Linear time-invariant ball screw driving system control method based on L1 adaptive control

Abstract

The invention relates to the technical field of intelligent compensation control, in particular to a linear time-invariant ball screw driving system control method based on self-adaptive control. The method comprises the following steps: establishing a state space model of a system; designing a baseline controller, obtaining a state feedback gain by solving a linear matrix inequality, and generating a baseline control signal; calculating a steady-state gain, and filtering the reference input signal to generate a steady-state feed-forward control signal; constructing a state predictor, estimating the total uncertainty on line, decomposing the total uncertainty into matching and mismatching signals, generating matching and mismatching compensation signals after gain mapping and low-pass filter band limiting processing, and synthesizing the matching and mismatching compensation signals into self-adaptive compensation signals; and superposing the three paths of signals to obtain a master control signal, and after amplitude saturation and change rate limitation, outputting a system to input a signal driving system. According to the control method provided by the invention, the tracking precision of the ball screw system and the resistance to uncertain factors and external disturbance are effectively improved.

Description

Technical Field

[0001] This invention relates to the field of intelligent compensation control technology, and in particular to a method based on A control method for an adaptive control linear time-invariant ball screw drive system. Background Technology

[0002] Ball screw drive systems are widely used in CNC machine tools, automated production lines, and precision positioning equipment. These systems are characterized by limited mechanical transmission stiffness, significant friction and hysteresis nonlinearity, and sensitivity to external disturbances. This makes it difficult for traditional linear controller-based design methods to simultaneously achieve optimal dynamic performance, steady-state accuracy, and robust stability.

[0003] In the prior art, commonly used control schemes include: Control and Status Feedback Adaptive control systems each have their limitations. Among them, Control systems, designed with weighted functions and robust performance indices, can effectively suppress model uncertainties and external disturbances; however, their fixed structure and insufficient real-time adaptability to parameter changes are problematic. In contrast, state feedback... Adaptive control, through its fast estimation and filtering decoupling mechanism, offers significant advantages in handling mismatched disturbances and unknown dynamics. However, when used alone... During control, the system is prone to high-frequency jitter or steady-state deviation due to the lack of baseline dynamic constraints.

[0004] Therefore, it is necessary to propose a method that can accurately and stably control the ball screw drive system. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention proposes a method based on... An adaptive control method for linear time-invariant ball screw drive systems is proposed to achieve high-precision tracking and robust control of the ball screw drive system.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] This invention proposes a method based on An adaptive control method for a linear time-invariant ball screw drive system includes the following steps:

[0008] S1. Establish a linear time-invariant state-space model of the ball screw drive system, which is expressed in the following form:

[0009]

[0010] In the formula, Let be the system state vector. To control the input, For system output signals, For the system matrix, For the input matrix, This is the output matrix;

[0011] S2. Calculate the reference input signal With system output signal Tracking error between Based on the linear time-invariant state-space model established based on S1 and the preset... Robust performance metrics, obtaining state feedback gain And form a closed-loop matrix. , Based on the state feedback gain and tracking error Obtain baseline control signal ;

[0012] S3, the closed-loop matrix obtained through S2 Input matrix and output matrix Calculate steady-state gain , ; through the steady-state gain For the reference input signal The signal is processed to obtain the signal before filtering. ; through the first low-pass filter For the signal before filtering The signal is processed to obtain the steady-state feedforward control signal. ;

[0013] S4, Based on the closed-loop matrix The total uncertainty of the online estimation system and the total uncertainty Decomposed into matched signals With mismatch signal Mismatched signals are mapped using gain mapping. Convert to mapping mismatch signal Through the second low-pass filter For the matched signal Mismatch signal with mapping Band-limiting processing is performed separately to obtain the corresponding matching compensation signal. With mismatch compensation signal and the matching compensation signal With mismatch compensation signal Synthesize to obtain an adaptive compensation signal .

[0014] S5, Calculate the total control signal :

[0015]

[0016] For the total control signal The amplitude saturation limit and rate of change limit are applied sequentially to generate the system input signal. .

[0017] Furthermore, S2 specifically includes:

[0018] S201, Calculate the reference input signal With system output signal Tracking error between ;

[0019] S202, Based on System Matrix Input matrix Output matrix and Robust performance metrics are assessed by constructing a linear matrix inequality, solving the inequality, and obtaining the state feedback gain. And form a closed-loop matrix. ;

[0020] S203, Based on the state feedback gain Build The baseline controller will transfer the tracking error. enter The baseline controller receives the baseline control signal. .

[0021] Furthermore, S4 specifically includes:

[0022] S401, Closed-loop matrix obtained based on S2 Establish a state predictor:

[0023]

[0024] In the formula, To predict the state vector, For the input control signal, For the total uncertainty of the system, For feedback gain, >0;

[0025] S402, in each sampling period Within, based on prediction error Update total uncertainty , ;

[0026] S403, Input system matrix Orthogonal decomposition by channel:

[0027]

[0028] In the formula, To match the input channel matrix, For mismatched input channel matrix, =0;

[0029] Will The corresponding decomposition into matched signals With mismatch signal ;

[0030] S404, via gain mapping Mismatch signal Convert to mapping mismatch signal :

[0031]

[0032] Through the second low-pass filter For the matched signal Mismatch signal with mapping Band-limiting processing is performed separately to obtain the corresponding matching compensation signal. With mismatch compensation signal ;

[0033] S405, Calculate the adaptive compensation signal :

[0034] .

[0035] Furthermore, in S402, the total uncertainty... The update formula is:

[0036]

[0037] In the formula, It is a positive definite adaptive matrix.

[0038] Furthermore, the first low-pass filter The transfer function is in the form of:

[0039]

[0040] Second low-pass filter The transfer function is in the form of:

[0041]

[0042] In the formula, This is the cutoff frequency of the first low-pass filter. This is the cutoff frequency of the second low-pass filter.

[0043] Furthermore, in S2, the stated The robustness performance metric is the disturbance suppression level.

[0044] Furthermore, in S5, the total control signal is controlled by a saturation function. Amplitude saturation limiting processing is performed; during the rate of change limiting processing, the absolute value of the slope of the constraint signal is less than or equal to a preset threshold.

[0045] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0046] (1) This invention solves the linear matrix inequality to obtain the closed-loop matrix, and uses the closed-loop matrix as... The reference model and calculation basis of the adaptive control mechanism ensure the consistency between adaptive compensation and system baseline dynamics. Furthermore, this invention eliminates theoretical steady-state deviations by calculating the steady-state gain using a closed-loop matrix. Therefore, this control method, centered on a closed-loop matrix, enables the system to maintain... It exhibits strong robustness while also possessing high steady-state accuracy and rapid adaptive compensation capabilities.

[0047] (2) The present invention estimates the total uncertainty of the system online and decomposes the total uncertainty into matched signals and unmatched signals based on the input matrix of channel orthogonal decomposition. For the unmatched signals, the mapped unmatched signals are calculated by gain mapping, which can significantly enhance the system's ability to resist complex and variable disturbances. The present invention also performs band-limiting processing on the matched signals and mapped unmatched signals by using a low-pass filter, which suppresses the influence of high-frequency disturbances.

[0048] (3) The present invention The baseline controller obtains parameters by solving linear matrix inequalities based on a clearly defined disturbance suppression level index; the steady-state gain and gain mapping are directly calculated from the closed-loop matrix and the system matrix; the filter cutoff frequency can be directly selected based on physical characteristics such as system bandwidth. Therefore, the control method proposed in this invention can significantly reduce debugging complexity and has high repeatability and reliability in high-precision servo systems. Attached Figure Description

[0049] Figure 1 This is a structural block diagram of the control method proposed in an embodiment of the present invention;

[0050] Figure 2 This is a comparison chart of the tracking curves of the system output displacement when using different control methods on a ball screw experimental platform.

[0051] Figure 3 Only used in the experiment A graph showing the system output error when the controller is activated;

[0052] Figure 4 This is a graph showing the system output error when the control method proposed in the embodiments of this invention is used in the experiment. Detailed Implementation

[0053] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0054] Example

[0055] refer to Figure 1 This embodiment proposes a method based on An adaptive control method for a linear time-invariant ball screw drive system is presented. This method is applicable to scenarios such as CNC machine tool feed systems and precision positioning platforms. The specific implementation steps of the method are as follows:

[0056] S1. Establish a linear time-invariant state-space model of the ball screw drive system. This model is determined based on physical parameters such as the motor rotor inertia, the equivalent inertia of the screw and the worktable, and the torsional stiffness and damping of the transmission system. Its expression is as follows:

[0057]

[0058] In the formula, System state vector;

[0059] The control input is typically a torque or current command from the motor.

[0060] This is the system output signal, typically displacement or velocity;

[0061] For the system matrix, For the input matrix, This is the output matrix.

[0062] The model constructed in this step represents the nominal operating state of the system under ideal conditions, providing a foundation for subsequent controller design and predictive model construction.

[0063] S2. Calculate the reference input signal With system output signal Tracking error between Based on the linear time-invariant state-space model established based on S1 and the preset... Robust performance metrics, obtaining state feedback gain And form a closed-loop matrix. , Based on the state feedback gain and tracking error Obtain baseline control signal This step specifically includes the following sub-steps:

[0064] S201, Calculate the reference input signal With system output signal Tracking error between ;

[0065]

[0066] S202, Based on System Matrix Input matrix Output matrix and Robust performance metrics are established by constructing corresponding linear matrix inequalities, where... The robustness performance index is the disturbance suppression level. The state feedback gain is obtained by solving the linear matrix inequality using a solver. And form a closed-loop matrix. :

[0067]

[0068] S203, Based on the state feedback gain Build Baseline controller, built The state-space form of the baseline controller is:

[0069]

[0070] In the formula, For the internal state vector of the baseline controller, for Time derivative, For the baseline controller state matrix, Input matrix for baseline controller Baseline controller output matrix, This is the feedforward matrix for the baseline controller;

[0071] in , , , The following can be obtained directly by solving the linear matrix inequality in S202:

[0072]

[0073] In the formula, Let Laplace be a complex variable. To and Identity matrices of the same dimension.

[0074] The tracking error enter The baseline controller receives the baseline control signal. .

[0075] This step builds The baseline controller ensures that the closed-loop matrix meets stability requirements and preset parameters. Robust performance metrics provide the system with fundamental disturbance rejection capabilities.

[0076] S3. To further reduce the system steady-state error, the closed-loop matrix obtained from S2... Input matrix and output matrix Calculate steady-state gain :

[0077]

[0078] Through the steady-state gain For the reference input signal The signal is processed to obtain the signal before filtering. :

[0079]

[0080] To avoid high-frequency excitation caused by a step reference, a first-order low-pass filter is used. For the signal before filtering The signal is processed to obtain the steady-state feedforward control signal. :

[0081]

[0082]

[0083] In the formula, This is the cutoff frequency of the first low-pass filter.

[0084] S4, Based on the closed-loop matrix The total uncertainty of the online estimation system and the total uncertainty Decomposed into matched signals With mismatch signal Mismatched signals through gain mapping Convert to mapping mismatch signal Through the second low-pass filter For the matched signal Mismatch signal with mapping Band-limiting processing is performed separately to obtain the corresponding matching compensation signal. With mismatch compensation signal Finally, the matching compensation signal With mismatch compensation signal Synthesize to obtain an adaptive compensation signal This step specifically includes the following sub-steps:

[0085] S401, Closed-loop matrix obtained based on S2 Establish a state predictor:

[0086]

[0087] In the formula, To predict the state vector, For the input control signal, For the total uncertainty of the system, This is the feedback gain, used to accelerate convergence. >0;

[0088] S402, in each sampling period Within, based on prediction error The total uncertainty is updated using a piecewise constant adaptive law. :

[0089]

[0090]

[0091] In the formula, It is a positive definite adaptive matrix;

[0092] S403, Input system matrix Orthogonal decomposition by channel:

[0093]

[0094] In the formula, To match the input channel matrix, For a mismatched input channel matrix, satisfying =0;

[0095] Accordingly, The corresponding decomposition into matched signals With mismatch signal ,Right now lie in Zhang Cheng's space, lie in Zhang Cheng's space;

[0096] S404, via gain mapping Mismatch signal Convert to mapping mismatch signal :

[0097]

[0098] Through a first-order second low-pass filter For the matched signal Mismatch signal with mapping Band-limiting processing is performed separately to obtain the corresponding matching compensation signal. With mismatch compensation signal :

[0099]

[0100]

[0101]

[0102] In the formula, This is the cutoff frequency of the second low-pass filter.

[0103] S405, the matching compensation signal With mismatch compensation signal Synthesize to obtain an adaptive compensation signal :

[0104] .

[0105] S5. Combine the above three control signals and calculate the total control signal. :

[0106]

[0107] To prevent actuator saturation and sudden changes in control signals, the total control signal is... Post-processing:

[0108] Through saturation function For the total control signal Amplitude saturation limiting is performed to generate a saturated-limited signal. :

[0109]

[0110] Subsequently, the signal after saturation limitation was analyzed. The rate of change is limited to constrain the rate of change of the signal after saturation, ensuring that the absolute value of its slope is less than or equal to a preset threshold. To obtain safe and feasible system input signals .

[0111] System input signal The signal is sent to a power amplifier to drive the motor, thereby achieving high-precision position or speed tracking control of the ball screw system.

[0112] To verify the effectiveness of the present invention, the present invention will combine the control method proposed in the above embodiments with individual... The controller's performance was verified on a ball screw drive experimental platform. The platform consisted of a servo motor, a ball screw pair, a displacement sensor, a controller, and a host computer. The reference input was a smoothly changing displacement trajectory. A real-time control system was used for signal acquisition and execution. External disturbances were applied during the test. Verification results are referenced below. Figures 2 to 4 .

[0113] from Figure 2 As can be seen, using the control method proposed in the above embodiments, the output trajectory can closely track the reference input, with a steady-state error of less than 0.005 mm, while the individual... The controller exhibits significant hysteresis and steady-state deviation.

[0114] contrast Figure 3 and Figure 4 It can be seen that only by using When the controller is used, the system output error is large and high-frequency oscillation occurs when disturbed; by using the control method proposed in the above embodiments, the error fluctuation is significantly reduced, the response is smooth and there is no steady-state deviation.

[0115] In summary, the present invention will Robust stability of control, accurate tracking capability of steady-state feedforward and The adaptive and rapid disturbance compensation capabilities are organically combined to achieve high-precision tracking and robust control of the ball screw drive system.

[0116] The specific embodiments of the present invention are provided to enable those skilled in the art to understand or implement the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention.

[0117] It should be understood that the present invention is not limited to the content already described above, and various modifications and changes can be made without departing from its scope. The scope of the present invention is limited only by the appended claims.

Claims

1. A method based on An adaptive control method for a linear time-invariant ball screw drive system, characterized in that, Includes the following steps: S1. Establish a linear time-invariant state-space model of the ball screw drive system, which is expressed in the following form: In the formula, Let be the system state vector. To control the input, For system output signals, For the system matrix, For the input matrix, This is the output matrix; S2. Calculate the reference input signal With system output signal Tracking error between Based on the linear time-invariant state-space model established based on S1 and the preset... Robust performance metrics, obtaining state feedback gain And form a closed-loop matrix. , ; Based on the state feedback gain and tracking error Obtain baseline control signal ; S3, the closed-loop matrix obtained through S2 Input matrix and output matrix Calculate steady-state gain , ; through the steady-state gain For the reference input signal The signal is processed to obtain the signal before filtering. ; through the first low-pass filter For the signal before filtering The signal is processed to obtain the steady-state feedforward control signal. ; S4, Based on the closed-loop matrix The total uncertainty of the online estimation system and the total uncertainty Decomposed into matched signals With mismatch signal ; Mismatched signals are mapped using gain mapping. Convert to mapping mismatch signal Through the second low-pass filter For the matched signal Mismatch signal with mapping Band-limiting processing is performed separately to obtain the corresponding matching compensation signal. With mismatch compensation signal and the matching compensation signal With mismatch compensation signal Synthesize to obtain an adaptive compensation signal . S5, Calculate the total control signal : For the total control signal The amplitude saturation limit and rate of change limit are applied sequentially to generate the system input signal. .

2. Based on claim 1 An adaptive control method for a linear time-invariant ball screw drive system, characterized in that, S2 specifically includes: S201, Calculate the reference input signal With system output signal Tracking error between ; S202, Based on System Matrix Input matrix Output matrix and Robust performance metrics are assessed by constructing a linear matrix inequality, solving the inequality, and obtaining the state feedback gain. And form a closed-loop matrix. ; S203, Based on the state feedback gain Build The baseline controller will transfer the tracking error. enter The baseline controller receives the baseline control signal. .

3. Based on claim 1 An adaptive control method for a linear time-invariant ball screw drive system, characterized in that, S4 specifically includes: S401, Closed-loop matrix obtained based on S2 Establish a state predictor: In the formula, To predict the state vector, For the input control signal, For the total uncertainty of the system, For feedback gain, >0; S402, in each sampling period Within, based on prediction error Update total uncertainty , ; S403, Input system matrix Orthogonal decomposition by channel: In the formula, To match the input channel matrix, For mismatched input channel matrix, =0; Will The corresponding decomposition into matched signals With mismatch signal ; S404, via gain mapping Mismatch signal Convert to mapping mismatch signal : Through the second low-pass filter For the matched signal Mismatch signal with mapping Band-limiting processing is performed separately to obtain the corresponding matching compensation signal. With mismatch compensation signal ; S405, Calculate the adaptive compensation signal : 。 4. Based on claim 3 An adaptive control method for a linear time-invariant ball screw drive system, characterized in that, In S402, the total uncertainty The update formula is: In the formula, It is a positive definite adaptive matrix.

5. Based on claim 1 An adaptive control method for a linear time-invariant ball screw drive system, characterized in that, First low-pass filter The transfer function is in the form of: Second low-pass filter The transfer function is in the form of: In the formula, This is the cutoff frequency of the first low-pass filter. This is the cutoff frequency of the second low-pass filter.

6. Based on claim 1 An adaptive control method for a linear time-invariant ball screw drive system, characterized in that, In S2, the The robustness performance metric is the disturbance suppression level.

7. Based on claim 1 An adaptive control method for a linear time-invariant ball screw drive system, characterized in that, In S5, the total control signal is controlled by a saturation function. Amplitude saturation limiting processing is performed; during the rate of change limiting processing, the absolute value of the slope of the constraint signal is less than or equal to a preset threshold.

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