Decoupling control method for machine tool flexible ball screw system

Abstract

The present application relates to a kind of machine tool flexible ball screw system decoupling control method, first to the speed inner ring transfer function is decoupled, obtain the flexible modal item in system;Based on flexible modal item design shaping controller, the parameter of shaping controller is only determined by the anti-resonance frequency of system and anti-resonance damping ratio;Speed inner ring closed loop dynamic shaping is target second-order system, so that resonance suppression and bandwidth adjustment are realized independently by PI controller.In this way, the transfer function of position outer ring is decoupled, separates out the first order component of high-order flexible mode, and designs additional controller based on position difference feedback, the feedback gain is equal to the proportional gain size of P controller in position outer ring, and the sign is opposite, suppress the influence of the first order component of high-order flexible mode.The present application realizes the decoupling of shaping controller and P-PI controller parameter setting, simplifies parameter setting process, and improves the closed-loop bandwidth and industrial practicability of flexible ball screw feeding system.

Description

Technical Field

[0001] This invention belongs to the field of CNC machine tool control, specifically relating to a decoupling control method for a flexible ball screw system in a machine tool, and more particularly to a decoupling control method for resonance suppression and bandwidth enhancement in a flexible ball screw system in a machine tool. Background Technology

[0002] The flexible ball screw feed system of machine tools is a typical dual-mass flexible transmission system. In high-speed and high-precision machining scenarios, the elastic deformation of the screw and the mismatch of inertia between the motor side and the load side can easily cause mechanical resonance, resulting in a decrease in servo closed-loop bandwidth, an increase in tracking error, and a deterioration in machining accuracy. Therefore, resonance suppression and bandwidth improvement are the core control requirements of the flexible ball screw feed system of machine tools.

[0003] Under the existing fully closed-loop P-PI control framework, the control methods for suppressing resonance and improving bandwidth in flexible ball screw feed systems mainly rely on adding additional feedback to the speed inner loop of PI control. Typical solutions have the following common drawbacks:

[0004] 1. The traditional PI control combined with multi-path additional feedback resonance suppression method can achieve the configuration of resonant frequency and damping ratio and improve closed-loop bandwidth, but it requires simultaneous tuning of additional feedback gain and PI controller gain. The parameters are severely coupled, the on-site debugging is complex, and it is difficult to apply on a large scale in industrial machine tools.

[0005] 2. The bandwidth enhancement method based on speed difference feedback improves dynamic performance by introducing additional feedback based on speed difference in the inner speed loop. However, the integral part of the PI controller is ignored in the derivation, resulting in insufficient model accuracy. At the same time, the parameter tuning still has strong coupling, which limits the control robustness and adjustability, and cannot meet the engineering requirements of high bandwidth and low resonance.

[0006] The above methods only achieve local resonance suppression in the inner velocity loop, without systematically decoupling the inner velocity loop from the outer position loop. They cannot separate rigid body modal terms from flexible modal terms, and the first-order component of higher-order flexible modes constrains the bandwidth. This results in complex controller parameter tuning, limited room for improving closed-loop bandwidth, and difficulty in adapting to the control requirements of high-speed and high-precision feed in modern CNC machine tools.

[0007] It should be noted that the information disclosed in the background section above is only used to enhance the understanding of the background of the present invention, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0008] To overcome the problems existing in the current control methods for resonance suppression and bandwidth enhancement of flexible ball screw feed systems under full closed-loop P-PI control, this invention provides a decoupling control method for machine tool flexible ball screw systems, which achieves resonance suppression and bandwidth enhancement of the flexible ball screw feed system through decoupling control.

[0009] Other features and advantages of the invention will become apparent from the following detailed description, or may be learned in part by practice of the invention.

[0010] According to a first aspect of the present invention, a decoupling control method for a machine tool flexible ball screw system is provided, the method comprising:

[0011] A dual-mass model of a flexible ball screw feed system is constructed, and voltage normalization is performed on the dual-mass model.

[0012] Based on the voltage-normalized dual-mass model, the transfer function from the control voltage to the motor-side position and the transfer function from the control voltage to the load-side position are determined.

[0013] Based on the transfer function from the control voltage to the motor side position, the transfer function from the control voltage to the motor side speed is determined, i.e., the speed inner loop transfer function.

[0014] The velocity inner loop transfer function is structurally decoupled and is equivalent to the superposition of rigid modal terms and flexible modal terms, and the flexible modal terms are extracted.

[0015] The shaping controller is configured based on the flexible modal term, wherein the parameters of the shaping controller are determined only by the anti-resonance frequency and anti-resonance damping ratio of the machine tool flexible ball screw system; the shaping controller and the PI controller are connected in parallel in the speed inner loop to obtain the speed inner loop closed-loop transfer function and make the speed inner loop closed-loop dynamic equivalent to the target second-order system.

[0016] Based on the transfer function from control voltage to motor side position, the transfer function from control voltage to load side position, and the speed inner loop closed-loop transfer function, the position outer loop transfer function is determined, and the position outer loop transfer function is structurally decoupled to separate the first-order component of the higher-order flexible mode.

[0017] An additional controller is designed based on the first-order component of the high-order flexible mode; wherein, the additional controller is a feedback controller based on the position difference, and its feedback gain is equal in magnitude but opposite in sign to the proportional gain of the P controller in the position outer loop.

[0018] In some exemplary embodiments, the construction of the dual-mass model of the flexible ball screw feed system specifically involves:

[0019]

[0020] in, and These are the rotational inertia and viscous friction coefficient on the motor side, respectively. and These are the rotational inertia and viscous friction coefficient on the load side, respectively. , , These represent the angular displacement, angular velocity, and angular acceleration on the motor side, respectively. , , These represent the angular displacement, angular velocity, and angular acceleration on the load side, respectively. and These represent the current amplification factor and the torque amplification factor, respectively. Indicates the control voltage; Indicates the torque transmitted by the shaft; and These represent the disturbance torques on the motor side and the load side, respectively. and These represent shaft stiffness and shaft damping, respectively.

[0021] In some exemplary embodiments, the voltage normalization processing of the dual-mass model specifically includes:

[0022]

[0023] in, and These are the normalized equivalent mass coefficient and viscous damping coefficient of the voltage on the motor side, respectively. and These are the normalized equivalent quality coefficient and viscous damping coefficient of the load side, respectively. For transfer gain; , , These represent the position, velocity, and acceleration on the motor side, respectively. , , These represent the position, velocity, and acceleration on the load side, respectively. This represents the normalized equivalent interference of the motor-side voltage; This represents the normalized equivalent interference of the load-side voltage; and These represent voltage-normalized shaft stiffness and shaft damping, respectively. This indicates the voltage-normalized shaft-transmitted torque.

[0024] In some exemplary embodiments, the transfer function from the control voltage to the motor-side position and the transfer function from the control voltage to the load-side position are specifically as follows:

[0025]

[0026] in, Indicates from control voltage To the motor side position The transfer function; Indicates from control voltage To the load side position The transfer function; Indicates the ratio of inertia; For Lagrangian operators; and These represent the resonant frequency and the resonant damping ratio, respectively. and These represent the anti-resonance frequency and the anti-resonance damping ratio, respectively. For the resonant frequency and resonant damping ratio The characteristic polynomial of the resonance term is characterized. For the anti-resonant frequency and anti-resonance damping ratio Characteristic polynomial of the anti-harmonic term.

[0027] In some exemplary embodiments, the structural decoupling of the velocity inner loop transfer function is equivalent to the superposition of rigid and flexible modal terms, specifically as follows:

[0028]

[0029] in, Indicates from control voltage Speed ​​to the motor side The transfer function, For the system's first k First-order flexible modal term, and They represent the system's first... k The natural frequency and natural damping ratio of the first-order flexible modal term. and For the system number k The numerator coefficients of the first-order flexible modal term, This indicates that the current system contains a first-order flexible modal term; and These represent the rigid body modal term and the first-order flexible modal term of the system, respectively.

[0030] In some exemplary embodiments, the shaping controller specifically comprises:

[0031]

[0032]

[0033]

[0034]

[0035] in, For shaping controller, and These represent the anti-resonant matching frequency and the matching damping ratio, respectively. , For shaping controller The parameters.

[0036] In some exemplary embodiments, the velocity inner-loop closed-loop transfer function is specifically:

[0037]

[0038] in, Let the velocity be the closed-loop transfer function of the inner loop. , , These are intermediate coefficients used to simplify the expression. and These are the target natural frequency and the target damping ratio, respectively. This is the characteristic polynomial of the target second-order system after dynamic shaping of the inner loop velocity.

[0039] In some exemplary embodiments, the structural decoupling of the outer loop transfer function to separate the first-order component of the higher-order flexible mode specifically involves:

[0040]

[0041] in, For the position outer loop transfer function, and Let these represent the equivalent rigid body response term of the position loop and the first-order component of the higher-order flexible mode, respectively. This is the reference speed on the motor side.

[0042] In some exemplary embodiments, the design of the additional controller based on the first-order component of the higher-order flexible mode specifically includes:

[0043]

[0044] in, For an additional controller based on position difference feedback, This represents the proportional gain of the P controller in the position outer loop.

[0045] The decoupling control method for a machine tool flexible ball screw system provided in this invention first performs mathematical structural decoupling on the speed inner loop transfer function, separating the flexible mode terms, and then designs a targeted shaping controller. The parameters of this controller are determined solely by the anti-resonance frequency and anti-resonance damping ratio of the machine tool flexible ball screw system. This dynamically shapes the speed inner loop closed loop into a target second-order system, allowing the resonance suppression and bandwidth adjustment of the speed inner loop to be achieved simply by adjusting the PI controller parameters, greatly improving the feasibility of this method in practical industrial environments. Furthermore, the position outer loop transfer function is mathematically decoupled, separating the first-order components of the higher-order flexible modes in the system. An additional controller based on position difference feedback is designed to suppress the higher-order flexible modes. Its feedback gain is equal in magnitude but opposite in sign to the proportional gain of the PI controller in the position outer loop, ensuring that the resonance suppression and bandwidth adjustment of the position outer loop are achieved simply by adjusting the proportional gain of the PI controller.

[0046] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and are not intended to limit the invention. Attached Figure Description

[0047] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the invention and, together with the description, serve to explain the principles of the invention. It is obvious that the drawings described below are merely some embodiments of the invention, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.

[0048] Figure 1 This is a schematic flowchart of a decoupling control method for a flexible ball screw system in a machine tool according to an embodiment of the present invention;

[0049] Figure 2 A schematic diagram of a flexible ball screw system for machine tools and its corresponding model structure block diagram;

[0050] Figure 3 This is a schematic diagram of the dual-mass model after voltage normalization.

[0051] Figure 4 The result diagram and control structure diagram after structural decoupling of the velocity inner loop transfer function;

[0052] Figure 5 This is a block diagram of the speed inner loop closed-loop control, which includes two types of controllers.

[0053] Figure 6 The result diagram and control structure diagram after structural decoupling of the position outer loop transfer function;

[0054] Figure 7This is the overall control structure diagram obtained using the method of the present invention;

[0055] Figure 8 The above figures show the measured and simulated frequency response results of the velocity inner loop closed-loop system in the embodiments of the present invention.

[0056] Figure 9 The figures show the measured and simulated frequency response results of the velocity inner loop closed-loop system under different target damping ratios in the embodiments of the present invention.

[0057] Figure 10 The root locus diagram and Bode plot of the location outer loop closed-loop system in the embodiment of the method of the present invention;

[0058] Figure 11 The figure shows the load-side tracking error and the corresponding fast Fourier transform results in the embodiment of the method of the present invention. Detailed Implementation

[0059] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, they are provided so that the invention will be more comprehensive and complete, and will fully convey the concept of the exemplary embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0060] Furthermore, the accompanying drawings are merely illustrative of the invention and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted. Some block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities can be implemented in software, in one or more hardware modules or integrated circuits, or in different network and / or processor devices and / or microcontroller devices.

[0061] The existing technology "K. Szabat, T. Orlowska-Kowalska, Vibration suppression in atwo-mass drive system using PI speed controller and additional feedbacks—comparative study, IEEE Transactions on Industrial Electronics 54 (2007) 1193–1206." discloses a method for improving closed-loop bandwidth by adding additional feedback to the inner speed loop under PI control. This method reveals that for fourth-order flexible systems, at least two additional feedback paths are needed to simultaneously configure the natural frequency and damping ratio, thereby suppressing resonance and increasing bandwidth. However, this method suffers from severe parameter coupling during parameter tuning, requiring simultaneous adjustment of both the additional feedback controller parameters and the PI controller parameters, which greatly inconveniences its application in practical industrial settings.

[0062] The existing technology, "Z. Sun, P. Zahn, A. Verl, A. Lechler, A new control principle to increase the bandwidth of feed drives with large inertia ratio, International Journal of Advanced Manufacturing Technology 91 (2017) 1747–1752," discloses a method for improving closed-loop bandwidth based on speed difference feedback. This method improves the closed-loop bandwidth by adding an additional feedback quantity based on the speed difference to the speed inner loop under conventional PI control. However, in the theoretical derivation of this method, the integral gain in the speed inner loop PI controller is ignored, and parameter coupling problems also exist in the parameter tuning process, which limits the application of this method in practical industrial applications.

[0063] The typical characteristics of the above-mentioned existing technologies are: although they all achieve resonance suppression in the speed inner loop, they all have parameter coupling problems in the process of controller parameter tuning, which limits the application of such methods in actual industrial systems.

[0064] To address the shortcomings and deficiencies of existing technologies, this example embodiment provides a decoupling control method for a machine tool flexible ball screw system. First, the transfer functions of the speed inner loop and position outer loop under full closed-loop P-PI control are mathematically decoupled. Analysis reveals that the resonance and bandwidth reduction in the speed inner loop mainly originate from the flexible mode terms in the system. Furthermore, the first-order component of the higher-order flexible mode obtained by decoupling the position outer loop further limits the achievable bandwidth of the position outer loop. For the flexible mode terms obtained by decoupling the speed inner loop, a shaping controller is designed, whose parameters are determined solely by the anti-resonance frequency and anti-resonance damping ratio of the machine tool flexible ball screw system. Then, under the combined action of the shaping controller and the PI controller, the speed inner loop closed-loop is dynamically shaped into the target second-order system, and the system bandwidth and damping ratio can be freely set by adjusting the PI controller parameters. Next, for the first-order component of the higher-order flexible mode in the position outer loop, an additional controller based on position difference feedback is designed, whose parameters are equal in magnitude but opposite in sign to the proportional gain of the P controller in the position outer loop. Finally, through the combined action of the additional controller and the P controller, resonance suppression and arbitrary bandwidth adjustment of the flexible ball screw feed system under full closed-loop P-PI control are achieved. This invention decouples the tuning of the shaping controller parameters from the tuning of the P-PI controller parameters and proposes a new controller parameter tuning rule. By simply adjusting the P-PI controller parameters according to this rule, arbitrary setting of resonance suppression and bandwidth can be achieved, greatly improving the industrial applicability of this method.

[0065] refer to Figure 1 As shown, the specific steps may include:

[0066] A dual-mass model of a flexible ball screw feed system is constructed, and voltage normalization is performed on the dual-mass model.

[0067] Based on the voltage-normalized dual-mass model, the transfer function from the control voltage to the motor-side position and the transfer function from the control voltage to the load-side position are determined.

[0068] Based on the transfer function from the control voltage to the motor side position, the transfer function from the control voltage to the motor side speed is determined, i.e., the speed inner loop transfer function.

[0069] The velocity inner loop transfer function is structurally decoupled, and it is equivalent to the superposition of rigid body modal terms and flexible modal terms. The flexible modal terms are then extracted.

[0070] The shaping controller is configured based on the flexible modal term, wherein the parameters of the shaping controller are determined only by the anti-resonance frequency and anti-resonance damping ratio of the machine tool flexible ball screw system; the shaping controller and the PI controller are connected in parallel in the speed inner loop to obtain the speed inner loop closed-loop transfer function and make the speed inner loop closed-loop dynamic equivalent to the target second-order system.

[0071] Based on the transfer function from control voltage to motor side position, the transfer function from control voltage to load side position, and the speed inner loop closed-loop transfer function, the position outer loop transfer function is determined, and the position outer loop transfer function is structurally decoupled to separate the first-order component of the higher-order flexible mode.

[0072] An additional controller is designed based on the first-order component of the high-order flexible mode; wherein, the additional controller is a feedback controller based on the position difference, and its feedback gain is equal in magnitude but opposite in sign to the proportional gain of the P controller in the position outer loop.

[0073] The steps in this exemplary embodiment will now be described in more detail with reference to the accompanying drawings and examples.

[0074] The method proposed in this invention was tested on an open five-axis CNC machining platform. The sampling time interval of the control board... The value is 0.00025s. A machine tool is used. X The axis underwent speed inner loop sweep frequency testing under different controllers and cutting process testing under full closed-loop control. The structural decoupling control method in this invention was implemented in Matlab / Simulink 2021a.

[0075] The specific steps of the method in this embodiment are as follows:

[0076] Step 1: Model the machine tool flexible ball screw feed system using a dual-mass model:

[0077]

[0078] in, and These are the rotational inertia and viscous friction coefficient on the motor side, respectively. and These are the rotational inertia and viscous friction coefficient on the load side, respectively. , , These represent the angular displacement, angular velocity, and angular acceleration on the motor side, respectively. , , These represent the angular displacement, angular velocity, and angular acceleration on the load side, respectively. and These represent the current amplification factor and the torque amplification factor, respectively. Indicates the control voltage; Indicates the torque transmitted by the shaft. and These represent the disturbance torques on the motor side and the load side, respectively. and These represent shaft stiffness and shaft damping, respectively.

[0079] refer to Figure 2 The diagram shown is a schematic diagram of a machine tool flexible ball screw system and its corresponding model structure block diagram.

[0080] Step 2, based on , where, Indicates the motor side, Indicates the load side; transfer gain Defined as , For the lead screw, Rotational displacement can be converted into linear displacement, and the dual-mass model in step 1 can be normalized by voltage.

[0081]

[0082] in, and These are the normalized equivalent mass coefficient and viscous damping coefficient of the voltage on the motor side, respectively. and These are the normalized equivalent quality coefficient and viscous damping coefficient of the load side, respectively. , , These represent the position, velocity, and acceleration on the motor side, respectively. , , These represent the position, velocity, and acceleration on the load side, respectively. This represents the normalized equivalent interference of the motor-side voltage; This represents the normalized equivalent interference of the load-side voltage; and These represent voltage-normalized shaft stiffness and shaft damping, respectively. This indicates the voltage-normalized shaft-transmitted torque.

[0083] refer to Figure 3 The figure shown is a schematic diagram of the dual-mass model after voltage normalization.

[0084] Step 3: Transform the time-domain function from Step 2 to the Laplace domain, and the result from the control voltage can be derived. To the motor side position transfer function and from control voltage To the load side position transfer function :

[0085]

[0086] in, For the Lagrangian operator, , , The coefficients of the denominator polynomial are used to simplify the expression; they are derived from the model parameters. The combination yields the desired result.

[0087] However, in order to obtain a more compact transfer function to characterize the dominant mode of the system, the voltage-normalized viscous damping coefficient on the motor side is required. and the normalized viscous damping coefficient of the load side voltage This will be ignored in the following analysis. This simplification mainly affects the system's damping level and resonant peak value, while the resonant / anti-resonant frequency characteristics affected by the system's stiffness and inertia will be preserved. Therefore, the above transfer function can be expressed as follows:

[0088] .

[0089] Step 4: To facilitate subsequent derivation, the transfer function in Step 3 can be further expressed in the following more compact form:

[0090]

[0091] in, The inertia ratio is defined as follows: , For the resonant frequency and resonant damping ratio The characteristic polynomial of the resonance term is characterized. For the anti-resonant frequency and anti-resonance damping ratio The characteristic polynomial of the anti-resonance term is used to characterize the second-order dynamic factors corresponding to the resonance and anti-resonance of the system; the resonant frequency of the system. and anti-resonant frequency and the corresponding resonant damping ratio and anti-resonance damping ratio It can be expressed in the following form through calculation:

[0092]

[0093] Furthermore, based on the above formula, the following relationship can also be obtained:

[0094] .

[0095] Step 5: Adjust the control voltage. Speed ​​to the motor side The transfer function, i.e., the velocity inner loop transfer function, is mathematically used for structural decoupling:

[0096]

[0097] in, Indicates from control voltage Speed ​​to the motor side The transfer function, For the system's first k First-order flexible modal term, and They represent the system's first... k The natural frequency and natural damping ratio of the first-order flexible modal term. and For the system number k The numerator coefficients of the first-order flexible modal term, This indicates that the current system contains a first-order flexible modal term. and These represent the rigid body modal term and the first-order flexible modal term of the system, respectively. and These represent the velocity components of the rigid body modal term and the first-order flexible modal term, respectively, which cannot be directly measured. It is clear from the above equation that the vibration modes in the inner velocity loop mainly originate from the first-order flexible modal term of the system. The system bandwidth is mainly composed of rigid body modal terms. Therefore, a straightforward approach is to structurally decouple the rigid and flexible modal terms in the system, and then design separate controllers for each, thereby simultaneously achieving resonance suppression and bandwidth enhancement.

[0098] refer to Figure 4 The figure shows the result diagram and control structure diagram after structural decoupling of the velocity inner loop transfer function.

[0099] Step 6: Based on the decoupling results of the velocity inner loop transfer function in Step 5, design two controllers to simultaneously achieve resonance suppression and bandwidth enhancement of the velocity inner loop. At this point, the closed-loop transfer function of the velocity inner loop in the system can be expressed as follows:

[0100]

[0101] in, Let the velocity be the closed-loop transfer function of the inner loop. and It is an intermediate variable and has no specific physical meaning; It is a PI controller, because It is a fourth-order system. To achieve all-pole configuration, a shaping controller is set. , among them , , and These are the controller parameters to be defined. (Reference) Figure 5 The diagram shown is a speed inner loop control block diagram containing two types of controllers.

[0102] Obviously, It is a fourth-order system with two pairs of poles. and Defined in the following form:

[0103]

[0104] in, and This represents the target's natural frequency and the target's damping ratio. and Here, the anti-resonance matching frequency and the matching damping ratio are given, where i represents the imaginary unit and is defined as follows: At this point, the four parameters of the controller can be calculated in the following form:

[0105]

[0106] Substitute these parameters into In this case, the closed-loop transfer function of the system's inner velocity loop can be further expressed as follows:

[0107]

[0108] According to this formula, the zero point of the system and It can be calculated as:

[0109]

[0110] If A pair of poles Designed to be at zero point They must be identical, meaning they must satisfy the following equation:

[0111]

[0112] at this time, This will result in zero-pole cancellation, and the four parameters in the controller can be further expressed as:

[0113]

[0114] This parameter tuning rule clearly reveals the shaping controller parameters and Only with the anti-resonant frequency of the system and anti-resonance damping ratio This is relevant. At this point, simply adjusting the parameters of the PI controller according to the derived parameter tuning rules is sufficient to achieve resonance suppression and bandwidth adjustment of the speed inner loop.

[0115] Step 7: Indirectly obtain the velocity components of the first-order flexible modal term. The shaping controller in step 6 The implementation provides input. According to step 4, from the control voltage... Speed ​​to the motor side and load-side speed The transfer function can be expressed in the following form:

[0116]

[0117] in, To control voltage Speed ​​to the motor side The transfer function, To control voltage Speed ​​to load side The transfer function.

[0118] At this point, the velocity components of the first-order flexible mode term It can be calculated in the following way:

[0119]

[0120] From the above relationship, it can be seen that the velocity component of the first-order flexible mode term... The speed difference between the motor side and the load side can be obtained through constant gain. Obtained indirectly through transformation.

[0121] Step 8: Using the shaping controller added in Step 6 and the resulting parameter tuning rules, the velocity inner-loop closed-loop transfer function can now be shaped into the following target second-order system form:

[0122]

[0123] in, , , These are intermediate coefficients used to simplify the expression. This is the characteristic polynomial of the target second-order system after dynamic shaping of the inner loop velocity.

[0124] Step 9: Based on the tuning results of the velocity inner loop closed-loop transfer function in Steps 5-8, design the controller for the position outer loop using the same structural decoupling method. This is based on the transfer function from Step 3. and Motor side position To the load side position The transfer function can be expressed as:

[0125]

[0126] in, From the motor side position To the load side position The transfer function.

[0127] Based on the speed inner loop closed-loop transfer function obtained in step 8, the reference speed from the motor side is... To the load side position The transfer function, i.e., the position outer loop transfer function, can be expressed as:

[0128]

[0129] in, Reference speed from the motor side To the load side position The transfer function, i.e., the position outer loop transfer function.

[0130] Next, the transfer function is structurally decoupled mathematically, and the result is as follows:

[0131]

[0132] in, For the higher-order flexible modes of the system k First-order components, and For the system's higher-order flexible modes, the first k The first and second characteristic frequencies of the first-order component, and The first of the higher-order flexible modes of the system k The first characteristic damping ratio and the second characteristic damping ratio of the first-order component, This indicates that the current system contains a first-order component of a higher-order flexible mode. and Let these represent the equivalent rigid body response term of the position loop and the first-order component of the higher-order flexible mode, respectively. and These are the position components of the equivalent rigid body response term of the position loop and the first-order component of the higher-order flexible mode, respectively, and cannot be directly measured. Clearly, the system bandwidth is determined by... This is a limitation. Therefore, it is necessary to address... Design additional control strategies to improve the closed-loop bandwidth of the location outer loop.

[0133] refer to Figure 6 The figure shows the result diagram and control structure diagram after structural decoupling of the position outer loop transfer function.

[0134] Step 10: Based on the decoupling results of the outer loop structure in Step 9, add a controller. The design of the system is as follows. At this point, the outer-loop closed-loop transfer function of the system can be expressed as:

[0135]

[0136] in, Let be the location outer loop closed-loop transfer function. and It is an intermediate variable and has no specific physical meaning.

[0137] From the above formula, it can be seen that if we take The controller is designed as - ,in, This is the proportional gain of the P controller in the position outer loop; at this time, it is determined by... The introduced higher-order flexible modes will be effectively suppressed. This additional controller is a feedback control based on the position difference. At this point, the closed-loop transfer function of the system's outer position loop can be further expressed as follows:

[0138]

[0139] Clearly, at this point, the outer-loop closed-loop transfer function is a fifth-order system. Therefore, only the proportional gain needs to be adjusted. This allows for free adjustment of the position loop bandwidth.

[0140] Step 11: Indirectly obtain the position component of the first-order component of the higher-order flexible mode. For the additional controller in step 10 The implementation provides input. According to step 8... and in step 9 , Position component of the first-order component of the intermediate and high-order flexible modes It can be calculated in the following way:

[0141]

[0142] From the above relationship, it can be seen that the first-order component of the higher-order flexible mode... It can be indirectly constructed from the position difference signal between the motor side and the load side, serving as an additional controller. Input.

[0143] The final overall control structure diagram obtained by designing the shaping controller and the auxiliary controller using the decoupling control method of this invention is shown in the reference diagram. Figure 7 As shown.

[0144] The method of the present invention is further illustrated below with test result graphs and test data:

[0145] Figure 8Based on the frequency sweep results of the speed inner loop shaping controller (Case 3), PI controller (Case 1), and additional speed difference feedback controller (Case 2) in the method of this invention, it can be seen that the measured frequency response and the simulated frequency response have basically the same trend. Figure 9 To employ the method of this invention and the Case 1 method at a fixed target natural frequency and different target damping ratios A comparison of the inner loop frequency sweep results at different speeds is shown in the figure, with the target damping ratios corresponding to the values ​​from left to right. The frequency sweep results for 0.8, 1.0, and 1.4 show that, compared to the Case 1 method, as the target damping ratio... As the amplitude increases, the resonance amplitude of the method of the present invention also decreases significantly, while the closed-loop bandwidth continues to increase. Figure 10 The root locus diagrams and Bode plots of the additional controller and P-PI controller proposed in this invention show that, since the method of this invention simultaneously suppresses the resonance of the inner velocity loop and the outer position loop, the resonance peak value is significantly reduced compared to P-PI control. Figure 11 By comparing the load-side tracking error and the corresponding fast Fourier transform results of the method of the present invention and the P-PI controller method in the actual cutting process, it can be seen that the method of the present invention can effectively reduce the resonance peak near 40 Hz compared with the P-PI control.

[0146] Table 1 shows a comparison of key performance indicators of the speed inner loop frequency response for the three control methods. In the speed inner loop frequency response comparison, the resonant peak value of the Case 1 method is 1.98 dB (22 Hz), and the -3 dB bandwidth is 40 Hz. The Case 2 method can reduce the resonant peak value to 1.2 dB (20 Hz), but the -3 dB bandwidth is only 36 Hz, with little or no improvement in bandwidth. The resonant peak value is further reduced to 0.93 dB (35 Hz) using the method of this invention, while the -3 dB bandwidth is significantly increased to 140 Hz. Therefore, compared with Case 1, the method of this invention reduces the resonant peak value while increasing the -3 dB bandwidth of the speed inner loop from 40 Hz to 140 Hz, an increase of approximately 3.5 times. Furthermore, compared with Case 2, the method of this invention not only further reduces the resonant peak value but also achieves a significant bandwidth increase, indicating that the method of this invention can significantly improve the dynamic response capability of the system while suppressing resonance, with a more significant effect.

[0147] Table 2 shows a comparison of key speed inner-loop frequency response indicators between the proposed method and the PI control method under different target damping ratios. (The table also shows the comparison of different target damping ratios.) In the case of PI control (Case 1) and the method of the present invention (Case 3), it can be seen that when At that time, the resonant peak value of Case 1 was 3.4 dB (23 Hz), and the -3 dB bandwidth was 38 Hz; the resonant peak value of Case 3 was 1.7 dB (38 Hz), and the -3 dB bandwidth was 110 Hz. The method of this invention improves the bandwidth by approximately 2.9 times (from 38 Hz to 110 Hz) under these settings, while significantly reducing the resonant peak value. At that time, the resonant peak value of Case 1 was 2.5dB, and the -3dB bandwidth was 40Hz; the resonant peak value of Case 3 was 1.25dB (35Hz), and the -3dB bandwidth was 125Hz. The method of this invention increases the bandwidth by approximately 3.1 times (from 40Hz to 125Hz) and reduces the resonant peak value by approximately half. At that time, the resonant peak value of Case 1 was 1.6dB (19Hz), and the -3dB bandwidth was 40Hz; the resonant peak value of Case 3 was 0.72dB (33Hz), and the -3dB bandwidth was 165Hz. The method of the present invention improves the bandwidth by approximately 4.1 times (from 40Hz to 165Hz), and further reduces the resonant peak value. In summary, the method of the present invention can simultaneously achieve a reduction in the resonant peak value and a significant improvement in the velocity inner loop bandwidth under different target damping ratio settings, and the bandwidth improvement remains within the range of approximately 2.9 to 4.1 times as the target damping ratio setting changes, demonstrating the stable advantage and significant effect of the method of the present invention under different design parameters.

[0148] Table 1. Comparison of key performance indicators of the three control methods in the inner speed frequency response.

[0149]

[0150] Table 2 Comparison of key performance indicators of the inner-loop frequency response at different target damping ratios

[0151]

[0152] Furthermore, the above figures are merely illustrative of the processes included in the method according to exemplary embodiments of the present invention, and are not intended to be limiting. It is readily understood that the processes shown in the above figures do not indicate or limit the temporal order of these processes. Additionally, it is readily understood that these processes may be executed synchronously or asynchronously, for example, in multiple modules.

[0153] Other embodiments of the invention will readily occur to those skilled in the art upon consideration of the specification and practice of the invention herein. This application is intended to cover any variations, uses, or adaptations of the invention that follow the general principles of the invention and include common knowledge or customary techniques in the art not disclosed herein. The specification and embodiments are to be considered exemplary only, and the true scope and spirit of the invention are indicated by the claims.

[0154] It should be understood that the present invention is not limited to the precise structure described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of the invention is defined only by the appended claims.

Claims

1. A decoupling control method for a flexible ball screw system in a machine tool, characterized in that, The method includes: A dual-mass model of a flexible ball screw feed system is constructed, and voltage normalization is performed on the dual-mass model. Based on the voltage-normalized dual-mass model, the transfer function from the control voltage to the motor-side position and the transfer function from the control voltage to the load-side position are determined. Based on the transfer function from the control voltage to the motor side position, the transfer function from the control voltage to the motor side speed is determined, i.e., the speed inner loop transfer function. The velocity inner loop transfer function is structurally decoupled, and it is equivalent to the superposition of rigid body modal terms and flexible modal terms. The flexible modal terms are then extracted. A shaping controller is configured based on flexible modal terms, wherein the parameters of the shaping controller are determined only by the anti-resonant frequency and anti-resonant damping ratio of the machine tool's flexible ball screw system; the shaping controller and a PI controller are connected in parallel in the velocity inner loop to obtain the velocity inner loop closed-loop transfer function and make the velocity inner loop closed-loop dynamic equivalent to the target second-order system; the shaping controller is specifically: in, For shaping controller, and These represent the anti-resonant matching frequency and the matching damping ratio, respectively. , For shaping controller Parameters; Based on the transfer function from control voltage to motor side position, the transfer function from control voltage to load side position, and the speed inner loop closed-loop transfer function, the position outer loop transfer function is determined, and the position outer loop transfer function is structurally decoupled to separate the first-order component of the higher-order flexible mode. An additional controller is designed based on the first-order component of the high-order flexible mode; wherein, the additional controller is a feedback controller based on the position difference, and its feedback gain is equal in magnitude but opposite in sign to the proportional gain of the P controller in the position outer loop.

2. The decoupling control method for a machine tool flexible ball screw system according to claim 1, characterized in that, The construction of the dual-mass model for the flexible ball screw feed system is specifically as follows: in, and These are the rotational inertia and viscous friction coefficient on the motor side, respectively. and These are the rotational inertia and viscous friction coefficient on the load side, respectively. , , These represent the angular displacement, angular velocity, and angular acceleration on the motor side, respectively. , , These represent the angular displacement, angular velocity, and angular acceleration on the load side, respectively. and These represent the current amplification factor and the torque amplification factor, respectively. Indicates the control voltage; Indicates the torque transmitted by the shaft; and These represent the disturbance torques on the motor side and the load side, respectively. and These represent shaft stiffness and shaft damping, respectively.

3. The decoupling control method for a machine tool flexible ball screw system according to claim 2, characterized in that, The voltage normalization process for the dual-mass model is as follows: in, and These are the normalized equivalent mass coefficient and viscous damping coefficient of the voltage on the motor side, respectively. and These are the normalized equivalent quality coefficient and viscous damping coefficient of the load side, respectively. For transfer gain; , , These represent the position, velocity, and acceleration on the motor side, respectively. , , These represent the position, velocity, and acceleration on the load side, respectively. This represents the normalized equivalent interference of the motor-side voltage; This represents the normalized equivalent interference of the load-side voltage; and These represent voltage-normalized shaft stiffness and shaft damping, respectively. This indicates the voltage-normalized shaft-transmitted torque.

4. The decoupling control method for a machine tool flexible ball screw system according to claim 3, characterized in that, The transfer functions from the control voltage to the motor-side position and from the control voltage to the load-side position are specifically as follows: in, Indicates from control voltage To the motor side position The transfer function; Indicates from control voltage To the load side position The transfer function; Indicates the ratio of inertia; For Lagrangian operators; and These represent the resonant frequency and the resonant damping ratio, respectively. and These represent the anti-resonance frequency and the anti-resonance damping ratio, respectively. For the resonant frequency and resonant damping ratio The characteristic polynomial of the resonance term is characterized. For the anti-resonant frequency and anti-resonance damping ratio Characteristic polynomial of the anti-harmonic term.

5. The decoupling control method for a machine tool flexible ball screw system according to claim 4, characterized in that, The structural decoupling of the velocity inner loop transfer function, which is equivalent to the superposition of rigid and flexible modal terms, is as follows: in, Indicates from control voltage Speed ​​to the motor side The transfer function, For the system's first k First-order flexible modal term, and They represent the system's first... k The natural frequency and natural damping ratio of the first-order flexible modal term. and For the system number k The numerator coefficients of the first-order flexible modal term, This indicates that the current system contains a first-order flexible modal term; and These represent the rigid body modal term and the first-order flexible modal term of the system, respectively.

6. The decoupling control method for a machine tool flexible ball screw system according to claim 5, characterized in that, The specific velocity inner-loop closed-loop transfer function is as follows: in, Let the velocity be the closed-loop transfer function of the inner loop. , , These are intermediate coefficients used to simplify the expression. and These are the target natural frequency and the target damping ratio, respectively. This is the characteristic polynomial of the target second-order system after dynamic shaping of the inner loop velocity.

7. The decoupling control method for a machine tool flexible ball screw system according to claim 6, characterized in that, The structural decoupling of the outer loop transfer function to separate the first-order component of the higher-order flexible mode is specifically as follows: in, For the position outer loop transfer function, and Let these represent the equivalent rigid body response term of the position loop and the first-order component of the higher-order flexible mode, respectively. This is the reference speed on the motor side.

8. The decoupling control method for a machine tool flexible ball screw system according to claim 7, characterized in that, The additional controller designed based on the first-order component of the high-order flexible mode is specifically as follows: in, For an additional controller based on position difference feedback, This represents the proportional gain of the P controller in the position outer loop.

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