounded control input. In discrete systems, unstable zeros mainly come from: (1) non-collocated placement of actuators and sensors; (2) zero-order hold effect in the sampling process. Therefore, not all systems in industrial control systems are non-minimum phase systems, but they are still unavoidable in specific situations.

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

[0011] 1. Poor adaptability to non-minimum phase systems: Patents 202410105019.6 and 202410105099.5 use model-based iterative learning control methods. These methods will fail when faced with non-minimum phase systems. The reason is that the inverse model of a non-minimum phase system is unstable, and directly using such an inverse model will lead to an unstable control system. Non-minimum phase systems are common in CNC machine tools, such as systems with flexible connections or large time delays. This is particularly common in high-speed, high-precision CNC machine tools, such as large machines with insufficient rigidity or precision micro machines.

[0012] 2. System stability issues: When dealing with non-minimum phase systems, existing technologies often struggle to ensure system stability. This is because the zeros of a non-minimum phase system are in the right half plane, and the poles of its inverse system will also be in the right half plane, leading to system instability. This instability can severely affect control effectiveness and even cause the system to diverge, resulting in decreased workpiece precision or increased machine vibration during actual machining.

[0013] 3. Convergence speed and stability contradiction: Patent 201910977406.8 uses a PD-type iterative learning controller, which can guarantee stability but has slow convergence speed, requiring multiple iterations to achieve ideal control effectiveness. Some fast-converging methods (such as Patent 202410105019.6) can quickly reduce errors, but they struggle to ensure stability when faced with non-minimum phase systems. How to achieve fast convergence while ensuring stability has become a difficult problem.

[0014] 4. Defects of approximate inversion methods: Approximate model inversion methods based on ZPETC or ZMETC (such as the research by Dai L et al.), because they are not exact model inverse results, will produce phase and amplitude errors in certain frequency bands. This approximation can significantly affect control effectiveness, especially when dealing with non-minimum phase systems. In high-precision CNC machining, these errors may result in substandard machining precision.

[0015] The root cause of these shortcomings lies in the lack of effective stable inverse model methods for handling non-minimum phase systems. The characteristics of non-minimum phase systems make traditional model inversion methods unsuitable for direct application, while existing alternative methods struggle to achieve a good balance between stability, convergence speed, and accuracy. Therefore, effectively handling non-minimum phase systems and achieving 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 this invention is to at least address one of the shortcomings of the prior art and provide a method for iterative learning error compensation control of CNC machine tools based on a stable inverse model.

[0017] To achieve the above objectives, the present invention adopts the following technical solution:

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

[0019] Step 110: Obtain the desired trajectory r d The pre-established control model is initialized, which is a CNC machine tool iterative learning error compensation control model 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 and inversion calculation module (ILC). The real-time module includes an error calculation unit and a PID control unit. The offline module uses the control compensation amount u required for the (j-1)th iteration stored in the storage unit. j-1 and feedback control error e j-1 u is calculated through the iterative learning inversion calculation module. j The real-time module uses the desired trajectory r d Feedback control error e j and u j The actual position y is calculated. j ;

[0021] Step 120: Configure the conditions for the 0th iteration, that is, set the initial control compensation amount u0 = 0, and set the desired trajectory r... d Input the control model;

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

[0023] Step 140: Determine whether the maximum value of the difference between two consecutive feedback control errors is less than the preset threshold δ. If it exists, proceed to step 160; otherwise, proceed to step 150.

[0024] Step 150: Let j = j + 1, and control the error e according to the feedback. j and control compensation amount u j The control compensation amount u required for the (j+1)th iteration is calculated using the offline module. j+1 Return to step 130 and continue executing the trajectory tracking control task;

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

[0026] Furthermore, specifically, based on the feedback control error e j and control compensation amount u j The control compensation amount u required for the (j+1)th iteration is calculated using the offline module. j+1 ,include,

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

[0028] Where L e For learning the filter, L e For a robust filter, an error is constructed accordingly.

[0029] e j =r d -y j

[0030] Furthermore, based on the principle of model iterative learning control methods, it is necessary to find a control from u j to y j Mathematical model H, making L e =H -1 The discrete-domain transfer function can be expressed in state-space as follows: C P (A C B C C C D C ), P M (A m B m C m From this, we can obtain the state-space expression H(A,B,C,D), where the input and output relationships are expressed as follows:

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

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

[0033] where C = [0C m ], D = 0, however D is zero matrix, not full rank, for this to input y j [k] do n step delay processing to achieve process, at this time,

[0034] C ′ = CA n ,

[0035] D ′ = CA n-1 B;

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

[0037] Case 1, when the controlled object P M (z) is the minimum phase system, the error compensation amount can be calculated directly by model inverse, the input is e j , the output is Δu j , let Δu j in formula (1) = L e e j , then,

[0038] x[k+1] = (A - B(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, x[k] is expressed as where T contains the eigenvectors of (A - B(C ′ B) -1 C′A), so that

[0041]

[0042] Thus,

[0043]

[0044] where |λ(A s )|<1, and |λ(A u )|>1, i.e., A s contains all stable poles, A u contains unstable poles, and the stable state is solved as follows:

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

[0046] solved forward in time, and the stable state is solved as follows:

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

[0048] solved backward in time, finally, the ILC feedforward control command compensation quantity 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 quantity of the next iteration can be obtained as

[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 time delay process includes,

[0054] 1-step time delay,

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

[0056] If CB < sigma, sigma is a small enough number, then do n-step delay

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

[0058] Until CA n-1 B >= sigma.

[0059] Further, specifically, the value of sigma is set as sigma = 1 x 10 -5 .

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

[0061] Further, specifically, the preset threshold value delta takes the value of delta = 10 -6 mm.

[0062] The application also proposes a numerical control machine tool iterative learning error compensation control system based on a stable inverse model, comprising:

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

[0064] An offline module, comprising a storage unit and an iterative learning inversion calculation module ILC, is used to calculate u j-1 by the control compensation amount u j-1 required by the j-1 iteration stored in the storage unit and the feedback control error e j .

[0065] The numerical control machine tool feeding drive system comprises a motor, a shaft coupling, a ball screw mechanism and a platform mechanism.

[0066] The application has the following advantages:

[0067] The application proposes a numerical control machine tool iterative learning error compensation control method based on a stable inverse model, which regards the unstable part as a non-causal operation and generates a control input based on infinite preview, thereby realizing stable inversion of the system. This method not only ensures the stability of the system, but also realizes fast convergence while maintaining high-precision control effect. The application has the following advantages,

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

[0069] The present application solves the problem of inversion instability in non-minimum phase systems by decomposing the system state into stable and unstable parts using non-causal time-domain inversion techniques and processing the unstable poles using non-causal operations. This method effectively addresses the limitations of existing techniques in handling such systems.

[0070] 2. Balancing fast convergence and stability:

[0071] Compared to methods that use PD-type iterative learning controllers, the present application achieves faster convergence while ensuring system stability through the combination of iterative learning controllers and non-causal time-domain inversion techniques. This resolves the contradiction between convergence speed and stability in existing techniques.

[0072] 3. Improved control precision:

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

[0074] 4. Flexibility and scalability:

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

[0076] Wide range of applications:

[0077] Due to its ability to effectively handle non-minimum phase systems, the present application is applicable to a wider range of CNC machine types, including high-speed, high-precision CNC machines, and systems with flexible connections or large time delays.

[0078] In summary, the present application effectively addresses the stability, precision, and efficiency issues of existing techniques in handling non-minimum phase systems through innovative technical solutions, providing a comprehensive and efficient solution for CNC machine error compensation control. BRIEF DESCRIPTION OF DRAWINGS

[0079] The above and other features of the present disclosure will become more apparent from the following detailed description of embodiments taken in conjunction with the accompanying drawings, in which like reference characters indicate the same or similar elements throughout the drawings, and in which:

[0080] Figure 1 is the principle diagram of the CNC machine iterative learning error compensation control method based on the stable inverse model according to the present application.

[0081] Figure 2 is the structural principle block diagram of the ball screw feeding module of the numerical control machine tool feeding driving module;

[0082] Figure 3 is the logic principle block diagram of the present application;

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

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

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

[0086] Figure 7 is an error convergence result schematic diagram of X-axis and Z-axis under the ILC based on non-causal inversion in the experiment;

[0087] Figure 8 is a double-axis error result schematic diagram of the 10th iteration convergence in the experiment;

[0088] Figure 9 (a) is a ball bar measurement result schematic diagram of the XZ platform circular test when the present method is applied, Figure 9 (b) is a ball bar measurement result schematic diagram of the XZ platform circular test under the contrast method (ZPETC frequency domain approximate model inverse). DETAILED DESCRIPTION

[0089] The concept, specific structure and generated technical effects of the present application will be described clearly and completely in combination with embodiments and drawings to fully understand the purpose, scheme and effects of the present application. It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other without conflict. The same reference signs used in the drawings indicate the same or similar parts.

[0090] Embodiment 1, with reference to Figure 1 , Figure 2 , Figure 3 and Figure 4 , the present application proposes a numerical control machine tool iterative learning error compensation control method based on a stable inverse model, which acts on the feeding driving system of the numerical control machine tool. The method comprises the following steps:

[0091] Step 110, obtaining a desired trajectory r d , and initializing a pre-established control model, which is a numerical control machine tool iterative learning error compensation control model based on a stable inverse model;

[0092] The control model comprises a real-time module and an offline module, the offline module comprises a storage unit and an iterative learning inversion calculation module ILC, the real-time module comprises an error calculation unit and a PID control unit, the offline module calculates a control compensation amount u j-1 and a feedback control error e j-1 through the storage unit j , the real-time module calculates an actual position y d through the desired trajectory r j , the feedback control error e j and u j ;

[0093] Step 120, configure the 0th iteration condition, i.e., let the first control compensation amount u0=0, input the desired trajectory r d into the control model;

[0094] Step 130, execute the trajectory tracking control task, and acquire the desired trajectory r d and the feedback control error e j of the actual position y j of the motor end in real time;

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

[0096] Step 150, let j=j+1, calculate the control compensation amount u j of the j+1th iteration through the offline module according to the feedback control error e j and the control compensation amount u j+1 , and return to step 130 to continue executing the trajectory tracking control task;

[0097] Step 160, j=j+1; u j+1 =u j ; continue executing the trajectory tracking control task until the machining task is completed.

[0098] In this embodiment 1, in general, the method is understood as follows in combination with Figure 4 :

[0099] Step 1: initialization, obtain the model of the transfer function P M by using an identification method, and design a PID controller C PThe matrix parameters required for offline calculation of the inversion model in the offline module can be further obtained, and if the system is a minimum phase system, the model inverse calculation matrix is designed in the manner of case 1, otherwise the stable model inverse calculation matrix is designed in the manner of case 2. And the system starts to receive the interpolated and speed planned desired trajectory command r d ;

[0100] Step 2: Configure the 0th iteration condition, let the first control compensation amount be u0=0;

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

[0102] Step 4: If the maximum value of the difference between the front and rear two iteration errors is less than a given value, here taking δ=10 -6 mm, it indicates that the iteration has converged, go to step 6, and end the iteration learning; otherwise, go to step 5;

[0103] Step 5: Let j=j+1, according to the error e j and u j , the model inverse result calculated by the offline module initialized in step 1 is used to finally obtain the control compensation amount u j+1 required for the j+1 iteration, return to step 3, and continue to execute the trajectory tracking task;

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

[0105] Step 7: End.

[0106] As a preferred embodiment 2 of the present application, the present application will be further described in combination with the drawings and embodiments:

[0107] Figure 2 The schematic diagram of the feed drive system of the numerical control machine tool is shown, and the rotary motor drives the ball screw to realize the linear motion of the platform. According to the patent No. 202410105099.5, Figure 3 , the 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, q1, q2, q3, … q8 are system parameters to be identified.

[0110] On the basis of the transfer function, the above coefficients can be obtained by conventional system parameter identification method, for example, under open loop condition, input a set of excitation signals containing various frequency components, observe the output results, and finally calculate the parameters by least square method.

[0111] Figure 1 The numerical control machine tool iterative learning error compensation control system based on stable inverse model comprises an offline module, a real-time module and a numerical control machine tool feeding driving system, the offline module comprises a storage unit and an iterative learning backstepping calculation module, the real-time module comprises an error calculation unit and a PID control unit, and the numerical control machine tool feeding driving system comprises a motor, a coupling, a ball screw mechanism and a platform mechanism. Figure 2 The end of the motor is provided with a rotary encoder for detecting the actual position of the motor J is the current execution iteration number.

[0112] The error calculation unit in the real-time module needs to calculate the deviation amount 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, e j = r j -y j , wherein y j is the actual position obtained by the proportional conversion module from the motor encoder position; the PID control unit outputs a control amount under the action of e j , and the purpose is to suppress the size of e P , and combine with the control compensation amount u j in the offline module to input the numerical control machine tool feeding driving system, j as shown. Figure 2

[0113] The storage unit in the offline module is mainly used for storing historical data, such as error e j-1 , control compensation amount u j-1 ; on the basis of the above data, the iterative learning backstepping calculation module uses the iterative learning method based on the inverse model to calculate (non-real-time) the control compensation amount u j of the jth iteration offline, u j is injected into the output end of the PID control unit and combined with the output thereof.

[0114] The use of the iterative learning method based on the inverse of the stable model involves

[0115] u j+1 = L q ​(u j +L e e j )

[0116] i.e. according to the results of the last iteration, the next control compensation amount u j+1 is calculated, where L e is a learning filter, and L e is a robust filter, where L q is generally designed as a low-pass filter, and L e is implemented using a model inverse method, for which an error

[0117] e j = r d -y j

[0118] In addition, based on the principle of the model iterative learning control method, a mathematical model H is needed to be found from u j to y j , so that L e = H -1 . In the case of known system transfer function, it is not difficult, such as: C P (z), P M (z), but the expression of the transfer function in the frequency domain is the result of the frequency domain, and the method based on the frequency domain can only be designed as an approximate model inverse, and an accurate model inverse cannot be obtained, thereby resulting in poor control error. Therefore, the time domain state space method is used for expression. The transfer function in the discrete domain is written in the 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 , and D C are matrices in the state space equation corresponding to the controller C_P transfer function, which are known in control science, and H can be obtained from C_P, and the state space expression H(A, B, C, D) of H can be obtained, where A m , B m , C m , and 0 are matrices in the state space equation corresponding to the control object P_M transfer function (generally, the system is suitable, so D is D m = 0), which are known in control science, and P_M can be expressed, and the input and output relationship can be expressed as:

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

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

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

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

[0123] At this time, if CB< σ (σ is a small enough number, set σ = 1 x 10 -5 , if too small will introduce numerical calculation error), then do n step delay

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

[0125] until CA n-1 B≥ σ, at this time

[0126] C ′ = CA n

[0127] D ′ = CA n-1 B

[0128] Thus, a non-zero D matrix can be obtained, and then the following two different cases are processed.

[0129] (1) When the controlled object P M (z) is a minimum phase system, the error compensation amount can be directly calculated by model inversion, the input is e j , and the output is Δu j , let Δu j in the above formula (1) = L e e j

[0130] x[k+1] = (A-B(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 a non-minimum phase system, the unstable zero will become a pole of the system after model inversion, which leads to a matrix (A - B(C ′ B) -1 C'A) with eigenvalues outside the unit circle in the time domain, resulting in divergence / no solution and finally unstable system if calculated in a causal way. Therefore, the present application adopts a non-causal calculation method to deal with the unstable pole of model inversion (the unstable zero of the original model). It is not difficult to find a transformation matrix T mathematically, which can decompose the state in the first case into stable and unstable parts, for example: where T contains the eigenvectors of (A - B(C ′ B) -1 C'A) such that

[0133]

[0134] Thus

[0135]

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

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

[0138] solved forward in time, and the stable state is solved as follows:

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

[0140] solved backward in time. Finally, the ILC feedforward control command compensation amount 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 sample point of the signal sequence, L q is designed as a five-order Butterworth low-pass filter with a cutoff frequency of 110 Hz, aiming to eliminate high-frequency noise introduced in the signal measurement process. The Butterworth filter is chosen to ensure the maximum flat passband and good stability. The selection of the cutoff frequency is based on the bandwidth of the system and the desired learning trajectory smoothing effect. 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, and X s represents the stable part of the original system X, i.e., similar decoupling operation.

[0146] In specific applications,

[0147] Embodiment 1: System Case

[0148] This method is implemented on an XZ-axis numerical control lathe motion platform, and the transfer function of the dual-axis platform obtained through system identification is as follows

[0149]

[0150] The dual-axis motion system is controlled by a discrete-time PD controller, whose expression is:

[0151]

[0152] where T = 1 / f is the sampling period, K p and K d are the proportional and derivative gains, respectively, and T f is the filter time constant. The controller parameters are adjusted according to the identified model, aiming to balance between tracking performance and robustness. The final parameter values are: for the X-axis, K p = 169, K d = 2.01, and T f= 1.01 x 10 -5 K of the Z axis p = 221, K d = 3.21, T f = 1.05 x 10 -5 .

[0153] Embodiment 2: Actual results

[0154] In order to verify the effectiveness of the model-based iterative trajectory shaping and control compensation numerical control and wiping yellow control method designed by the application, an experiment of trajectory tracking was carried out on an actual XZ platform, and the hardware configuration Figure 5 The controller is implemented in the NI Compact RIO real-time hardware platform, and through the FPGA wiring board of the platform, an effective real-time module can be realized. The error data e j and the compensation data u j are collected at a sampling time of 1KHz, and are transmitted to the upper PC machine through Ethernet. After the MATLAB matrix calculation is run in the PC and the next iteration control compensation u j+1 is obtained by operating according to the method of the application, it is transmitted to the NI Compact RIO for real-time control of the numerical control double-axis platform through Ethernet.

[0155] Figure 6 The experiment input is a circular trajectory command of a double-axis, with a radius of 50mm, so the trajectory command of the two axes is a circular trajectory command controlled by acceleration and deceleration.

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

[0157] Figure 8 The double-axis error results of the 10th iteration convergence

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

[0159] Embodiment 3, the application also proposes a numerical control machine tool iterative learning error compensation control system based on a stable inverse model, comprising:

[0160] The real-time module, including an error calculation unit and a PID control unit, is used to determine the desired trajectory r. d Feedback control error e j and u j The actual position y is calculated. j

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

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

[0163] Furthermore, the functional modules in the various embodiments of the present invention can be integrated into one processing module, or each module can exist physically separately, or two or more modules can be integrated into one module. The integrated modules described above can be implemented in hardware or as software functional modules.

[0164] If the integrated module is implemented as a software functional module and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the above embodiments of the present invention can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or system capable of carrying the computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc.

[0165] Although the description of the application has been quite detailed and particularly with respect to several described embodiments, it is not intended to limit the application to any of these details or embodiments or any particular embodiment, but rather it is intended to cover the intended scope of the application as provided by the appended claims, which should be interpreted as broadly as the prior art will permit, effectively encompassing the intended range of the application. Furthermore, the above description of the application is made by way of example with the embodiments that the inventors can foresee, and the purpose is to provide a useful description, and those non-essential changes to the application that have not yet been foreseen can still represent equivalent changes to the application.

[0166] The above description is only the preferred embodiments of the present application, and the present application is not limited to the above-described embodiments, but any technical solutions and / or embodiments within the protection scope of the present application, as long as they achieve the same technical effects by the same means, should belong to the protection scope of the present application.

Claims

1. A numerical control machine tool iterative learning error compensation control method based on a stable inverse model, characterized by, Acting on a feed drive system of a numerical control machine tool, the method comprises The following: Step 110, obtaining a desired trajectory r d and initializing a pre-established control model, which is a stable inverse model based iterative learning error compensation control model for a CNC machine tool; The control model comprises a real-time module and an offline module, the offline module comprises a storage unit and an iterative learning inversion calculation module ILC, the real-time module comprises an error calculation unit and a PID control unit, the offline module calculates a control compensation amount u j-1 and a feedback control error e j-1 The offline module calculates a control compensation amount u j The real-time module calculates an actual position y d , a feedback control error e j and u j j ;​ Step 120, configure the 0th iteration condition, i.e. let the first control compensation amount u0=0, and the expected trajectory r d input the control model; Step 130, perform trajectory tracking control task, and acquire expected trajectory r in real time d feedback control error e of actual position y of motor end j feedback control error e of actual position y of motor end j feedback control error e of actual position y of motor end Step 140, judge whether the maximum value of the difference between the feedback control errors of the previous two times is less than the preset threshold δ, if yes, go to step 160, if not, go to step 150; Step 150, let j = j + 1, according to the feedback control error e j And control compensation u j The control compensation u required for the j+1 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 perform the trajectory tracking control task until the machining task is completed; Specifically, according to the feedback control error e j and the control compensation amount u j The control compensation amount u required for the j+1 iteration is calculated by the offline module j+1 , including, u j+1 = L q (u j + L e e j ) (1) where L e is the learning filter, L q is the robust low-pass filter, and e is the error for which this is constructed. e j = r d - y j In addition, based on the principle of model-based iterative learning control method, it is necessary to find a mathematical model H from u j to y j , such that L e = H -1 . The transfer function of the discrete domain is written in the state space as follows: C P (A C , B C , C C , D C ), P M (A m , B m , C m , 0), and thus the state space expression H(A, B, C, D) of H can be obtained. The input and output relationship therein is expressed as follows: x[k + 1] = Ax[k] + Bu j [k] y j [k] = Cx[k] where C = [0C m ], D = 0, however D is a zero matrix, not full rank, for this to input y j [k] do n-step delay processing to achieve process, at this time, C ′ = CA n , D ′ = CA n-1 B; Thus, a non-zero D matrix can be obtained, and then the following two different cases are processed; Case 1, when the controlled object P M (z) is a minimum phase system, the error compensation amount can be directly calculated by the model inversion method, the input is e j , the output is Δu j , let Δu j in formula (1) be L e e j , then, x[k + 1] = (A - B(C ′ B) -1 C'Ax[k] + BD' -1 e j [k] Δu j [k] = D ′-1 C'x[k] + D ′-1 e j [k+n] Case 2, when the controlled plant P M (z) is a non-minimum phase system, x[k] is expressed as where T contains the eigenvectors of (A - B(C ′ B) -1 C'A) such that Thus, there are where |λ(A s )| < 1 and |λ(A u )| > 1, i.e., A s contains all stable poles, A u contains unstable poles, and the stable state solution is given by: x s [k+1] = A s x s [k] + B s e j [k], x[-∞] = 0, Solving forward in time, and the stable 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 amount can be obtained as: Δu j [k] = C s x s [k] + C u x u [k] + De j [k], Finally, the actual error compensation amount of the next iteration can be obtained u j+1 [k] = L q {u j [k] + Δu j [k]}, Where k is the kth sampling point of the signal sequence.

2. The stable inverse model based iterative learning error compensation control method for CNC machine tools according to claim 1, characterized in that, Specifically, the n-step delay process includes, Make 1-step delay, y j [k + 1] = CAx[k] + CBu[k], At this time, if CB<σ, σ is a small enough number, then make n-step delay y j [k+n] = CA n x[k] + CA n-1 Bu[k], Until CA n-1 B > σ.

3. The CNC machine tool iterative learning error compensation control method based on stable inverse model according to claim 2, characterized in that, In particular, the value of σ is set to σ = 1 x 10 -5 .

4. The stable inverse model based iterative learning error compensation control method for CNC machine tools according to claim 1, characterized in that, In particular, L q is a fifth order Butterworth low pass filter with a cutoff frequency of 110 Hz.

5. The stable inverse model based iterative learning error compensation control method for CNC machine tools according to claim 4, characterized in that, In particular, the preset threshold value δ takes a value δ = 10 -6 mm.

6. An iterative learning error compensation control system for a numerically controlled machine tool based on a stable inverse model, characterized by, The system comprises the steps of the method of any one of claims 1-5, a real-time module comprising an error calculation unit, a PID control unit for calculating the actual position y d from the desired trajectory r j feedback control error e j and u j An offline module including a storage unit and an iterative learning inversion calculation module ILC, for calculating the control compensation amount u needed in the jth iteration through the control compensation amount u stored in the storage unit in the j-1th iteration j-1 and the feedback control error e j-1 through the iterative learning inversion calculation module j ; The feed drive system of the numerical control machine tool comprises a motor, a shaft coupling, a ball screw mechanism and a platform mechanism.

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