An intelligent control method for high-precision rotary table based on improved ESO

Abstract

This invention specifically relates to a high-precision intelligent control method for a turntable based on an improved ESO (Electronic State Observation) system, belonging to the field of turntable control technology. The method includes: observing the residual disturbance obtained from the black-box decomposition in step one to obtain residual disturbance observation values, and using these residual disturbance observation values ​​as compensation quantities for a reduced-order extended state observer. In this invention, the total disturbance of the turntable system is divided into known disturbances that can be accurately modeled using physical laws and geometric constraints, and residual disturbances that are difficult to model accurately, thus optimizing the processing logic of unified observation of the total disturbance in traditional schemes. The dominant large-amplitude, low-frequency deterministic disturbance is directly compensated through a physical feedforward channel bound to the turntable load characteristics and installation constraint depth, reducing the observation burden of the extended state observer and avoiding the observation saturation risk caused by large-amplitude disturbances.

Description

Technical Field

[0001] This invention relates to the field of turntable control technology, and in particular to a high-precision intelligent control method for turntables based on an improved ESO. Background Technology

[0002] Servo turntables are core actuators in fields such as laser ranging, photoelectric tracking, aerospace precision measurement and control, and high-end intelligent manufacturing. Their angle tracking accuracy, dynamic response speed, and full-band disturbance suppression capability directly determine the working performance and upper limit of the entire application system.

[0003] Active disturbance rejection control (ADRC) technology, with its core advantages of not relying on an accurate mathematical model of the controlled object and strong robustness, has been widely applied in the field of servo turntable control and has undergone in-depth technological iteration. Among them, the extended state observer (ESO) is the core unit of ADRC technology, which undertakes the real-time observation and compensation function of the system's lumped disturbance. Existing technologies have carried out a lot of research around the structural optimization, adaptive parameter tuning, and anti-saturation design of ESO, forming a mature technical system that effectively improves the control stability and disturbance rejection capability of servo turntable systems.

[0004] With the widespread application of high-precision optical payloads, servo turntables have placed higher demands on control accuracy. The system simultaneously contains multi-scale, wide-band disturbance components, such as large-amplitude low-frequency deterministic disturbances, coupled disturbances caused by optical payload installation geometric deviations, high-frequency structural resonances, and random disturbances. This places more stringent combined demands on the response speed of disturbance observation, the accuracy of compensation phase, and the efficiency of embedded algorithm implementation.

[0005] To further adapt to the high-performance control requirements of high-precision turntables under all working conditions, a high-precision turntable intelligent control method based on improved ESO is proposed to address the aforementioned problems. Summary of the Invention

[0006] The purpose of this invention is to propose a high-precision intelligent control method for a turntable based on an improved ESO in order to solve the above-mentioned problems.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] A high-precision intelligent control method for a turntable based on an improved ESO includes:

[0009] Step 1: Construct the basic rotational dynamics equations of the turntable, perform decoupling and reconstruction on the total disturbance, and decompose the total disturbance into white-box known disturbance and black-box residual disturbance;

[0010] Step 2: Construct a physical model feedforward channel for the known disturbances of the white box obtained in Step 1. Based on the installation geometric constraints of the laser rangefinder sensor and the real-time pitch angle of the turntable, use the modified laser rangefinder observation equation to calculate the actual observation distance of the target and map the pointing deviation corresponding to the actual observation distance of the target into a known compensation torque.

[0011] Step 3: After completing the feedforward compensation of the known disturbance of the white box based on the known compensation torque output in Step 2, design a reduced-order extended state observer for the residual disturbance state space of the turntable, observe the residual disturbance of the black box obtained in Step 1 to obtain the residual disturbance observation value, and use the residual disturbance observation value as the compensation amount of the reduced-order extended state observer.

[0012] Step 4: Obtain the feedback control quantity of the turntable. Add the feedback control quantity, the feedforward compensation quantity obtained in Step 2, and the residual disturbance observation value obtained in Step 3 to obtain the final motor control input torque of the turntable.

[0013] Preferably, in step one, constructing the basic rotational dynamics equations of the turntable includes:

[0014] The origin O of the global coordinate system OXYZ is the geometric center of the turntable's pitch rotation axis. The OZ axis is perpendicular to the horizontal plane and points upwards, the OX axis points horizontally towards the turntable's initial zero position, and the OY axis coincides with the turntable's pitch rotation axis. The angle of rotation of the turntable around the OY axis is defined as the pitch angle. ;

[0015] Based on this, the fundamental rotational dynamics equations of the turntable are established: ;

[0016] in,

[0017] It is the equivalent moment of inertia; To control the input torque; It is a nonlinear frictional torque; This is the eccentric gravitational moment of the load; This is an external disturbance.

[0018] Preferably, the decoupling rules and boundary definitions for the total disturbance are as follows:

[0019] Decompose the total disturbance into white-box known disturbances. Residual disturbances from the black box Two parts, namely: ;

[0020] Only disturbance terms that simultaneously meet the following three conditions can be included. Category:

[0021] First, the mechanism of the disturbance is consistent with physical laws or geometric constraints, and there is no fundamental error.

[0022] Second, all input quantities required to calculate disturbances can be acquired in real time by the sensors configured in the system, or obtained through pre-calibration before leaving the factory;

[0023] Third, the calculation process of the disturbance is a pure algebraic operation;

[0024] Based on the above rules The specific composition is the gravitational torque component. Viscous friction component Torque components corresponding to optical geometric deterministic deviations;

[0025] Perturbation terms that fail to meet the above three conditions are classified as... The scope of.

[0026] Preferably, in step two, the derivation process of the laser ranging observation equation is as follows:

[0027] Let the light output port of the laser sensor be point A. The center of rotation of the turntable is point 1. Vertical installation height difference For point The vertical distance to the pitch axis of the turntable, and The line connecting the laser beams always remains perpendicular to the laser beam direction.

[0028] When the turntable is at the zero position, the laser output port The coordinates are At this time, the sensor measures the original distance. Light output port to ground target point Distance, center of rotation To the target point The actual distance is .

[0029] Preferably, when the turntable rotates about the OY axis After the angle, the angle between the laser emission direction and the OZ axis is... At this time, the laser beam forms an angle with the vertical direction. Ground target point Located on a horizontal plane, the length of the laser beam The corresponding vertical component is , light outlet The vertical coordinate is Therefore, the center of rotation To the target point The actual vertical distance is .

[0030] Preferably, the target observation distance Center of rotation To the target point The straight-line distance, combined with geometric relationships, allows us to derive the corrected laser ranging observation equation: ;

[0031] in, These are the raw measurement values ​​from the laser rangefinder sensor; The vertical mounting height difference between the laser sensor's output axis and the turntable's rotation axis; This is the real-time pitch angle of the turntable.

[0032] Preferably, after obtaining the actual observation distance of the target through the modified equation, it needs to be converted into the feedforward compensation torque of the servo motor. The conversion process logic is as follows:

[0033] Based on the corrected observation distance Using the pre-known global coordinates of the target point, the required pitch angle correction can be calculated. ,in The global X-axis coordinates of the target point. The global X-axis coordinate of the turntable's rotation center. The desired pointing angle of the turntable;

[0034] Angle deviation The derivative with respect to time can be obtained through analytical differentiation: ,in for right Analytical derivative; angular acceleration It can also be obtained through analytical differentiation;

[0035] Based on the dynamic equations of the turntable, angular deviation The corresponding feedforward compensation torque consists of three parts:

[0036] First, it counteracts the component of the change in gravitational torque;

[0037] Second, to counteract the component of viscous friction changes;

[0038] Third, the torque component required to drive the turntable to track the angular deviation;

[0039] Adding the three parts together gives the final feedforward compensation amount.

[0040] Preferably, the definition of the residual disturbance state space in step three is as follows:

[0041] The final control input torque Decomposed into feedforward compensation amount With feedback control quantity Substituting into the original dynamic equation, we get: ;

[0042] because The design goal is complete compensation Ideally Therefore, the equation can be simplified to: .

[0043] Preferably, the step of using the residual perturbation observation as a compensation amount for the reduced-order extended state observer specifically includes:

[0044] Assuming residual disturbance rate of change It is bounded, meaning there exists a constant. Make For all moments Established;

[0045] Let the system output be the measured angular velocity value. Then, taking the derivative with respect to y, we get ,Will As the only observed extended state, the following observation law is constructed:

[0046] ;

[0047] ;

[0048] in For the internal state variables of RESO, For the observer gain of RESO, These are the observations of residual perturbations.

[0049] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0050] 1. This invention optimizes the processing logic of unified observation of total disturbance in traditional schemes by dividing the total disturbance of the turntable system into known disturbances that can be accurately modeled by physical laws and geometric constraints, and residual disturbances that are difficult to model accurately. It also directly compensates for the dominant large-amplitude low-frequency deterministic disturbances through a physical feedforward channel that is bound to the turntable load characteristics and installation constraint depth, thereby reducing the observation burden of the extended state observer and avoiding the observation saturation risk caused by large-amplitude disturbances.

[0051] 2. This invention achieves zero-phase accurate compensation for deterministic disturbances by using feedforward compensation based on the sensor measurement value and analytical calculation at the current moment. It eliminates the need for integral and numerical differentiation, which can easily introduce lag. This significantly improves the system's ability to suppress low-frequency disturbances and its angle tracking accuracy, while retaining the inherent strong robustness of active disturbance rejection control. Attached Figure Description

[0052] Further details, features, and advantages of this application are disclosed in the following description of exemplary embodiments in conjunction with the accompanying drawings, in which:

[0053] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

[0054] Several embodiments of this application will now be described in more detail with reference to the accompanying drawings to enable those skilled in the art to implement this application. This application may be embodied in many different forms and for various purposes and should not be limited to the embodiments set forth herein. These embodiments are provided to make this application thorough and complete, and to fully convey the scope of this application to those skilled in the art. The embodiments described do not limit this application.

[0055] Unless otherwise defined, all terms used herein (including technical and scientific terms) shall have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains. It will be further understood that terms such as those defined in commonly used dictionaries shall be interpreted as having a meaning consistent with their meaning in the relevant field and / or the context of this specification, and shall not be interpreted in an idealized or overly formal sense unless expressly defined herein.

[0056] Example 1

[0057] Its specific implementation method is combined with the appendix Figure 1 Please provide a detailed explanation.

[0058] Appendix Figure 1 The flowchart of a high-precision turntable intelligent control method based on improved ESO provided in this embodiment of the invention shows the complete steps from constructing the basic rotational dynamics equations of the turntable to obtaining the final motor control input torque of the turntable.

[0059] In this embodiment, it includes:

[0060] Step 1: Construct the basic rotational dynamics equations of the high-precision turntable, and perform decoupling and reconstruction on the lumped total disturbance under the traditional active disturbance rejection control framework. The total disturbance is decomposed into white-box known disturbance and black-box residual disturbance. The white-box known disturbance is a low-frequency, large-amplitude deterministic torque that can be calculated in real time through physical laws or sensor geometric relationships. The black-box residual disturbance is a high-frequency, low-amplitude random disturbance that cannot be obtained through physical modeling.

[0061] This step packages all non-control inputs into the standard processing logic for the total disturbance:

[0062] At the level of control principle: the disturbance observation task originally undertaken by ESO is broken down into two parts: physical feedforward direct compensation and ESO observation residual disturbance. This reduces the observation burden of ESO from the root and avoids the inherent defects of traditional ESO such as observation lag and easy saturation of the observer when facing large amplitude low frequency disturbance.

[0063] Establishment and parameter calibration of the basic dynamic equations:

[0064] This embodiment is based on a single-axis pitch turntable equipped with a laser rangefinder. Each rotational degree of freedom of a multi-axis turntable can be independently derived using this logic without adjusting the core rules.

[0065] First, clearly define the system coordinate system and basic parameters: the origin O of the global coordinate system OXYZ is the geometric center of the turntable's pitch rotation axis. The OZ axis is perpendicular to the horizontal plane and points upwards. The OX axis points horizontally towards the initial zero position of the turntable. The OY axis coincides with the turntable's pitch rotation axis. The angle of rotation of the turntable around the OY axis is defined as the pitch angle. That is, the angle between the normal to the load plane of the turntable and the OZ axis when rotating counterclockwise. It is positive, and its value ranges from -90° to +90°.

[0066] Based on this, the fundamental rotational dynamics equations of the turntable are established. These equations strictly follow Newton's laws of motion for rigid body rotation and have no fundamental errors. ;

[0067] in,

[0068] Equivalent moment of inertia: refers to the total equivalent moment of inertia attributed to the motor output shaft. The specific measurement method is as follows: After installing the turntable load (including all mounted equipment such as the laser rangefinder and optical lens), disconnect the motor's power connection cable and apply a step torque of known magnitude to the motor output shaft using a calibrated torque wrench. The angular acceleration response under the step torque is collected by a high-resolution photoelectric encoder mounted on the turntable. Through formula Complete a single measurement; repeat the measurement 10 or more times and take the average value as the result. The final value of .

[0069] If the turntable is equipped with a harmonic reducer, planetary reducer, or other transmission mechanism, the moment of inertia on the load side needs to be reduced according to the square of the reduction ratio, i.e. ,in This is the motor's nominal moment of inertia. The measured moment of inertia on the load side. This represents the reduction ratio of the speed reducer.

[0070] To control the input torque: This refers to the actual torque output by the servo motor and attributed to the rotating shaft. It is output in real time by the servo driver based on the received torque command. Its upper limit is the rated torque of the motor, which can be directly read through the parameter configuration of the servo driver.

[0071] Nonlinear frictional torque refers to all frictional resistance torques generated between the turntable transmission mechanism and the rotating pair, including static friction torque, Coulomb friction torque, viscous friction torque, and the Stribeck nonlinear effect in the low-speed range; among them, the viscous friction torque is proportional to the rotational angular velocity of the turntable, and the rest are nonlinear terms that are difficult to model accurately.

[0072] Eccentric gravitational moment: refers to the gravitational moment caused by the misalignment of the load's center of mass with the turntable's rotation axis; its magnitude varies with the pitch angle. The real-time changes are typical of large-amplitude, low-frequency deterministic disturbances.

[0073] External disturbances refer to all external torques experienced by the turntable during operation, including wind load, high-frequency vibrations transmitted from the base, cable tension torque, etc. Among them, low-frequency components such as steady-state wind load can be calculated through physical modeling, while dynamic components such as gusts and high-frequency vibrations are random disturbances.

[0074] Decoupling rules and boundary definitions for lumped disturbances:

[0075] In the traditional ADRC framework, all non-control inputs are... The items are packaged together as a total disturbance. ,Right now All disturbance observation and compensation are handled by the ESO. While this approach simplifies controller design, it also requires the ESO to handle all disturbances with extremely large amplitude differences and a very wide frequency coverage, resulting in an inherent performance bottleneck.

[0076] This scheme explicitly proposes quantifiable perturbation decoupling rules, decomposing the total perturbation into white-box known perturbations. Residual disturbances from the black box Two parts, namely: ;

[0077] Only disturbance terms that simultaneously meet the following three conditions can be included. Category:

[0078] First, the generation mechanism of the disturbance fully conforms to the widely verified physical laws or geometric constraints, and there is no fundamental error.

[0079] Second, all the input quantities required to calculate the disturbance can be acquired in real time by the sensors already configured in the system, or obtained through pre-calibration before leaving the factory, without the need for additional hardware costs;

[0080] Third, the calculation process of the disturbance is a pure algebraic operation, without integration, numerical differentiation or other steps that may introduce phase lag or noise amplification.

[0081] Based on the above rules, in this embodiment The specific components are as follows:

[0082] Accurately modelable gravitational torque components The eccentricity of the load's center of mass relative to the turntable's rotation axis. Eccentricity can be obtained through pre-calibration. The calibration method is as follows: adjust the turntable to different pitch angles. Disconnect the control input to allow the turntable to rotate freely, record the angle and torque balance relationship when the turntable is stationary, and then fit the data. get The possible values ​​of , where For the total load mass, This represents the local gravitational acceleration. Since this calculation only requires real-time data acquisition... The value is constant and conforms to the physical law of the torque of a rigid body, therefore it belongs to... It is a core component.

[0083] Accurately modelable viscous friction components : Coefficient of viscous friction Calibration can be achieved through open-loop experiments, i.e., controlling the turntable to rotate at different constant angular velocities, recording the corresponding control input torque, and obtaining the result through linear fitting. ,in The real-time rotational angular velocity of the turntable can be calculated from the measurement value of the photoelectric encoder, therefore it also belongs to... Components of.

[0084] Torque components corresponding to optical geometric deterministic deviations This refers to the compensating torque corresponding to the pointing deviation caused by the installation geometric error of the laser rangefinder sensor. The specific calculation logic is explained in detail in step two. Its calculation is based on strict spatial geometric relationships and conforms to... The inclusion criteria.

[0085] All remaining disturbance terms that fail to meet the above three conditions are classified as... The scope specifically includes: static friction, Coulomb friction and Stribeck effect components in nonlinear frictional torque, and calibration error components of gravitational torque (such as small offsets of the load center of mass and eccentricity). The measurement errors, dynamic components in external disturbances (such as gusts, high-frequency vibrations above 10Hz transmitted from the base), and unmodeled dynamics of the system (such as hysteresis errors of harmonic reducers, transmission backlash, torque fluctuations of motors, quantization noise, etc.) are all factors to consider. These disturbances share common characteristics: small amplitude (usually not exceeding 10% of the total peak-to-peak value of the disturbance) and high frequency (mainly concentrated above 10Hz). They cannot be accurately calculated using physical or geometric equations and are suitable for observational compensation by ESO.

[0086] Decoupling rational verification rules:

[0087] To ensure the scientific rigor of the perturbation decomposition and avoid insufficient decoupling leading to an excessive burden on subsequent ESOs, this step explicitly specifies the verification method for the rationality of decoupling:

[0088] Under no-load and no external disturbances, the control turntable rotates at a constant angular velocity of 0.5 rad / s, and the control input torque at this time is collected. Simultaneously calculate Theoretical value Calculate the residual The peak-to-peak value of the residual is determined; if the residual peak-to-peak value does not exceed 10% of the total disturbance peak-to-peak value, the decoupling boundary is reasonable; if it exceeds 10%, the relevant parameters of gravitational torque and viscous friction need to be recalibrated, and any missing modelable deterministic disturbances need to be checked until the residual meets the requirements.

[0089] Step 2: Construct a physical model feedforward channel for the known perturbations of the white box obtained in Step 1. Based on the installation geometric constraints of the laser rangefinder sensor and the real-time pitch angle of the turntable, calculate the actual observation distance of the target using the modified laser rangefinder observation equation. Map the pointing deviation corresponding to the actual observation distance of the target to a known compensation torque through the Jacobian matrix of the turntable's mechanical kinematics. The calculation logic of the modified laser rangefinder observation equation is as follows:

[0090] The actual observation distance of the target is equal to the sum of the original measurement value of the laser rangefinder and the difference in vertical installation height between the laser sensor's output axis and the turntable's rotation axis, divided by the cosine of the pitch angle; the compensation torque is known to be a pure algebraic calculation result without integral or differential components, and has zero phase lag characteristics;

[0091] This step is the key to achieving deep coupling between physical laws and control algorithms. Most existing ADRC improvement schemes only focus on parameter adjustment or structural optimization of the ESO itself, which are general algorithm improvements; while this step provides physical support for subsequent reduced-order ESO applications by deeply binding feedforward calculation rules with the specific application scenario of the turntable, sensor installation parameters, and spatial geometric relationships.

[0092] Derivation and parameter calibration of physical / geometric observation equations:

[0093] In this embodiment, the turntable is equipped with a laser rangefinder sensor for high-precision ranging and pointing of ground targets. The laser rangefinder sensor is fixedly installed on the load plane of the turntable, and its light emission direction coincides with the normal of the load plane.

[0094] During actual installation, due to limitations in machining accuracy and assembly process, the laser sensor's output axis cannot completely pass through the pitch rotation center of the turntable; that is, there is a vertical installation height difference between the output axis and the rotation center. This installation error will cause a deviation between the sensor's original ranging value and the actual distance from the turntable's rotation center to the target, and the deviation will increase with the pitch angle. The variation changes accordingly, which is a typical deterministic deviation that can be precisely calculated through geometric relationships, and therefore it is included. Feedforward compensation is performed within the scope of [the data / scope].

[0095] First, a rigorous derivation of this geometric deviation is performed:

[0096] Let the light output port of the laser sensor be point A. The center of rotation of the turntable is point 1. Vertical installation height difference For point The vertical distance to the pitch axis (OY axis) of the turntable, and The line connecting the laser beams always remains perpendicular to the laser beam direction.

[0097] When the turntable is at zero position ( When the laser output direction is 0 (and the light output direction is perpendicular to the OZ axis downwards), the laser output port... The coordinates are At this time, the sensor measures the original distance. Light output port to ground target point Distance, center of rotation To the target point The actual distance is No angular deviation;

[0098] When the turntable rotates around the OY axis After the angle, the angle between the laser emission direction and the OZ axis is... At this time, the laser beam forms an angle with the vertical direction. Ground target point Located on a horizontal plane, the length of the laser beam The corresponding vertical component is , light outlet The vertical coordinate is Therefore, the center of rotation To the target point The actual vertical distance is ; Due to the target observation distance defined in this embodiment Center of rotation To the target point The straight-line distance, combined with geometric relationships, allows us to derive the corrected laser ranging observation equation: ;

[0099] in,

[0100] The original measurement value of the laser rangefinder sensor is output in real time by the sensor's digital interface. The sampling period is consistent with the sampling period of the control system. In this embodiment, it is 10kHz, and the measurement accuracy is ±1mm.

[0101] The calibration method for the vertical installation height difference between the laser sensor's output axis and the turntable's rotation axis is as follows: Adjust the turntable to... =0 at the zero position, multiple standard calibration targets at different distances are placed in the laser emission direction, and the actual distance from each calibration target to the rotation center O is... The original sensor measurements for each calibration target were obtained using a high-precision total station and recorded. ,because =0 Therefore, by fitting The average value is obtained from multiple measurements. The final value of .

[0102] The real-time pitch angle of the turntable is measured in real time by a 23-bit high-resolution photoelectric encoder mounted on the turntable, with the sampling period consistent with that of the control system.

[0103] The applicable boundaries of this equation are clear: when the pitch angle is... When the absolute value is greater than 85°, A value less than 0.087 will cause the measurement noise to be excessively amplified, therefore when | When the angle is greater than 85°, you can switch to a correction method based on small angle approximation, or turn off the geometric correction channel to avoid introducing excessive computational noise.

[0104] The derivation process of the revised laser ranging observation equation is as follows:

[0105] Rotation center The coordinates of the point are (0,0,0). First, substitute them into the equation. The complete expression for point coordinates:

[0106] ;

[0107] ;

[0108] ;

[0109] Rotation center arrive The straight-line distance is the modulus of the coordinate system: ;

[0110] Substitute, expand, and simplify (using) , );

[0111] ;

[0112] when When the exact equation is approximated by a Taylor expansion, it simplifies to: .

[0113] Mapping rules for feedforward compensation:

[0114] The actual observation distance of the target is obtained through the above modified equation. Then, it needs to be converted into the feedforward compensation torque of the servo motor. The transformation process is implemented based on the Jacobian matrix of the turntable's mechanical kinematics, and the specific logic is as follows:

[0115] First, calculate the angular deviation of the laser direction. The desired pointing angle of the turntable is: That is, the laser is expected to be directed at the target point. The theoretical pitch angle at that time, but due to the difference in installation height... The existence of the turntable when it is in At that time, the actual position of the laser beam relative to the target point There is a bias; based on the corrected observation distance Using the pre-known global coordinates of the target point, the required pitch angle correction can be calculated. ,in The global X-axis coordinates of the target point. The global X-axis coordinate is the center of rotation of the turntable.

[0116] Due to angle deviation It is based on algebraic calculations of real-time measurements, and its derivative with respect to time can be obtained analytically without numerical differentiation. ,in for right The analytical derivative can be obtained by directly differentiating the above deviation formula, and there is no phase lag; similarly, angular acceleration... It can also be obtained through analytical differentiation.

[0117] angular acceleration How to obtain: .

[0118] Based on the dynamic equations of the turntable, angular deviation The corresponding feedforward compensation torque consists of three parts:

[0119] First, the component that counteracts the change in gravitational torque. ;

[0120] Second, the component that counteracts changes in viscous friction. ;

[0121] Third, the torque component required to drive the turntable to track the angular deviation. .

[0122] Adding the three parts together gives the final feedforward compensation amount. The calculation process involves only algebraic operations and analytical differentiation, without integration or numerical differentiation, so there is no phase lag.

[0123] To avoid excessive feedforward causing motor overcurrent, it is necessary to... Set a limit, with the limit threshold being 80% of the motor's rated torque. If the calculated... If the value exceeds the threshold, the output will be based on the upper limit of the threshold to ensure system security.

[0124] The core advantage of this feedforward channel is "zero phase lag," which can be verified through comparative experiments: A 1Hz sinusoidal reference angle command with an amplitude of 5° is applied to the turntable input. The disturbance observation lag is measured using only traditional ESO compensation, and the compensation lag is measured using this feedforward channel. Traditional ESO requires the use of state values ​​from multiple historical moments for disturbance estimation, resulting in an observation lag of 30-50ms for low-frequency, large-amplitude disturbances such as gravitational torque. In contrast, this feedforward channel's calculation relies solely on the sensor measurement at the current moment, with a calculation delay equal to the system's sampling period (0.1ms in this embodiment), exhibiting almost no phase lag. This addresses the lag issue of traditional ESO when observing large-amplitude, low-frequency disturbances, reducing the system's angle tracking error.

[0125] Step 3: After completing the feedforward compensation for the known disturbance of the white box based on the known compensation torque output in Step 2, a reduced-order extended state observer is designed for the residual disturbance state space of the turntable. The high-precision angular position and angular velocity measurement signals already collected by the system are directly called. Only the residual disturbance of the black box obtained in Step 1 is observed to obtain the residual disturbance observation value. The residual disturbance observation value is used as the compensation amount of the reduced-order extended state observer. The order of the reduced-order extended state observer is lower than that of the traditional third-order full-order extended state observer that simultaneously observes position, velocity and total disturbance.

[0126] Definition of residual perturbation state space:

[0127] By introducing a physical feedforward channel, the turntable's dynamic equations can be reconstructed: the final control input torque can be... Decomposed into feedforward compensation amount With feedback control quantity Substituting into the original dynamic equation, we get: ;

[0128] because The design goal is complete compensation Ideally Therefore, the equation can be simplified to: ;

[0129] At this point, the system's state variables include: angular position. (Measured in real time by a photoelectric encoder, with an accuracy of ±0.5 arcseconds), angular velocity (Measured in real time by encoder differential or tachogenerator, accuracy ±0.001 rad / s), residual disturbance (To be observed). Traditional full-order ESOs require simultaneous observation. Three states, at least a third-order observer, while in this scheme... and All values ​​are known, high-precision measurements, requiring no observation; therefore, only the design of [specific measures / measures] is needed. The reduced-order observer reduces the order of the observer and the computational load.

[0130] Design and parameter tuning of the reduced-order observation law:

[0131] This embodiment employs a first-order RESO design, whose observation law is derived based on the boundedness assumption of the residual perturbation: assuming the residual perturbation... rate of change It is bounded, meaning there exists a constant W such that For all moments Established.

[0132] Let the system output be the measured angular velocity value. Then, taking the derivative with respect to y, we get ,Will As the only observed extended state, the following observation law is constructed: ;

[0133] ;

[0134] in For the internal state variables of RESO, For the observer gain of RESO, These are the observations of residual perturbations.

[0135] The observer is a first-order system and only requires adjustment of one gain parameter. The gain parameters required to be adjusted are much lower than those of a traditional third-order ESO, reducing the difficulty of engineering implementation.

[0136] Observer Gain The tuning method is fully reproducible, employing a combination of bandwidth method and experimental fine-tuning:

[0137] First, determine the highest observation frequency of the residual disturbance. In this embodiment, the highest frequency disturbance to be observed is the structural resonance of the turntable (approximately 150Hz), therefore the bandwidth of the RESO is... Must meet That is, at least 1884 rad / s, the initial value of the observer gain l is set to .

[0138] Experimental fine-tuning: Disconnect the feedforward channel, inject a sinusoidal disturbance with a frequency of 150Hz and an amplitude of 5% of the motor's rated torque into the system, and collect RESO observations. The phase difference and amplitude error between the actual injected disturbance value and the actual value gradually increase. The optimal gain is reached when the phase difference is less than 10° and the amplitude error is less than 5%.

[0139] Gain constraint: To avoid the observer amplifying measurement noise, The maximum value must not exceed 10000 rad / s. If adjusting to this value still cannot meet the observation accuracy requirements, the filtering parameters for angular velocity measurement need to be optimized first to reduce measurement noise before adjusting the gain.

[0140] Discretization and engineering implementation details of RESO:

[0141] Since RESO operates on digital controllers such as DSPs or FPGAs, the continuous observation law needs to be converted into a discrete form. This embodiment uses the Euler forward discretization method, and the discretized observation law is as follows (sampling period is...). , (At the current sampling time)

[0142] Calculate the approximate value of the derivative of the angular velocity at the current moment: ,in The measured angular velocity value at the current moment. This is the measured angular velocity value at the previous moment.

[0143] Update RESO's internal state: ,in This is the feedback control variable at the current moment.

[0144] Calculate the observations of the residual disturbance: .

[0145] RESO initialization rules are clearly defined: when the system powers on, its internal state... The initial value is set to 0, and the initial value of the residual disturbance observation is also set to 0 to avoid excessive surge output upon power-up. At the same time, to avoid observer saturation, it is necessary to... Set a limit, with the limit threshold being 20% ​​of the motor's rated torque. If the limit is exceeded, the output will be based on the upper limit.

[0146] Validation of the advantages of reduced-order ESO:

[0147] Compared with the traditional third-order ESO, the RESO solution of this scheme has two core advantages: First, the computational load is significantly reduced: the traditional third-order ESO requires 6 multiplication operations and 3 addition operations per sampling cycle, while the first-order RESO solution of this scheme only requires 3 multiplication operations and 2 addition operations. For a system with a 10kHz sampling cycle, the computation time in a single sampling cycle is reduced from 1.2μs to 0.4μs, which can save 67% of the computational resources, leaving enough computational space for other functions such as laser ranging signal processing and fault diagnosis, and is especially suitable for embedded controller applications with limited resources.

[0148] Second, the observation bandwidth is improved: Traditional full-order ESOs need to observe low-frequency disturbances with large amplitudes. To avoid observer saturation, the bandwidth can usually only be set below 50Hz, making it impossible to observe high-frequency disturbances. However, the residual disturbance amplitude observed by the RESO in this scheme is only less than 10% of the total disturbance, and there is no saturation problem caused by large amplitude disturbances. The bandwidth can be increased to more than 200Hz, which can effectively observe and compensate for disturbances such as high-frequency resonance and high-frequency vibration above 100Hz that traditional ESOs cannot handle, greatly improving the dynamic performance and control accuracy of the system.

[0149] Step 4: Obtain the feedback control quantity of the turntable. Add the feedback control quantity, the feedforward compensation quantity obtained in Step 2, and the residual disturbance observation value obtained in Step 3 directly to obtain the final motor control input torque of the turntable. Output the final motor control input torque directly to the current loop or torque loop of the servo driver. During the output process, it is prohibited to perform secondary output fusion or add additional low-pass filtering circuit to the final motor control input torque.

[0150] This step ensures that the system's control performance meets design requirements by establishing clear control law synthesis rules and engineering implementation constraints.

[0151] Composition rules of composite control laws and tuning rules for each component:

[0152] The final motor control input torque of the turntable It consists of three parts added together, the formula is: ;

[0153] in,

[0154] For feedback control: a conventional PD control law is used to ensure system stability and basic tracking performance. Its calculation formula is as follows: ,in For the desired pitch angle, For the desired angular velocity, For proportional gain, This is the differential gain.

[0155] Based on the turntable dynamic parameters calibrated in step one, the pole placement method is used to directly calculate... , No critical oscillation test is required, resulting in higher safety and suitability for high-precision turntables with small-range motion scenarios.

[0156] Based on the equivalent moment of inertia calibrated in step one viscous friction coefficient The open-loop transfer function of the turntable system is obtained as follows: ;

[0157] Set the system's expected closed-loop bandwidth (Recommended frequency: 50-100Hz, higher than the low-frequency disturbance frequency and lower than the RESO bandwidth), damping ratio Choose 0.707 (optimal damping ratio, which can ensure overshoot <5%).

[0158] Based on the pole placement rules of second-order systems, the following is derived: , Calculated value:

[0159] ; .

[0160] The method for tuning the PD parameters is as follows: disconnect the feedforward channel and the RESO channel, retain only the PD feedback, and gradually increase the PD parameters. Record the critical gain at the point when the system exhibits constant-amplitude oscillations. With oscillation cycle Initial parameters are set based on the Ziegler-Nichols method: , Then, through experimental fine-tuning, the overshoot of the system's step response can be made to be less than 5% and the settling time to be less than 20ms.

[0161] To avoid amplifying noise in the differential circuit, a first-order low-pass filter can be applied to the angular velocity measurement value, with the filter bandwidth set to be more than 5 times the PD control bandwidth, to avoid introducing excessive phase lag.

[0162] The physical feedforward quantity is the feedforward compensation quantity calculated in step two. Its parameter tuning has been completed in step two and no additional adjustment is required.

[0163] RESO compensation amount: i.e., the residual perturbation observation value obtained in step three. It is used to compensate for residual high-frequency small-amplitude disturbances, and its parameter tuning has been completed in step three.

[0164] To ensure system stability upon power-up, a smooth switching logic must be used for the access of the three components: when the system is first powered on or the angle tracking error is greater than 0.1°, only PD feedback control is connected, and the weights of the feedforward channel and the RESO channel start from 0 and increase linearly to 1 within 1 second to avoid system oscillation caused by shocks when the channels are connected.

[0165] Detailed rules for output pass-through and anti-hysteresis constraints:

[0166] The core constraint in this step is the "composite control quantity". The constraint that "the current / torque loop of the servo driver must be directly connected to the output" is crucial to ensuring that the system has no additional phase lag and fully utilizes the feedforward and RESO performance. Two types of operations that may introduce lag must be explicitly prohibited:

[0167] Secondary output fusion is prohibited: that is, it is strictly forbidden to perform secondary output fusion after obtaining composite control quantities. Then, fuzzy control, neural networks, weighted averaging, and other methods are used to further... Performing secondary adjustments not only introduces additional computational delays but may also disrupt the zero-phase characteristics of the feedforward channel and the perturbation compensation effect of the RESO.

[0168] Adding additional low-pass filtering is prohibited: It is strictly forbidden to perform any form of low-pass filtering on the control quantity *u* before it is output to the servo driver. While low-pass filtering can reduce output noise, it introduces significant phase lag. For example, a 1kHz first-order low-pass filter will produce approximately 18° of phase lag for a 100Hz signal, completely negating the performance advantage of the high bandwidth of the RESO. If it is absolutely necessary to reduce output noise, filtering should be performed during the preprocessing stage of the sensor measurements, and not at the final control output.

[0169] Simultaneously, the matching requirements of the servo driver need to be clearly defined: the current loop bandwidth of the servo driver must be more than three times the RESO bandwidth. In this embodiment, the RESO bandwidth is 200Hz, therefore the current loop bandwidth needs to be greater than 600Hz to ensure the control quantity... It can be responded to quickly by the servo drive without introducing additional phase lag. Control quantity The output must be completed in the interrupt service routine of the controller, and the calculation is immediately sent to the servo driver through high-speed communication buses such as SPI and EtherCAT after completion.

[0170] The foregoing has only described certain exemplary embodiments of the present invention by way of illustration. Undoubtedly, those skilled in the art can modify the described embodiments in various ways without departing from the spirit and scope of the present invention. Therefore, the foregoing drawings and descriptions are illustrative in nature and should not be construed as limiting the scope of protection of the claims of the present invention.

[0171] It should be noted that, in this document, the use of relational terms such as "first" and "second" is merely for distinguishing one entity or operation from another, and does not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes the element.

[0172] It should be understood that in the various embodiments of this application, the order of the above-mentioned processes does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.

[0173] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0174] Those skilled in the art will understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0175] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0176] In addition, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit.

[0177] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

[0178] The foregoing has only described certain exemplary embodiments of the present invention by way of illustration. Undoubtedly, those skilled in the art can modify the described embodiments in various ways without departing from the spirit and scope of the present invention. Therefore, the foregoing drawings and descriptions are illustrative in nature and should not be construed as limiting the scope of protection of the claims of the present invention.

Claims

1. A high-precision intelligent control method for a turntable based on an improved ESO, characterized in that, include: Step 1: Construct the basic rotational dynamics equations of the turntable, perform decoupling and reconstruction on the total disturbance, and decompose the total disturbance into white-box known disturbance and black-box residual disturbance; Step 2: Construct a physical model feedforward channel for the known disturbances of the white box obtained in Step 1. Based on the installation geometric constraints of the laser rangefinder sensor and the real-time pitch angle of the turntable, use the modified laser rangefinder observation equation to calculate the actual observation distance of the target and map the pointing deviation corresponding to the actual observation distance of the target into a known compensation torque. Step 3: After completing the feedforward compensation of the known disturbance of the white box based on the known compensation torque output in Step 2, design a reduced-order extended state observer for the residual disturbance state space of the turntable, observe the residual disturbance of the black box obtained in Step 1 to obtain the residual disturbance observation value, and use the residual disturbance observation value as the compensation amount of the reduced-order extended state observer. Step 4: Obtain the feedback control quantity of the turntable. Add the feedback control quantity, the feedforward compensation quantity obtained in Step 2, and the residual disturbance observation value obtained in Step 3 to obtain the final motor control input torque of the turntable.

2. The high-precision intelligent control method for a turntable based on an improved ESO as described in claim 1, characterized in that, In step one, the basic rotational dynamics equations of the turntable are constructed as follows: The origin O of the global coordinate system OXYZ is the geometric center of the turntable's pitch rotation axis. The OZ axis is perpendicular to the horizontal plane and points upwards, the OX axis points horizontally towards the turntable's initial zero position, and the OY axis coincides with the turntable's pitch rotation axis. The angle of rotation of the turntable around the OY axis is defined as the pitch angle. ; Based on this, the fundamental rotational dynamics equations of the turntable are established: ; in, It is the equivalent moment of inertia; To control the input torque; It is a nonlinear frictional torque; For the eccentric gravity moment of the load; This is an external disturbance.

3. The high-precision intelligent control method for a turntable based on an improved ESO as described in claim 2, characterized in that, The decoupling rules and boundary definitions for the total disturbance are as follows: Decompose the total disturbance into white-box known disturbances. Residual disturbances from the black box Two parts, namely: ; Only disturbance terms that simultaneously meet the following three conditions can be included. Category: First, the mechanism of the disturbance is consistent with physical laws or geometric constraints, and there is no fundamental error. Second, all input quantities required to calculate disturbances can be acquired in real time by the sensors configured in the system, or obtained through pre-calibration before leaving the factory; Third, the calculation process of the disturbance is a pure algebraic operation; Based on the above rules The specific composition is the gravitational torque component. Viscous friction component Torque components corresponding to optical geometric deterministic deviations; Perturbation terms that fail to meet the above three conditions are classified as... The scope of.

4. The high-precision intelligent control method for a turntable based on an improved ESO as described in claim 1, characterized in that, In step two, the derivation process of the laser ranging observation equation is as follows: Let the light output port of the laser sensor be point A. The center of rotation of the turntable is point 1. Vertical installation height difference For point The vertical distance to the pitch axis of the turntable, and The line connecting the laser beams always remains perpendicular to the laser beam direction. When the turntable is at the zero position, the laser output port The coordinates are At this time, the sensor measures the original distance. Light output port to ground target point Distance, center of rotation To the target point The actual distance is .

5. The high-precision intelligent control method for a turntable based on an improved ESO as described in claim 4, characterized in that, When the turntable rotates around the OY axis Then, the angle between the laser emission direction and the OZ axis is... At this time, the laser beam forms an angle with the vertical direction. Ground target point Located on a horizontal plane, the length of the laser beam The corresponding vertical component is , light outlet The vertical coordinate is Therefore, the center of rotation To the target point The actual vertical distance is .

6. The high-precision intelligent control method for a turntable based on an improved ESO as described in claim 5, characterized in that, Due to the target observation distance Center of rotation To the target point The straight-line distance, combined with geometric relationships, allows us to derive the corrected laser ranging observation equation: ; in, These are the raw measurement values ​​from the laser rangefinder sensor; The vertical mounting height difference between the laser sensor's output axis and the turntable's rotation axis; This is the real-time pitch angle of the turntable.

7. A high-precision intelligent control method for a turntable based on an improved ESO as described in claim 6, characterized in that, After obtaining the actual observation distance of the target through the modified equation, it needs to be converted into the feedforward compensation torque of the servo motor. The conversion process logic is as follows: Based on the corrected observation distance Using the pre-known global coordinates of the target point, the required pitch angle correction can be calculated. ,in The global X-axis coordinates of the target point. The global X-axis coordinate of the turntable's rotation center. The desired pointing angle of the turntable; Angle deviation The derivative with respect to time can be obtained through analytical differentiation: ,in for right Analytical derivative; angular acceleration It can also be obtained through analytical differentiation; Based on the dynamic equations of the turntable, angular deviation The corresponding feedforward compensation torque consists of three parts: First, it counteracts the component of the change in gravitational torque; Second, to counteract the component of viscous friction changes; Third, the torque component required to drive the turntable to track the angular deviation; Adding the three parts together gives the final feedforward compensation amount.

8. The high-precision intelligent control method for a turntable based on an improved ESO as described in claim 1, characterized in that, Definition of the residual perturbation state space in step three: The final control input torque Decomposed into feedforward compensation amount With feedback control quantity Substituting into the original dynamic equation, we get: ; because The design goal is complete compensation Ideally Therefore, the equation can be simplified to: .

9. A high-precision intelligent control method for a turntable based on an improved ESO as described in claim 8, characterized in that, The residual perturbation observations are used as compensation for the reduced-order extended state observer, specifically including: Assuming residual disturbance rate of change It is bounded, meaning there exists a constant. Make For all moments Established; Let the system output be the measured angular velocity value. Then, taking the derivative with respect to y, we get ,Will As the only observed extended state, the following observation law is constructed: ； ； in For the internal state variables of RESO, For the observer gain of RESO, These are the observations of residual perturbations.

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