Control strategy based on pre-filter friction compensator combined with improved repetitive control

Abstract

The application discloses a control strategy based on combination of a pre-filter friction compensator and improved repetitive control, and specifically comprises the following steps: step 1, a pre-filter friction compensator is added to a P / PI cascade controller to improve the anti-friction interference capability of a driving system; step 2, a transfer function of an output voltage of the driving system and a tracking error is determined; step 3, specific parameters of a LuGre model in the pre-filter friction compensator are obtained; step 4, a repetitive controller is designed; step 5, an action time period of the repetitive controller determined in step 4 is set at motion commutation to obtain a segmented repetitive control; and step 6, the segmented repetitive control obtained in step 5 is combined with the designed pre-filter friction compensator to form an improved repetitive control framework. The method combines the pre-filter friction compensation control with the segmented repetitive control, greatly improves the error and convergence rate at the motion commutation of each cycle, and reduces the influence of the friction interference on the product processing quality.

Description

Technical Field

[0001] This invention belongs to the field of mechanical design and manufacturing technology, specifically relating to a control strategy based on a combination of a pre-filtered friction compensator and improved repetitive control. Background Technology

[0002] Drive systems are susceptible to frictional disturbances during operation. Failure to effectively suppress these disturbances reduces the system's motion accuracy, consequently affecting product quality. To address this issue, researchers have proposed various control strategies, such as fuzzy PID control, sliding mode control, and active disturbance rejection control (ADRC), to overcome the impact of frictional disturbances. However, these methods have limitations. For instance, fuzzy PID control has limited self-adjustment capabilities, sliding mode control can produce chatter, and ADRC has a complex structure and numerous parameters. Therefore, the selection of a control strategy must be carefully weighed based on actual operating conditions to significantly improve the tracking accuracy and anti-interference capability of the drive control system. Summary of the Invention

[0003] The purpose of this invention is to provide a control strategy based on a combination of a pre-filtered friction compensator and improved repetitive control. By combining pre-filtered friction compensation control with segmented repetitive control, the error and convergence rate at the motion reversal point of each cycle are significantly improved, and the impact of friction interference on product processing quality is reduced.

[0004] The technical solution adopted in this invention is a control strategy based on a pre-filtered friction compensator combined with improved repetitive control, specifically implemented according to the following steps:

[0005] Step 1: Add a pre-filtered friction compensator to the P / PI cascaded controller to improve the anti-friction interference capability of the drive system;

[0006] Step 2: Determine the transfer function of the output voltage of the drive system and the tracking error;

[0007] Step 3: Use the least squares method to obtain the specific parameters of the LuGre model in the pre-filtered friction compensator; use the fruit fly optimization algorithm to obtain the optimal dynamic parameter prediction.

[0008] Step 4: Design a low-pass filter and a linear phase lead compensator. Introduce the designed low-pass filter and dynamic compensator into a traditional P / PI cascaded controller to obtain a repetitive controller.

[0009] Step 5: Set the action time period of the repetitive controller determined in Step 4 at the motion reversal point to obtain segmented repetitive control;

[0010] Step 6: Combine the segmented repetitive control obtained in Step 5 with the designed pre-filtered friction compensator to form an improved repetitive control framework.

[0011] The invention is further characterized in that,

[0012] Step 1 is implemented in the following steps:

[0013] Step 1.1: First, determine the closed-loop transfer function G for the reference displacement and the actual displacement. YX Represented as:

[0014]

[0015] In the formula: X R X is the reference displacement; F G represents the actual displacement. m For mechanical systems; F CF C is a pre-filtered friction compensator; C is a P / PI cascade controller.

[0016] Determine the system disturbance force f F Transfer function G of the actual trajectory Yd The relationship is represented as:

[0017]

[0018] From equation (2), it can be seen that interference suppression is only related to F CF Related, via F CF Optimal suppression characteristics can be obtained;

[0019] Step 1.2: Based on equations (1) and (2), and on the basis of the P / PI cascade control strategy, a pre-filtered friction compensator is designed to optimize the control system; the pre-filtered friction compensator uses the real data of the drive system to predict the inverse solution of the control model, and combines it with the LuGre friction model to form a pre-filtered processing of the reference trajectory, thereby reducing the tracking error e caused by friction. F Represented as:

[0020]

[0021] Where: f F For friction; X RF For the pre-filtered friction compensator F CF The generated pre-compensation signal; the inverse model of the P / PI cascade controller C is obtained using a system identification method, f F Use friction models to make accurate predictions.

[0022] Step 2 is implemented in the following steps:

[0023] Using reciprocating trajectory closed-loop tracking tests to identify the inverse solution H of the control system model F =C -1The transfer function of the output voltage and tracking error of the drive system is expressed as:

[0024]

[0025] Where: e L For tracking error; Y p To control the output voltage of the system. Equation (4) is used to represent the dynamics of the linear servo controller. Most linear servo controllers can be represented by mapping their parameters to the gain K of the PID controller. p K d and K i Therefore, the proposed method can capture the dynamic characteristics of most industrial servo system linear controllers.

[0026] In step 3, the specific parameters of the LuGre model are σ0, σ1, σ2, and F. c F s and v s It consists of six parameters, and its mathematical expression is as follows:

[0027]

[0028] Where: σ0 is the stiffness coefficient; σ1 is the damping coefficient; σ2 is the viscous friction coefficient; F, F c F s These represent total friction, Coulomb friction, and maximum static friction, respectively; v s For Stribeck speed.

[0029] Step 4 is implemented in the following steps:

[0030] Step 4.1: The design method for the low-pass filter Q(z) is as follows:

[0031] The cutoff frequency of the low-pass filter Q(z) depends on the stability condition ||Q F || ∞ =||Q(z)(1-A(z)H(z))|| ∞ When designing for frequencies < 1, in the low-frequency range, |(1-A(z)H(z))| < 1, so |Q(z)| is set close to 1; in the high-frequency range, |(1-A(z)H(z))| > 1, so |Q(z)| is set far from 1, thus satisfying ||Q F || ∞ Stability condition <1;

[0032] Step 4.2: Design method of linear phase lead compensator A(z):

[0033] Design a linear phase lead compensator A(z), the specific expression of which is as follows:

[0034] A(z)=K a Z m (7)

[0035] Equation (7) consists of two parts: K a It is the gain portion with a phase of 0; Z m It is the phase part with a gain of 1, where m is a positive integer.

[0036] Step 4.3: Design the parameters of the linear phase lead compensator based on the following conditions: ① Design a stable feedback control G c (z) Let the controlled object G m (z) Stable; ② Select a K based on the characteristics of the controller and the controlled object. a This provides the drive system with sufficient stability margin.

[0037] Then, by introducing the parameters of the designed linear phase lead compensator into the traditional P / PI control architecture, repetitive control is achieved, resulting in a repetitive controller.

[0038] Step 5 is implemented in the following steps:

[0039] Step 5.1: Determine the error at the motion reversal point based on the following characteristics:

[0040] (1) At the point where the drive system reverses direction, the actual trajectory curve becomes distorted and gradually deviates from the reference curve.

[0041] (2) At the point where the drive system reverses direction, the reference speed curve will cross the zero mark, that is, when the system reverses direction, the reference speed will cross zero.

[0042] (3) At the point of motion reversal of the drive system, the integral term input force of the control system has the opposite sign to the reference speed and approaches in a steep slope state;

[0043] Step 5.2: Based on the pattern determined in Step 5.1, find the starting position of the motion reversal of the drive system, as shown in Equation (8):

[0044]

[0045] Among them, K vi u is the integral term control input force; v - v(t) represents the reference velocity value at the previous time step; v(t) represents the reference velocity value at the current time step. The above formula shows the following rules: ① The product of the reference velocity at the previous time step and the current reference velocity is not greater than 0; ② The reference velocity and the output force of the integral controller have opposite signs. Based on the above formula, the starting position of the error at the motion reversal point can be accurately found.

[0046] Step 5.3: By constructing a pulse triggering model and controlling the time between two rising edges, a pulse signal is generated, thereby determining the action time period of the repetitive controller. The action time period of the repetitive controller is set at the motion reversal point to obtain segmented repetitive control.

[0047] The beneficial effects of this invention are:

[0048] (1) The method of this invention first corrects the trajectory through a pre-filtered friction compensator, thereby suppressing friction interference in advance. Subsequently, piecewise repetitive control is used to reduce the impact of model uncertainty on the drive system through repeated learning, further improving the tracking accuracy of the system. A key feature of this invention is the combination of two control strategies, effectively overcoming the limitations of traditional repetitive control.

[0049] (2) The method of the present invention saves the computational resources required by traditional repetitive control, especially the problem of excessive information storage when the reference period is too large or the control period is too small; it reduces the vibration generated by traditional repetitive control in the vicinity of a large range of feed speed; it makes up for the defect that traditional repetitive control is difficult to compensate for the first cycle, greatly improves the convergence speed and dynamic tracking performance of the control system error learning, and improves the tracking accuracy of the first cycle; it combines the pre-filtered friction compensator with repetitive control, increases the number of effective repetitive learning, and reduces the dependence of the pre-filtered friction compensator on the model recognition accuracy.

[0050] (3) The method of the present invention effectively solves the problem of learning by means of improved repetitive control and effectively solves the dependence of pre-filtered friction compensation control on identification accuracy; by combining pre-filtered friction compensation control with segmented repetitive control, the error and convergence rate at the motion reversal point of each cycle are greatly improved; the method of the present invention is very necessary for improving the machining accuracy of machine tools, especially for optimizing ball screw drive control. Attached Figure Description

[0051] Figure 1 This is a control block diagram of the pre-filtered friction compensator of the present invention;

[0052] Figure 2 This is a schematic diagram of the insert-type repetitive control structure of the present invention;

[0053] Figure 3 These are experimental results of the sinusoidal trajectory tracking error of the drive system;

[0054] Figure 4 This is the result of the peak error amplitude for each cycle;

[0055] Figure 5 This is a comparison diagram of the reference trajectory and the actual trajectory at the motion reversal point of this invention;

[0056] Figure 6This is a comparison diagram of the reference speed and tracking error at the motion reversal point of this invention;

[0057] Figure 7 This is a comparison diagram of the integral output force and reference velocity at the motion reversal point of this invention;

[0058] Figure 8 This is a diagram showing the start position of the repeated control setting at the motion reversal point of the present invention;

[0059] Figure 9 This is a schematic diagram of the segmented repetitive control trigger principle;

[0060] Figure 10 This is a simulation effect of segmented repetitive control;

[0061] Figure 11 This is a schematic diagram of the control strategy of this invention;

[0062] Figure 12 This is a comparison chart of the maximum error at the forward reversal point of the experiment. Detailed Implementation

[0063] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0064] This invention provides a control strategy based on a combination of a pre-filtered friction compensator and improved repetitive control, specifically implemented according to the following steps:

[0065] Step 1: Add a pre-filtered friction compensator to the P / PI cascaded controller to improve the anti-friction interference capability of the drive system.

[0066] Step 1.1: The schematic diagram of the control system is as follows. Figure 1 As shown, the closed-loop transfer function G for the reference displacement and the actual displacement is first determined. YX Represented as:

[0067]

[0068] In the formula: X R X is the reference displacement; F G represents the actual displacement. m For mechanical systems; F CF C is a pre-filtered friction compensator; C is a P / PI cascade controller; from equation (4), it can be seen that the tracking characteristics are related to C and F. CF They are all related, through C and F. CF Together, they achieve good tracking performance. On the other hand, they determine the system disturbance force f. F Transfer function G of the actual trajectory Yd The relationship is represented as:

[0069]

[0070] From equation (2), it can be seen that interference suppression is only related to F CF Related, via F CF Optimal suppression characteristics can be obtained;

[0071] Step 1.2: Based on equations (1) and (2), and on the basis of the P / PI cascade control strategy, a pre-filtered friction compensator is designed to optimize the control system; this pre-filtered friction compensator uses the real data of the drive system to predict the inverse solution of the control model, and combines it with the LuGre friction model to form a pre-filtered processing of the reference trajectory. Figure 1 In the middle, the tracking error e caused by friction will be... F Represented as:

[0072]

[0073] Where: f F For friction; X RF For the pre-filtered friction compensator F CF The generated pre-compensation signal; it can be seen from equation (3) that if the error e caused by friction is to be reduced... F It becomes 0 only when X RF =C -1 f F This can only be satisfied under certain conditions. Therefore, in order to construct X... RF The signal requires a clear understanding of the inverse model of the P / PI cascade controller C and an estimation of the actual frictional force f. F The inverse model of the P / PI cascade controller C is obtained using a system identification method, f F Use friction models to make accurate predictions.

[0074] Step 2: Use reciprocating trajectory to perform closed-loop tracking tests to identify the inverse solution H of the control system model. F =C -1 The transfer function of the output voltage and tracking error of the drive system is expressed as:

[0075]

[0076] Where: e L For tracking error; Y p To control the output voltage of the system. Equation (4) is used to represent the dynamics of the linear servo controller. Most linear servo controllers can be represented by mapping their parameters to the gain K of the PID controller. p K d and K i Therefore, the proposed method can capture the dynamic characteristics of most industrial servo system linear controllers.

[0077] Step 3: Using the least squares method, obtain the specific parameters of the LuGre model in the pre-filtered friction compensator. Its main advantage in engineering and control fields is its relative simplicity, while covering most factors crucial to the control system. The specific parameters of the LuGre model are σ0, σ1, σ2, and F. c F s and v s It consists of six parameters, and its mathematical expression is as follows:

[0078]

[0079] Where: σ0 is the stiffness coefficient; σ1 is the damping coefficient; σ2 is the viscous friction coefficient; F, F c F s These represent total friction, Coulomb friction, and maximum static friction, respectively; v s For Stribeck speed.

[0080] Then, the experimental results were fitted using the least squares method to identify the Stribeck-related parameters. The optimal dynamic parameter prediction was obtained using the fruit fly optimization algorithm; finally, a pre-filtered friction compensator was designed.

[0081] Step 4: Design a low-pass filter and a linear phase lead compensator. Introducing the designed low-pass filter and dynamic compensator into a traditional P / PI cascaded controller yields a repetitive controller, such as... Figure 2 As shown, X R (z), X F (z), F(z), and E(z) represent the reference, output, disturbance, and error signals of the discrete driving system, respectively; G c (z) is the discrete transfer function of the control system; G m (z) represents the mechanical system; Q(z) and A(z) are a low-pass filter and a linear phase lead compensator, respectively, used to enhance the stability of the system; G(z) = G c (z)G m (z) represents a generalized controlled object. Figure 2 The uncompensated control model H(z) can be represented as:

[0082]

[0083] Step 4.1: The design method for the low-pass filter Q(z) is as follows:

[0084] The cutoff frequency of the low-pass filter Q(z) depends on the stability condition ||Q F || ∞ =||Q(z)(1-A(z)H(z))|| ∞In the design, at low frequencies, |(1-A(z)H(z))|<1, so |Q(z)| is set close to 1. This effectively preserves the low-frequency signal in the drive system, thereby achieving tracking of the reference signal and meeting the control accuracy requirements of the drive system. At high frequencies, |(1-A(z)H(z))|>1, so |Q(z)| is set far from 1, thus satisfying ||Q F || ∞ The stability condition is <1. Based on the above analysis, the low-pass filter needs to ensure that Q is as close to 1 as possible in the low-frequency range. F To ensure the system's convergence rate, the value should be close to 1, while at high frequencies, Q(z) needs to be much less than 1 to guarantee system stability. Therefore, the low-pass filter should be designed to have a wide 0dB range at low frequencies and significant attenuation characteristics at high frequencies, thereby achieving stable and fast convergence. However, the phase lag characteristic of the low-pass filter and the time delay element contained in the repetitive controller require the introduction of a linear phase lead compensator A(z) to compensate for the amplitude and phase of the control model H(z).

[0085] Step 4.2: Design method of linear phase lead compensator A(z)

[0086] A dynamic compensator with optimal amplitude and phase compensation is designed as A(z) = K a H(z) can quickly stabilize repetitive control. However, in most cases, if the controlled object is a non-minimum phase system or its dynamic characteristics cannot be adequately modeled, the inverse model of H(z) cannot be used as a stabilizing compensator. In this case, a linear phase lead compensator A(z) is designed, with the following specific expression:

[0087] A(z)=K a Z m (7)

[0088] Equation (7) consists of two parts: K a It is the gain portion with a phase of 0; Z m It is the phase part with a gain of 1, where m is a positive integer.

[0089] Step 4.3: Design the parameters of the linear phase lead compensator based on the following conditions: ① Design a stable feedback control G c (z) Let the controlled object G m (z) Stable; ② Select a suitable K based on the characteristics of the controller and the controlled object. a Thus, given sufficient stability margin for the drive system, repetitive control is achieved by introducing it into the traditional P / PI control architecture, resulting in a repetitive controller.

[0090] Step 5: Set the action time period of the repetitive controller determined in Step 4 at the motion reversal point (at... Figure 3 (As shown in the black dashed box) segmented repetitive control is obtained to solve the peak error at the motion reversal of the system and improve the tracking performance of the drive system.

[0091] In order to accurately apply the repetitive controller at the motion reversal point ( Figure 4 As shown by the black dotted line, in practical use it is necessary to find the location where the direction of movement changes. This invention constructs the following method:

[0092] Step 5.1: Determine the error at the motion reversal point based on the following characteristics:

[0093] (1) At the reversal point of the drive system, the actual trajectory curve exhibits a distorted state and gradually deviates from the reference curve, such as... Figure 5 As shown;

[0094] (2) At the point of reversal in the drive system, the reference speed curve will cross the zero mark, meaning that the reference speed will cross zero when the system reverses direction. Figure 6 As shown;

[0095] (3) At the point where the drive system reverses direction, the integral term input force of the control system has the opposite sign to the reference speed, approaching in a steep slope manner, such as... Figure 7 As shown;

[0096] Step 5.2: Based on the pattern determined in Step 5.1, find the starting position of the motion reversal of the drive system, as shown in Equation (8):

[0097]

[0098] Among them, K vi u is the integral term control input force; v - v(t) represents the reference velocity value at the previous time step; v(t) represents the reference velocity value at the current time step. The above formula shows the following rules: ① The product of the reference velocity at the previous time step and the current reference velocity is not greater than 0; ② The reference velocity and the output force of the integral controller have opposite signs. Based on the above formula, the starting position of the error at the motion reversal point can be accurately found (e.g., v(t) is the reference velocity value at the previous time step; v(t) is the reference velocity value at the current time step). Figure 8 (As shown).

[0099] Step 5.3: Next, the duration of the repetitive controller needs to be set to determine its action path. This is done by constructing... Figure 9 The pulse-triggered model shown generates a pulse signal by controlling the time between two rising edges, thereby determining the action time period of the repetitive controller (e.g., ...). Figure 10 As shown, segmented repetitive control is achieved by setting the action time period of the repetitive controller at the motion reversal point. This method can automatically find the position of the motion reversal point during periodic changes, making it easy to apply and adjust.

[0100] Step 6: Combine the piecewise repetitive control obtained in Step 5 with the pre-filtered friction compensator designed in Step 3 to form an improved repetitive control framework (e.g., Figure 11 (As shown). The improved repetitive control strategy effectively solves the problems of repetitive control not working in the first cycle and having a slow convergence speed, thus significantly improving the tracking performance of the repetitive control system. The combined control framework is shown below. Figure 11 As shown.

[0101] In the experiment, the drive table used in this invention includes a Panasonic A6 servo driver (driver model: MBDLT25SF, matching motor model: MHMF042L1V2M, rated output torque: 1.27 N·m), a ball screw motion table (model: GQ2504, diameter: 25 mm, lead: 4 mm, total length: 600 mm), and a grating ruler displacement sensor (model: Guiyang Xintian JCXE, resolution: 0.5 μm). The servo motor is equipped with a 23-bit 2500-line resolution incremental rotary encoder for real-time detection of the motor rotation angle. Furthermore, the motion table uses ball screw transmission to drive the load (mass: 12 kg) in linear motion.

[0102] To verify the feasibility and effectiveness of the proposed pre-filtered friction compensator, this invention develops two different control schemes to compare the tracking performance of different control strategies. Experimental scheme one uses a traditional feedforward P / PI cascade control strategy to ensure good tracking of the reference target; experimental scheme two uses a piecewise repetitive control scheme based on the pre-filtered friction compensator. While maintaining the same control parameters, the actual trajectory and tracking error are compared with experimental scheme one to verify the actual effect of the compensator.

[0103] Figure 12 The diagram compares four types of controllers: the first uses only a P / PI feedback controller; the second uses a P / PI controller with segmented repetitive control; the third uses a P / PI controller with a pre-filtered friction compensator; and the fourth uses a P / PI controller with a pre-filtered friction compensator and segmented repetitive control. Figure 12 Experimental results show that the control architecture with added pre-filtered friction compensator can effectively suppress tracking errors caused by friction interference at motion reversal points. However, the above method heavily relies on the recognition accuracy of the system model and the friction model. To compensate for this deficiency, a repetitive control strategy will be introduced to reduce the algorithm's dependence on the model while significantly improving its ability to suppress uncertain interference.

[0104] Figure 12 Experimental results for feedforward P / PI cascade control and piecewise repetitive control based on a pre-filtered friction compensator, obtained through experimental measurements, are presented. Figure 12It can be seen that the peak value of the positive tracking error decreases to 0.0125 mm after 5 repetitions of the periodic trajectory and to 0.0081 mm after 10 repetitions, significantly improving the motion control performance of the drive system. For ease of observation and analysis, the experimental results are summarized in Table 1. Table 1 shows that, compared to feedforward P / PI cascade control, the control strategy based on a pre-filtered friction compensator and improved repetitive control reduces the maximum positive and negative errors by 57.14% and 49.78% respectively after 5 repetitions, and the root mean square error by 45.24%. After 10 repetitions, the maximum positive and negative tracking errors decrease by 66.94% and 60.17% respectively, and the root mean square error decreases by 54.76%.

[0105] Table 1 Comparison of workbench tracking errors under different control schemes

[0106]

[0107] The method of this invention learns by means of improved repetitive control, which effectively solves the dependence of pre-filtered friction compensation control on identification accuracy; by combining pre-filtered friction compensation control with piecewise repetitive control, the error at the motion reversal point of each cycle and the convergence rate are greatly improved.

Claims

1. A control strategy based on the combination of a pre-filter friction compensator and an improved repetitive control, characterized in that, The specific steps are as follows: Step 1: Add a pre-filtered friction compensator to the P / PI cascaded controller to improve the anti-friction interference capability of the drive system; Step 1 is implemented in the following steps: Step 1.1: First, determine the closed loop transfer function of the reference displacement to the actual displacement is represented as: （1） In the formula: X R For reference displacement; X F This represents the actual displacement; G m For mechanical systems; F CF For pre-filtered friction compensators; C It is a P / PI cascade controller; Determining system disturbance forces f F The transfer function of the actual trajectory is represented as: （2） From equation (2) it is clear that the interference rejection is only dependent on F CF the ratio of the signal to the interference F CF the optimal rejection characteristics are obtained; Step 1.2: Based on equations (1) and (2), and on the basis of the P / PI cascade control strategy, a pre-filtered friction compensator is designed to optimize the control system; the pre-filtered friction compensator uses the real data of the drive system to predict the inverse solution of the control model, and combines it with the LuGre friction model to form a pre-filtered processing of the reference trajectory, thereby reducing the tracking error caused by friction. e F Represented as: （3） in: f F Friction; X RF For pre-filtered friction compensator F CF The generated pre-compensation signal; P / PI cascade controller C The inverse model is obtained using a system identification method. f F Use friction models to make accurate predictions; Step 2: Determine the transfer function of the output voltage of the drive system and the tracking error; Step 3: Use the least squares method to obtain the specific parameters of the LuGre model in the pre-filtered friction compensator; use the fruit fly optimization algorithm to obtain the optimal dynamic parameter prediction. Step 4: Design a low-pass filter and a linear phase lead compensator. Introduce the designed low-pass filter and linear phase lead compensator into a traditional P / PI cascaded controller to obtain a repetitive controller. Step 4 is implemented in the following steps: Step 4.1: The design method for the low-pass filter Q(z) is as follows: low-pass filter Q ( z The cutoff frequency is determined based on the stability condition. Q F || ∞ =|| Q ( z (1-) A ( z ) H ( z ))|| ∞ <1 Design: In the low-frequency range, at this time |(1- A ( z ) H ( z ))|<1, will | Q ( z | is set to be close to 1; at high frequencies, |(1- A ( z ) H ( z ))|>1, will | Q ( z | Set to be far from 1, thus satisfying || Q F || ∞ Stability condition <1; Step 4.2: Linear Phase Lead Compensator A ( z Design methodology: Designing linear phase lead compensator A z The specific expression is as follows:​ （7） Equation (7) consists of two parts: K a It is the gain portion with a phase of 0; Z m It is the phase part with a gain of 1, where m is a positive integer; Step 4.3: Design the parameters of the linear phase lead compensator based on the following conditions: ① Design a stable feedback control. G c ( z ) to the controlled object G m ( z ① Stable; ② Select one based on the characteristics of the controller and the controlled object. K a This provides the drive system with sufficient stability margin. Then, by introducing the parameters of the designed linear phase lead compensator into the traditional P / PI control architecture, repetitive control is achieved, resulting in a repetitive controller. Step 5: Set the action time period of the repetitive controller determined in Step 4 at the motion reversal point to obtain segmented repetitive control; Step 5 is implemented in the following steps: Step 5.1: Determine the error at the motion reversal point based on the following characteristics: (1) At the point where the drive system reverses direction, the actual trajectory curve will be distorted and will gradually deviate from the reference curve; (2) At the point where the drive system reverses direction, the reference speed curve will cross the zero mark, that is, when the system reverses direction, the reference speed will cross zero; (3) At the point where the drive system reverses direction, the integral term input force of the control system has the opposite sign to the reference speed, and approaches in a steep slope state; Step 5.2: Based on the pattern determined in Step 5.1, find the starting position of the motion reversal of the drive system, as shown in Equation (8): （8） in, K vi u The integral term controls the input force; v - ( t () represents the reference velocity value for the previous time step; v ( t The current time step reference speed value is given; the above formula can accurately pinpoint the starting position of the error at the motion reversal point. Step 5.3: By constructing a pulse triggering model, controlling the time between two rising edges, a pulse signal is generated, and the action time period of the repetitive controller is determined. The action time period of the repetitive controller is set at the motion reversal point to obtain segmented repetitive control. Step 6: Combine the segmented repetitive control obtained in Step 5 with the designed pre-filtered friction compensator to form an improved repetitive control framework.

2. The control strategy based on the combination of pre-filter friction compensator and improved repetitive control according to claim 1, characterized in that, Step 2 is implemented in the following steps: Closed loop tracking test using a reciprocating trajectory to identify a control system model inverse solution H F = C -1 The transfer function representing the output voltage of the drive system to the tracking error is determined as: （4） in: e L For tracking error; Y p To control the output voltage of the system.

3. The control strategy based on the combination of pre-filter friction compensator and improved repetitive control according to claim 2, characterized in that, In step 3, the specific parameters of the LuGre model are determined by... σ 0、 σ 1. σ 2. F c , F s and v s It consists of six parameters, and its mathematical expression is as follows: （5） in: σ 0 represents the stiffness coefficient; σ 1 represents the damping coefficient; σ 2 represents the coefficient of viscous friction; F , F c , F s These represent total friction, Coulomb friction, and maximum static friction, respectively. v s For Stribeck speed.

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