Friction Compensation Method for Feed System Based on Reset Integral Control

Abstract

The present invention discloses a friction compensation method for a feed system based on reset integral control, which is specifically implemented according to the following steps: Step 1: Optimize and improve the integral term of the traditional architecture of the feedforward P / PI cascade control strategy to design a feedforward reset integral P / PI control strategy; Step 2: Swap the summing point and the branching point of the disturbance observer, and add new control gains to the low-pass filter and the inverse model of the controlled object, thereby constructing a disturbance suppressor. This method can suppress the friction disturbance of the system while ensuring the operation efficiency, and thus achieve the goal of improving the motion accuracy of the feed system.

Description

Technical Field

[0001] The present invention belongs to the technical field of mechanical design and manufacturing, and particularly relates to a friction compensation method for a feed system based on reset integral control. Background Art

[0002] With the relentless pursuit of machining accuracy and efficiency in advanced manufacturing fields such as numerically controlled machine tools, 3D printing, laser engraving, and semiconductor processing, the research on precise and efficient feed drive systems has received increasing attention. However, during operation, the ball screw feed system is often interfered by non-linear friction, resulting in limitations in its motion accuracy and tracking performance, and further reducing the machining accuracy and efficiency of workpieces. Therefore, how to effectively suppress the non-linear interference of friction on the premise of ensuring the operating efficiency of the feed system has become a research hotspot and key point in precise drive control. At present, domestic and foreign scholars have conducted a large number of studies on the problem that non-linear friction affects the motion accuracy of the system, and proposed motion control methods such as linear controllers, friction feedforward compensation strategies, sliding mode control, iterative learning control, and disturbance observers, in order to achieve the goal of improving the motion accuracy of the system. However, the above methods have many limitations in practical applications. For example, the control effect of linear controllers is not good, the application scope of friction feedforward compensation and traditional iterative learning control is single, and sliding mode control is prone to cause system chattering and other problems, resulting in it being difficult for them to completely solve the non-linear friction interference problem of the feed system. Therefore, how to more effectively suppress the adverse effects brought by friction interference and then improve the motion accuracy of the feed system is of great significance to the development of China's high-end manufacturing industry. Summary of the Invention

[0003] The purpose of the present invention is to provide a friction compensation method for a feed system based on reset integral control, which can suppress the friction interference of the system while ensuring the operating efficiency, and then achieve the goal of improving the motion accuracy of the feed system.

[0004] The technical solution adopted by the present invention is a friction compensation method for a feed system based on reset integral control, which is specifically implemented according to the following steps:

[0005] Step 1: Optimize and improve the integral term of the traditional architecture of the feedforward P / PI cascade control strategy to design a feedforward reset integral P / PI control strategy;

[0006] Step 2: Exchange the summing point and the branching point of the disturbance observer, and add new control gains to the low-pass filter and the inverse model of the controlled object, thereby constructing a disturbance suppressor; use the feedforward reset integral P / PI control strategy in combination with the disturbance suppressor to control the tracking performance and motion accuracy of the feed system.

[0007] The features of the present invention also lie in that

[0008] Step 1 is implemented as follows:

[0009] Step 1.1: Consider the motion of the feed system as a single mass sliding on a horizontal plane, and assume that the equivalent viscous damping coefficient B is 0. The dynamic equation of the feed system is given as:

[0010]

[0011] Where x(t) is the actual displacement of the system; v(t) is the actual velocity of the system; M is the equivalent mass of the system; a(t) is the actual acceleration of the system; u(t) is the control input force of the system; f d (t) is the friction disturbance represented by the LuGre friction model; t is time;

[0012] Step 1.2: Based on the traditional architecture of the feedforward P / PI cascade control strategy, the time domain expression of the feedforward P / PI cascade control strategy is given as:

[0013]

[0014] Where, e(t) is the position tracking error; e v (t) is the velocity error; Z is the integral of the velocity error; u(t) is the control input force of the system; K pp is the position loop proportional gain; K vp K is the speed loop proportional gain; vi K is the speed loop integral gain; vf is the speed feedforward gain; K af is the acceleration feedforward gain;

[0015] Perform quality normalization on equations (1) to (2), and the normalized parameters are re-expressed as:

[0016]

[0017] Step 1.3: Substitute the mass-normalized equation (3) into equation (1) to obtain the mass-normalized system dynamics equation:

[0018]

[0019] Where the actual trajectory, velocity, and acceleration of the system are represented by the state vector ψ, i.e., ψ = [x(t), v(t), a(t)];

[0020] Based on the system dynamics equation shown in formula (4), the motion state of the system in the pre-slip stage is expressed by the state vector η as follows:

[0021]

[0022] Step 1.4: Re-improve the integral term of the feedforward P / PI cascade control strategy into a reset integrator to obtain a feedforward reset integral P / PI control strategy, such that the control input force in Equation (5) is greater than the interference force, so as to overcome the friction interference at time t to the greatest extent. The specific expression is as follows:

[0023]

[0024] where Z + is the updated value of Z after reset; the design parameter α ∈ [0, 1] is the reset degree of the adjustable integrator;

[0025] Step 1.5: According to the state law at the system displacement commutation point, give the trigger condition of the reset integrator as shown in Equation (7):

[0026]

[0027] where K vi Z is the integral term control input force; v - (t) is the actual speed value of the previous time step; v(t) is the actual speed value of the current time step; ε is the error limit.

[0028] In Step 1.5, the state law at the system displacement commutation point is as follows:

[0029] (1) The tracking error and the integral term control input force of the controller have opposite signs;

[0030] (2) The product of the actual speed of the system at the previous time step and the current actual speed is not greater than 0;

[0031] (3) Add an error limit to prevent the system from repeatedly triggering within an acceptable tracking error range.

[0032] The specific implementation of Step 2 is as follows:

[0033] Step 2.1: First, through the traditional disturbance observer control architecture, the mathematical expression of the total control input force f(t) of the system is given as:

[0034]

[0035] where f(t) is the total control input force of the system; f^ d (t) is the interference force estimated by the disturbance observer; f^ ld (t) is the filtered estimated interference force; τ lpf is the time constant of the cut-off frequency of the low-pass filter;

[0036] The actual acting force f a (t) received by the controlled object, fa (t) is expressed as:

[0037] f a (t) = f(t) - f d (t) (9)

[0038] In the formula, f d (t) is the actual interference force received by the system; f a (t) is the actual acting force of the system;

[0039] Substitute Equation (8) into Equation (9), and the actual acting force f a (t) received by the controlled object is re-expressed as:

[0040]

[0041] Subsequently, by reverse-deducing Equation (10), the actual interference force f d (t) received by the system is obtained as:

[0042]

[0043] Through the inverse model G(s) of the controlled object -1 and the end position signal x(t), estimate the actual acting force f a (t), and the specific estimation relationship is:

[0044] f^ a (t) = G(s) -1 x(t) (12)

[0045] In the formula, G(s) -1 is the inverse model of the controlled object;

[0046] Finally, replace the actual acting force f a (t) of the controlled object in Equation (11) with the estimated acting force f^ a (t), and at the same time replace the actual interference force f d (t) with the estimated interference force f^ d (t). After derivation, the interference force f^ d (t) estimated by the interference observer is obtained as:

[0047]

[0048] Step 2.2: Introduce the interference observer into the system. The inverse transfer function after introduction is expressed as:

[0049]

[0050] In the formula, e ppi_dob(t) is the tracking error after the P / PI cascade control is combined with the disturbance observer; G(s) is the controlled object;

[0051] Step 2.3: According to the inverse transfer function of the traditional disturbance observer in Equation (14), change the control framework of the traditional disturbance observer to obtain the disturbance suppressor control architecture;

[0052] Step 2.4: Through the disturbance suppressor control architecture obtained in Step 2.3, give the inverse transfer function of the system after introducing the disturbance suppressor, as shown in Equation (15):

[0053]

[0054] In the formula, e ppi_dsu (t) is the tracking error of the system after introducing the disturbance suppressor. The gain values K and β can be used to adjust the suppression degree of the "inverse response" error and the waveform of the cross-quadrant error. Divide the inverse transfer function of the system after introducing the disturbance suppressor into two parts, namely e1(t) and e2(t):

[0055]

[0056]

[0057] e in the above formula nppi (t) is expressed as:

[0058]

[0059] In Step 2.3, according to the inverse transfer function of the traditional disturbance observer in Equation (14), the changes made to the control framework of the traditional disturbance observer are as follows:

[0060] (1) Interchange the positions of the branch point and the summing point;

[0061] (2) The control gains K and β are respectively added to the filter and the inverse model area of the controlled object.

[0062] The beneficial effects of the present invention are:

[0063] The method of the present invention is based on a control strategy of feedforward reset integral P / PI control + disturbance suppressor; by optimizing and improving the integral term of the feedforward P / PI cascade control, a reset integrator with a trigger condition is designed, thereby reducing the cumulative time of the integrator for the error differential and solving the defect that the traditional linear control strategy is difficult to effectively suppress the cross-quadrant error. At the same time, in order to compensate for the friction force that has not been overcome in the feed system, the summing point and the branch point of the disturbance observer are interchanged, and new control gains are added in the low-pass filter and the inverse model region of the controlled object, and then a disturbance suppressor is constructed, solving the defect that the traditional observer will cause the system to exhibit an "inverse response" phenomenon. Accordingly, the method of the present invention adopts a control method combining feedforward reset integral P / PI and a disturbance suppressor, improving the tracking performance and motion accuracy of the ball screw feed system. Description of the Drawings

[0064] Figure 1 is a schematic structural diagram of the feedforward reset integral P / PI of the present invention;

[0065] Figure 2 is a schematic structural diagram of the traditional disturbance observer of the present invention;

[0066] Figure 3 is a schematic structural diagram of the disturbance suppressor of the present invention;

[0067] Figure 4 is the actual trajectory curve under different schemes in the embodiment;

[0068] Figure 5 is Figure 4 the partial enlarged view at I in;

[0069] Figure 6 is Figure 4 the partial enlarged view at II in;

[0070] Figure 7 is Figure 4 the partial enlarged view at III in;

[0071] Figure 8 is the error curve under different schemes in the embodiment;

[0072] Figure 9 is Figure 4 the partial enlarged view at IV in;

[0073] Figure 10 is Figure 4 the partial enlarged view at V in;

[0074] Figure 11 is Figure 4 the partial enlarged view at VI in;

[0075] Figure 12It is a comparison chart of root mean square error and maximum error in the embodiments.

[0076] In the figure, e x (t) is the position tracking error; e v (t) is the velocity error and also the velocity input command of the velocity loop PI controller; K pp is the position loop proportional gain; K vp is the velocity loop proportional gain; K vi is the velocity loop integral gain; K vf is the velocity feedforward gain; K af is the acceleration feedforward gain; u(t) is the control input force calculated by the linear control strategy; x(t) is the actual trajectory; f(t) is the total control input force of the system; f d (t) is the actual disturbance force received by the system; f^ d (t) is the disturbance force estimated by the disturbance observer; f^ ld (t) is the filtered estimated disturbance force; f a (t) is the actual acting force of the system; f^ a (t) is the estimated actual acting force; τ lpf and τ nlpf are the time constants of the cut-off frequency of the low-pass filter, used to filter the high-frequency noise of the system; the gain values K and β can be used to adjust the suppression degree of the "inverse response" error and the waveform of the quadrant-crossing error; G(s) is the controlled object; G(s) -1 is the inverse model of the controlled object. Specific embodiments

[0077] The present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0078] The present invention provides a friction compensation method for a feed system based on reset integral control, and verifies the effectiveness of the method through examples. The specific implementation steps are as follows:

[0079] Step 1: Optimize and improve the integral term of the traditional architecture of the feedforward P / PI cascade control strategy to design a feedforward reset integral P / PI control strategy;

[0080] The structure of the feedforward reset integral P / PI control, as Figure 1 shown, includes two cascaded loops and feedforward control. The inner loop is the velocity loop, which adopts a PI (Proportional-Integral) controller based on the reset principle; the outer loop is the position loop, which adopts a P (Proportional) controller. The feedforward control consists of two parts: velocity feedforward and acceleration feedforward. After differentiating the reference trajectory by velocity feedforward, it is then added to the velocity loop through the velocity feedforward gain value K vf After differentiating the reference trajectory twice by acceleration feedforward, it is then passed through the acceleration feedforward gain value Kaf It is superimposed after the speed-loop PI controller. The main control idea of the feedforward reset integral P / PI control strategy proposed by the present invention is that when the feed system enters the displacement commutation stage, that is, the triggering condition of the reset integrator is satisfied, the integrator is quickly switched to the reset integrator, so that the integrator skips the cumulative process of the error differential, and reaches near the friction force value to be overcome through the updated value Z + to ensure that the system can overcome the friction force interference to the greatest extent, thereby improving the commutation smoothness of the system, so as to achieve the goal of reducing the over-quadrant error of the system. After the reset integrator is successfully triggered, in order to ensure the stability and continuity of the system during reciprocating motion, the use of the conventional integrator is restored, and the proportional controller is used to continue to overcome the friction force in other stages of the system.

[0081] The specific implementation of Step 1 is carried out according to the following steps:

[0082] Step 1.1: Consider the motion of the feed system as the sliding of a single mass block on a horizontal plane, and assume that the equivalent viscous damping coefficient B is 0, and the dynamic equation of the feed system is given as:

[0083]

[0084] where x(t) is the actual displacement of the system; v(t) is the actual velocity of the system; M is the equivalent mass of the system; a(t) is the actual acceleration of the system; u(t) is the control input force of the system; f d (t) is the friction force interference characterized by the LuGre friction model; t is time;

[0085] Step 1.2: According to the traditional architecture of the feedforward P / PI cascade control strategy, the time-domain expression of the feedforward P / PI cascade control strategy is given as:

[0086]

[0087] where e(t) is the position tracking error; e v (t) is the velocity error; Z is the integral of the velocity error; u(t) is the control input force of the system; K pp is the position-loop proportional gain; K vp is the speed-loop proportional gain; K vi is the speed-loop integral gain; K vf is the speed feedforward gain; K af is the acceleration feedforward gain;

[0088] For the convenience of analysis, mass normalization is performed on Equations (1) to (2), and the re-expressed parameters after normalization are:

[0089]

[0090] Step 1.3: Substitute the mass-normalized equation (3) into equation (1), and then the mass-normalized system dynamics equation is obtained as follows:

[0091]

[0092] In the formula, the actual trajectory, velocity, and acceleration of the system are represented by the state vector ψ, that is, ψ = [x(t), v(t), a(t)];

[0093] Based on the system dynamics equation shown in equation (4), the motion state of the system in the pre-slip stage is represented by the state vector η as:

[0094]

[0095] Step 1.4: Re-improve the integral term of the feedforward P / PI cascade control strategy into a reset integrator to obtain the feedforward reset integral P / PI control strategy, so that the control input force in equation (5) is greater than the interference force to overcome the friction interference at time t to the greatest extent. The specific expression is as follows:

[0096]

[0097] In the formula, Z + is the updated value of Z after reset; the design parameter α ∈ [0, 1] is the reset degree of the adjustable integrator;

[0098] Step 1.5: According to the following state law at the system displacement commutation, the trigger condition of the reset integrator is given as shown in equation (7):

[0099] (1) The tracking error and the integral term control input force of the controller have opposite signs;

[0100] (2) The product of the actual velocity of the system in the previous time step and the current actual velocity is not greater than 0;

[0101] (3) Add an error limit to prevent the system from repeatedly triggering within an acceptable tracking error range;

[0102]

[0103] In the formula, K vi Z is the integral term control input force; v - (t) is the actual velocity value in the previous time step; v(t) is the actual velocity value in the current time step; ε is the error limit.

[0104] Step 2: Swap the summing point and the branch point of the disturbance observer, and add new control gains to the low-pass filter and the inverse model of the controlled object, and then a disturbance suppressor is constructed;

[0105] The structure of the interference suppressor control of the present invention is as follows Figure 3 As shown, it includes a controlled object, an inverse of the controlled object, and a low-pass filter. During the motion control process, the disturbance observer can use the end signal x(t) and the inverse model G(s) of the controlled object -1 to estimate the actual acting force f a (t) of the system, and obtain the estimated value f^ a (t) of the interference term by comparing the total control input force f(t) and the estimated acting force f^ d (t). However, since the second derivative of the end signal x(t) will amplify the high-frequency noise of the system, it is necessary to filter the estimated value f^ d (t) of the interference term, and finally superimpose it with the control input force u(t) calculated by the linear control strategy and send it to the controlled object G(s) to realize the estimation and compensation of the interference term of the system.

[0106] The specific implementation of step 2 is as follows:

[0107] Step 2.1: First, through Figure 2 the traditional disturbance observer control architecture shown, the mathematical expression of the total control input force f(t) of the system is given as:

[0108]

[0109] In the formula, f(t) is the total control input force of the system; f^ d (t) is the interference force estimated by the disturbance observer; f^ ld (t) is the filtered estimated interference force; τ lpf is the time constant of the cut-off frequency of the low-pass filter;

[0110] The actual acting force f a (t) received by the controlled object is given, and f a (t) is expressed as:

[0111] f a (t) = f(t) - f d (t) (9)

[0112] In the formula, f d (t) is the actual interference force received by the system; f a (t) is the actual acting force of the system;

[0113] Substitute formula (8) into formula (9), and the actual acting force f a (t) received by the controlled object is re-expressed as:

[0114]

[0115] Subsequently, by inversely deducing Equation (10), the actual interference force f d received by the system is obtained as follows:

[0116]

[0117] Through the inverse model G(s) of the controlled object -1 and the end position signal x(t), the actual acting force f a (t) is estimated. The specific estimation relationship is:

[0118] f^ a (t) = G(s) -1 x(t) (12)

[0119] In the formula, G(s) -1 is the inverse model of the controlled object;

[0120] Finally, the actual acting force f a (t) in Equation (11) is replaced by the estimated acting force f^ a (t), and at the same time, the actual interference force f d (t) is replaced by the estimated interference force f^ d (t). After derivation, the interference force f^ d estimated by the interference observer is as follows:

[0121]

[0122] Step 2.2: Introduce the interference observer into the system. The inverse transfer function after introduction is expressed as:

[0123]

[0124] In the formula, e ppi_dob (t) is the tracking error after the P / PI cascade control is combined with the interference observer; G(s) is the controlled object;

[0125] Step 2.3: According to the inverse transfer function of the traditional interference observer in Equation (14), make the following changes to the control framework of the traditional interference observer (as Figure 3 shown), to obtain the control architecture of the interference suppressor; to avoid the second-order differentiation of the numerator of Equation (14), and thus achieve the purpose of suppressing the "inverse response" error:

[0126] (1) Interchange the positions of the branch point and the summing point;

[0127] (2) The control gains K and β are respectively added to the filter and the inverse model region of the controlled object;

[0128] Step 2.4: Through as Figure 3The interference suppressor (DSU) control architecture obtained in step 2.3 shown gives the inverse transfer function of the system after the interference suppressor is introduced, as shown in Equation (15):

[0129]

[0130] In the formula, e ppi_dsu (t) is the tracking error of the system after the interference suppressor is introduced. The gain values K and β can be used to adjust the suppression degree of the "inverse response" error and the waveform of the cross-quadrant error. The inverse transfer function of the system after the interference suppressor is introduced is divided into two parts, namely e1(t) and e2(t):

[0131]

[0132]

[0133] e in the above formula nppi (t) is expressed as:

[0134]

[0135] Through the analysis results of the inverse transfer functions of Equations (16) to (17) above, it can be found that when the system is in the negative displacement commutation stage, if e1(t) and e2(t) satisfy e1(t) < 0, e2(t) > 0 and |e1(t)| > |e2(t)|, it will cause the error value e ppi_dsu (t) = e1(t) + e2(t) < 0, that is, the system has an "inverse response" error, and the situation is similar when the system is in the positive displacement commutation stage. It can be seen from this that when taking the error waveform in the negative displacement commutation stage as the reference, if the maximum value time T of the "inverse response" error can be accurately recorded and the magnitudes of e1(T) and e2(T) are changed by adjusting the different control gains of the interference suppressor so that e1(T) + e2(T) > 0, the goal of suppressing the "inverse response" error can be achieved, and at the same time, the cross-quadrant error of the system can be further reduced.

[0136] Embodiment

[0137] To demonstrate the effectiveness of the feedforward reset integral P / PI combined with the interference suppressor, the present invention studies the control effects of different control strategies through comprehensive experimental comparisons (Scheme 1: feedforward P / PI control; Scheme 2: feedforward reset integral P / PI control; Scheme 3: feedforward reset integral P / PI + interference observer; Scheme 4: feedforward reset integral P / PI + interference suppressor). The final experimental results are as Figure 4-11 shown, respectively showing the comprehensive comparison diagrams of the actual trajectories and tracking errors under different experimental schemes. The corresponding experimental data are shown in Tables 1 to 2.

[0138] FromFigure 4 and Figure 5-7 From the corresponding locally enlarged regions Ⅰ, Ⅱ, and Ⅲ, it can be seen that when the feed system adopts a linear control strategy combined with the compensation method of a disturbance observer or a disturbance suppressor (RESET+DOB / DSU), the tracking performance of the actual trajectory of the system with respect to the solid reference trajectory is significantly better. Especially after adopting the RESET+DSU compensation strategy designed by the present invention, the tracking performance at the displacement commutation of the system has been further improved.

[0139] Through Figure 8 and Figure 9-11 From the corresponding locally enlarged regions Ⅳ, Ⅴ, and Ⅵ, it can be found that when the feed system only adopts feedforward P / PI or RESET control, the motion accuracy in the steady-state motion stage and the commutation stage is significantly insufficient. After introducing DOB / DSU on this basis, the tracking errors and the durations of the over-quadrant errors in different motion stages are significantly reduced. Especially when using the RESET+DSU control method proposed by the present invention, while eliminating the "inverse response" error of the system (the maximum values of the "inverse response" errors in the positive / negative motion stages are reduced from 1.9 μm and -1.3 μm to 0.2 μm and -0.1 μm respectively), the over-quadrant error at the displacement commutation of the system is further reduced (the maximum values of the over-quadrant errors in the positive / negative motion stages are reduced from -6.3 μm and 7.3 μm to -2.1 μm and 2.2 μm respectively).

[0140] Table 1 shows the experimental results of the maximum tracking error and the root mean square error of the system under different schemes. To more clearly compare the control performance under different schemes, the absolute values of the experimental data in Table 1 are plotted in the form of a Cartesian coordinate system (as Figure 12 shown).

[0141] From Table 2 and Figure 12 it can be seen that when the system only adopts a linear control strategy (feedforward P / PI or RESET), the positive / negative maximum tracking errors of Scheme Ⅱ are reduced by 34.78% and 30.67% compared with Scheme Ⅰ, and the root mean square errors are reduced by 27.77%. When the system adopts a method combining linear control and friction compensation strategy (RESET+DOB / DSU), compared with only adopting feedforward P / PI control, Scheme Ⅲ and Scheme Ⅳ reduce the positive maximum tracking error by 56.52% and 66.67% respectively, the negative maximum tracking error by 58.67% and 68.00% respectively, and the root mean square error by 56.11% and 61.67% respectively.

[0142] Comparison of experimental data of different control schemes

[0143]

[0144] Table 2 shows the suppression effect of the disturbance suppressor on the "inverse response" error of the system. It can be seen from Table 2 that compared with the traditional disturbance observer, the disturbance suppressor constructed in this paper can significantly suppress the "inverse response" error of the system, where the positive / negative "inverse response" errors are reduced by 90.48% and 85.71% respectively.

[0145] Table 2 Experimental results of the disturbance suppressor suppressing the "inverse response" error

[0146]

[0147] Through the performance comparison under the above different control schemes, it can be seen that on the premise of ensuring the system stability, the control method of the feedforward reset integral P / PI combined with the disturbance suppressor (RESET+DSU) proposed in this paper can effectively suppress the cross-quadrant error caused by the non-linear friction force, improve the motion accuracy in the steady state stage of the system, and at the same time make up for the defect that the traditional disturbance observer will cause the "inverse response" error of the system.

Claims

1. A friction compensation method for a feed system based on reset integral control, characterized in that, The implementation is specifically carried out according to the following steps: Step 1: Optimize and improve the integral term of the traditional architecture of the feedforward P / PI cascade control strategy to design the feedforward reset integral P / PI control strategy; The specific implementation of Step 1 is carried out according to the following steps: Step 1.1: Consider the motion of the feed system as the sliding of a single mass block on a horizontal plane, and assume that the equivalent viscous damping coefficient B is 0. The dynamic equation of the feed system is given as: where x(t) is the actual displacement of the system; v(t) is the actual velocity of the system; M is the equivalent mass of the system; a(t) is the actual acceleration of the system; u(t) is the control input force of the system; f d (t) is the frictional force disturbance characterized by the LuGre friction model; t is time; Step 1.2: According to the traditional architecture of the feedforward P / PI cascade control strategy, the time-domain expression of the feedforward P / PI cascade control strategy is given as: where, e(t) is the position tracking error; e v (t) is the velocity error; Z is the integral of the velocity error; u(t) is the control input force of the system; K pp is the proportional gain of the position loop; K vp is the proportional gain of the velocity loop; K vi is the integral gain of the velocity loop; K vf is the velocity feedforward gain; K af is the acceleration feedforward gain; Perform mass normalization on equations (1) to (2). After normalization, the various parameters are re-expressed as: Step 1.3: Substitute the mass-normalized equation (3) into equation (1), and then obtain the mass-normalized system dynamic equation as: In the formula, the actual trajectory, velocity, and acceleration of the system are represented by the state vector ψ, that is, ψ = [x(t), v(t), a(t)]; Based on the system dynamic equation shown in equation (4), the motion state of the system in the pre-slip stage is represented by the state vector η as: Step 1.4: Re-improve the integral term of the feedforward P / PI cascade control strategy into a reset integrator to obtain the feedforward reset integral P / PI control strategy. The specific expression is as follows: where Z + is the updated value of Z after reset; the design parameter α ∈ [0, 1] is the reset degree of the adjustable integrator; Step 1.5: According to the state law at the system displacement commutation, give the trigger condition of the reset integrator, as shown in equation (7): where K vi Z is the integral term control input force; v - (t) is the actual speed value at the previous time step; v(t) is the actual speed value at the current time step; ε is the error limit; Step 2: Exchange the summing point and the branch point of the disturbance observer, and add new control gains to the low-pass filter and the inverse model of the controlled object, and then construct a disturbance suppressor.

2. The friction compensation method for the feed system based on reset integral control according to claim 1, wherein In Step 1.5, the state law at the system displacement commutation is as follows: (1) The tracking error and the integral term control input force of the controller have opposite signs; (2) The product of the actual speed of the system in the previous time step and the current actual speed is not greater than 0; (3) Add an error limit to prevent the system from repeatedly triggering within the acceptable tracking error range.

3. The friction compensation method for the feed system based on reset integral control according to claim 2, characterized in that, The specific implementation of Step 2 is carried out according to the following steps: Step 2.1: First, through the traditional disturbance observer control architecture, give the mathematical expression of the total control input force f(t) of the system as: where \(f(t)\) is the total control input force of the system; \(f\) ^ d (t) is the disturbance force estimated by the disturbance observer; \(f\) ^ ld (t) is the filtered estimated disturbance force; \(\tau\) lpf is the time constant of the cut-off frequency of the low-pass filter; Give the actual acting force f received by the controlled object a (t), where f a (t) is expressed as: f a (t) = f(t) - f d (t) (9) where f d (t) is the actual interference force on the system; f a (t) is the actual acting force on the system; Substitute Equation (8) into Equation (9), and the actual force f a (t) received by the controlled object is re-expressed as: Subsequently, by inversely deducing Equation (10), the actual interference force f d (t) acting on the system is obtained as follows: Through the inverse model G(s) of the controlled object -1 and the end position signal x(t), the actual acting force f a (t) is estimated. The specific estimation relationship is as follows: f ^ a f(t) = G(s) -1 x(t) (12) where G(s) -1 is the inverse model of the controlled object; Finally, replace the actual acting force f a (t) of the controlled object in Equation (11) with the estimated acting force f ^ a (t), and at the same time replace the actual disturbance force f d (t) with the estimated disturbance force f ^ d (t). After derivation, the disturbance force f ^ d (t) estimated by the disturbance observer is as follows: Step 2.2: Introduce the disturbance observer into the system. The inverse transfer function after introduction is expressed as: where, e ppi_dob (t) is the tracking error after the P / PI cascade control is combined with the disturbance observer; G(s) is the controlled object; Step 2.3: According to the inverse transfer function of the traditional disturbance observer in equation (14), change the control framework of the traditional disturbance observer to obtain the disturbance suppressor control architecture; Step 2.4: Through the disturbance suppressor control architecture obtained in Step 2.3, give the inverse transfer function of the system after introducing the disturbance suppressor, as shown in equation (15): where, e ppi_dsu (t) is the tracking error after the system introduces the disturbance suppressor. The gain values K and β can be used to adjust the suppression degree of the "inverse response" error and the waveform of the cross-quadrant error. The inverse transfer function after the system introduces the disturbance suppressor is divided into two parts, namely e1(t) and e2(t): e in the above formula nppi (t) is expressed as:

4. The friction compensation method for the feed system based on reset integral control according to claim 3, wherein In Step 2.3, according to the inverse transfer function of the traditional disturbance observer in equation (14), the changes made to the control framework of the traditional disturbance observer are as follows: (1) Exchange the positions of the branch point and the summing point; (2) Control gains K and β are respectively added to the filter and the inverse model area of the controlled object.

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