Motor motion curve optimization method and device based on iterative learning

Abstract

The application belongs to the field of electromechanical transmission and motion control, and particularly relates to a motor motion curve optimization method and device based on iterative learning, which comprises the following steps: performing system identification modeling on an absolute gravimeter transmission control system, establishing a transfer function model capable of representing system dynamic response characteristics; constructing a three-level closed-loop control loop and introducing speed feedforward compensation and acceleration feedforward compensation to form a servo basic control architecture; defining a comprehensive error evaluation index and an iterative convergence criterion; on the basis of a traditional PID type iterative learning law, integrating three improvement mechanisms of error normalization, real-time feedback correction and error decay suppression to construct an improved iterative learning control law; taking an ideal trajectory of a trolley as an initial control instruction, performing multi-cycle iterative learning through the improved iterative learning control law to output an optimal trolley speed motion command. A new method is provided for high-precision control of the absolute gravimeter transmission control system.

Description

Technical Field

[0001] This application relates to the field of electromechanical transmission and motion control, specifically to a method and apparatus for optimizing motor motion curves based on iterative learning. Background Technology

[0002] Laser interferometric absolute gravimeters are core equipment for acquiring high-precision Earth gravity field data. They are widely used in basic surveying, resource exploration, earthquake monitoring, and crustal deformation research. Their micro-gallon level measurement accuracy is highly dependent on the motion control performance of the trolley. When the trolley is working, it needs to perform high-speed, high-repetition, and high-precision linear reciprocating motion in multiple cycles, which places stringent requirements on the stability of the motion trajectory, tracking accuracy, and multi-cycle operation stability.

[0003] Existing traditional control schemes have inherent defects: the use of trapezoidal and S-shaped trajectory planning methods has the problem of sudden acceleration, which can easily induce mechanical shock in the electromechanical transmission system and produce obvious trajectory tracking deviations; conventional closed-loop control can only achieve error suppression within a single motion cycle and cannot effectively compensate for the error accumulation caused by load disturbances, mechanical wear and other factors during multi-cycle continuous operation, making it difficult to meet the stringent requirements of micro-galvanic gravity measurement for the stability of the vehicle's motion and trajectory synchronization.

[0004] The Iterative Learning Control (ILC) algorithm, commonly used in the field of periodic motion control, still has many shortcomings when applied to this scenario: traditional iterative learning laws have a slow convergence speed and cannot quickly compensate for trajectory lag caused by system inertial delay; their ability to suppress guide rail friction fluctuations, load disturbances, and measurement noise is limited, and error oscillations and divergences are prone to occur during the iteration process; at the same time, they lack a collaborative mechanism with the real-time closed-loop feedback of the servo system, and cannot take into account both single-cycle real-time error correction and multi-cycle iterative optimization; moreover, the application of existing iterative learning control technology in the motion control of absolute gravimeter trolleys is still not in-depth enough, and real-time feedback correction and error attenuation links are generally not designed, which cannot simultaneously meet the requirements of convergence speed and anti-disturbance, thus restricting the further improvement of the measurement accuracy and overall performance of domestic absolute gravimeters. Summary of the Invention

[0005] To address the aforementioned issues, this application provides a method and apparatus for optimizing motor motion curves based on iterative learning. With the core objective of improving the tracking accuracy of the absolute gravimeter trolley motion trajectory, an improved iterative learning control strategy is designed that integrates error normalization, real-time feedback correction, and error attenuation suppression. This aims to provide a new technical solution for high-precision control of the absolute gravimeter transmission control system, thereby overcoming or at least partially overcoming the shortcomings of the prior art.

[0006] Firstly, this application provides a method for optimizing motor motion curves based on iterative learning, including: System modeling steps: Perform system identification and modeling of the absolute gravimeter transmission control system, and establish a transfer function model that can characterize the dynamic response characteristics of the system; Basic control architecture construction: Construct a three-level closed-loop control loop of current loop - speed loop - position loop, and introduce speed feedforward compensation and acceleration feedforward compensation to form a servo basic control architecture; Error evaluation construction steps: Define the comprehensive error evaluation index and the iterative convergence judgment criterion. The comprehensive error evaluation index includes: root mean square error of velocity following and absolute error of velocity integral. Improved learning law construction steps: Based on the traditional PID-type iterative learning law, three improvement mechanisms are integrated: error normalization, real-time feedback correction, and error decay suppression, to construct an improved iterative learning control law; Iterative trajectory optimization steps: Using the ideal trajectory of the motorcycle as the initial control command, the motorcycle undergoes multi-cycle iterative learning through an improved iterative learning control law to output the optimal motorcycle speed movement command.

[0007] Secondly, this application also provides a motor motion curve optimization device based on iterative learning, the device comprising: The system modeling unit is used to perform system identification and modeling of the absolute gravimeter transmission control system, and to establish a transfer function model that can characterize the dynamic response characteristics of the system. The basic control architecture unit is used to construct a three-level closed-loop control loop of current loop-speed loop-position loop, and introduces speed feedforward compensation and acceleration feedforward compensation to form a servo basic control architecture; The error evaluation construction unit is used to define the comprehensive error evaluation index and the iterative convergence judgment criterion. The comprehensive error evaluation index includes: the root mean square error of velocity following and the absolute error of velocity integral. An improved learning law construction unit is used to construct an improved iterative learning control law by integrating three improvement mechanisms—error normalization, real-time feedback correction, and error decay suppression—on the basis of the traditional PID-type iterative learning law. The iterative trajectory optimization unit is used to take the ideal trajectory of the motorcycle as the initial control command, and to perform multi-cycle iterative learning through an improved iterative learning control law to output the optimal motorcycle speed motion command.

[0008] Thirdly, this application also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the above-described method for optimizing motor motion curves based on iterative learning.

[0009] Fourthly, this application also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the above-described method for optimizing motor motion curves based on iterative learning.

[0010] This application can achieve at least the following beneficial effects: First, the motor motion curve optimization method based on iterative learning proposed in this application is highly compatible with the strong periodic reciprocating motion characteristics of the laser interferometric absolute gravimeter trolley. It can make full use of the multi-cycle repetitive operation law, effectively suppress the accumulation of multi-cycle errors caused by load disturbance, mechanical wear and transmission elastic deformation, and improve the trajectory tracking deviation from the root.

[0011] Second, the motor motion curve optimization method based on iterative learning proposed in this application achieves the organic synergy of single-cycle real-time error correction and multi-cycle iterative optimization. Compared with traditional iterative learning algorithms, it has a faster convergence speed, significantly improves trajectory tracking accuracy and motion stability, and can effectively reduce the acceleration lag and deceleration overshoot of the motorcycle, and reduce the mechanical shock and vibration of the transmission system.

[0012] Third, the numerical simulation results and hardware prototype experimental results of this application are in high agreement, which fully verifies the feasibility and engineering applicability of the control strategy of this invention. It can be directly applied to the performance optimization of the servo control system of domestic absolute gravimeter, providing reliable technical support for improving the micro-gallon level gravity measurement accuracy of absolute gravimeter.

[0013] Fourth, the improved iterative learning control law proposed in this application can converge stably within 8 iterations. The root mean square error, integral absolute error, and comprehensive error of the vehicle speed tracking are all reduced by more than 62%. The hardware experimental results and simulation results are in agreement of more than 90%, which verifies the engineering practicality of the strategy. It can significantly improve the tracking accuracy and dynamic stability of the vehicle motion trajectory, and provides core technical support for the accurate release and measurement accuracy of the absolute gravimeter. Attached Figure Description

[0014] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings: Figure 1 A flowchart illustrating an embodiment of a motor motion curve optimization method based on iterative learning according to this application is shown. Figure 2 A schematic diagram of a motor motion curve optimization device based on iterative learning according to an embodiment of this application is shown. Figure 3 A schematic diagram of the structure of an electronic device according to an embodiment of this application is shown. Detailed Implementation

[0015] To make the objectives, technical claims, and advantages of this application clearer, the technical application of this application will be clearly and completely described below with reference to specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0016] High-precision information on the absolute gravity field has significant application value in fields such as basic surveying, resource exploration, and aerospace. Gravity is ubiquitous in our daily lives and is the gravitational force exerted by the Earth on objects on or near the Earth's surface. Gravitational acceleration (usually denoted by g) is the acceleration of an object on the Earth's surface under the influence of gravity. An absolute gravimeter is an instrument that directly and accurately measures gravitational acceleration near the Earth's surface. It plays an important role not only in earthquake monitoring and crustal deformation but is also widely used in basic surveying, geophysical prospecting, sea level and earthquake monitoring, precise determination of the geoid, and research on vertical crustal deformation. Its measurement accuracy directly determines the reliability of data in related fields and represents the level of data acquisition on the Earth's gravity field.

[0017] Among them, laser interferometric absolute gravimeters, with their micro-gallon-level measurement accuracy, have become the mainstream commercial equipment in the field of absolute gravity measurement. The core of their measurement accuracy depends on the motion accuracy of the trolley under the control of the electromechanical transmission system. As the core driving unit for the trolley's motion, the electromechanical transmission system needs to complete high-speed, high-repeatability, and high-precision reciprocating motion in multiple cycles, placing stringent requirements on motion control accuracy and operational stability. Traditional trapezoidal and S-shaped trajectory planning methods suffer from sudden acceleration changes, easily leading to mechanical shocks in the transmission system and trajectory tracking deviations. Conventional closed-loop control can only suppress errors within a single cycle and cannot compensate for the accumulation of errors caused by load disturbances, mechanical wear, and other factors during multi-cycle operation, resulting in a decrease in trolley motion accuracy with each iteration. These are the core issues restricting the improvement of absolute gravimeter measurement accuracy.

[0018] Iterative Learning Control (ILC) is a control method designed for systems with periodic repetitive motion. It uses multiple iterations to correct subsequent control inputs based on the tracking error of previous motions, gradually converging the trajectory tracking error to a minimum. This approach is highly suitable for the characteristics of absolute gravimeters, such as fixed measurement periods, repetitive trolley trajectories, and high precision requirements. Some existing studies employ closed-loop PI-type offline iterative learning compensation strategies to address the periodic position error problem of permanent magnet synchronous linear motors. Experiments have verified a reduction in trajectory tracking error of 20.8%-24.2%, but these strategies suffer from limitations such as inability to handle time-varying disturbances, slow convergence, and limited verification scenarios. Other existing studies use basic proportional iterative learning control algorithms to dynamically correct the stopping lead by tracking the actual weight error of the weighing hopper, while introducing a cumulative error compensation mechanism to solve the overshoot problem caused by residual material in the air. Still other studies propose finite-time iterative learning error tracking control methods, constructing a desired error trajectory independent of the reference trajectory. A saturated iterative attraction law is used to achieve finite-time convergence of the tracking error, relaxing the initial value consistency condition of traditional iterative learning. However, existing research on the application of iterative learning control in the optimization of the motion trajectory of an absolute gravimeter trolley is still not in-depth enough. The iterative learning algorithms used are relatively simple in structure, and most of them do not have error attenuation and noise suppression links, or do not integrate real-time feedback correction and have a single error processing mechanism. Not only is error divergence easy to occur during the iteration process, but it is also difficult to meet the stringent requirements of motion stability for micro-galvanic level measurements.

[0019] To address the aforementioned issues, this application focuses on improving the tracking accuracy of an absolute gravimeter's trolley motion trajectory. It designs an improved iterative learning control strategy that integrates error normalization, real-time feedback correction, and error attenuation suppression. First, dynamic characteristic modeling and error mechanism analysis of the electromechanical transmission system were completed, clarifying the optimization objective of the iterative learning control. Second, an iterative optimization model of the trolley's motion trajectory was constructed, defining the quantization error index and convergence criterion, and an improved discrete-domain iterative learning law was designed. Finally, numerical simulations and hardware experiments verified the strategy's effectiveness in improving trolley motion accuracy, providing a new technical solution for high-precision control of the absolute gravimeter's transmission control system.

[0020] Figure 1 The diagram illustrates a flowchart of an iterative learning-based method for optimizing motor motion curves according to this application. Figure 1 As can be seen, this embodiment includes steps S110 to S150: System modeling step S110: Perform system identification and modeling on the absolute gravimeter transmission control system, and establish a transfer function model that can characterize the dynamic response characteristics of the system.

[0021] Specifically, for the modeling of the absolute gravimeter transmission control system, the motor command speed of the absolute gravimeter transmission control system is used as the input and the actual measured speed of the trolley movement by the laser interferometer is used as the output. A second-order zero-pole transfer function model characterizing the dynamic characteristics of the electromechanical transmission is established by adopting a data-driven system identification method.

[0022] The absolute gravimeter transmission control system consists of a MAXON RE40 servo motor, a vacuum drive shaft, a steel belt drive mechanism, and a trolley drop assembly. The motor converts the rotary motion into the linear reciprocating motion of the trolley through the steel belt drive.

[0023] Based on the Matlab system identification toolbox, using the motor command speed as input and the actual speed of the motorcycle acquired by the laser interferometer as output, a second-order zero-pole transfer function model was identified after data preprocessing. The model fit reached 97%, and the final prediction error and mean square error were as low as 1.144 × 10⁻⁶. -6 The magnitude can accurately characterize the dynamic properties of the system.

[0024] The S120 basic control architecture is constructed by building a three-level closed-loop control loop consisting of a current loop, a speed loop, and a position loop, and introducing speed feedforward compensation and acceleration feedforward compensation to form the basic servo control architecture.

[0025] For the underlying control foundation of motorcycle trajectory tracking, this application constructs a servo-based control architecture with three-loop closed-loop coordination and feedforward compensation as the underlying control foundation for motorcycle trajectory tracking.

[0026] Specifically, a three-level closed-loop control system consisting of current loop, speed loop, and position loop is adopted. At the same time, speed feedforward compensation and acceleration feedforward compensation are introduced to construct a composite control system that combines closed-loop feedback and feedforward compensation, providing a stable basic control layer for iterative learning and optimization.

[0027] This application leverages the mature three-level closed-loop architecture of current loop, speed loop, and position loop in the existing servo motion control field to implement low-level control: the current loop serves as the inner loop, responsible for rapid tuning and current limiting protection of the motor armature current, suppressing electromagnetic disturbances; the speed loop serves as the middle loop, tracking speed commands in real time and damping mechanical oscillations to improve operational stability; the position loop serves as the outer loop, using position deviation as input to achieve precise trajectory position tracking. Simultaneously, speed feedforward compensation and acceleration feedforward compensation are introduced into the position command output path, applying control quantities in advance based on the speed and acceleration information of the desired trajectory to compensate for system inertial lag and dynamic tracking errors. By superimposing and fusing the feedforward compensation quantity with the three-loop closed-loop feedback output quantity, a composite control system with closed-loop feedback active correction and feedforward compensation for advance prediction is constructed. Based on the excellent dynamic response stability and basic trajectory tracking accuracy of this system, a stable, reliable, and repeatable underlying operational control layer is provided for subsequent multi-cycle iterative optimization of improved iterative learning control.

[0028] Error evaluation construction step S130: Define the comprehensive error evaluation index and the iterative convergence judgment criterion, wherein the comprehensive error evaluation index includes: the root mean square error of velocity following and the absolute error of velocity integral.

[0029] Motion control errors in the transmission and control system of an absolute gravimeter can cause deviations in the initial velocity and attitude of the falling object, thereby reducing the accuracy of gravity measurements. Considering the system's operating characteristics, its core errors manifest in the following two forms: First, there is the position tracking error, which refers to the deviation between the ideal and actual trajectory of the motorcycle. This error is mainly affected by three factors: the transmission ratio deviation and preload fluctuation caused by the elastic stretching of the steel belt's slack side, resulting in a deviation in the mapping relationship between the motor rotation angle and the motorcycle displacement; the adjustment lag and insufficient robustness of conventional closed-loop controllers to nonlinear disturbances, making it impossible to quickly compensate for trajectory deviations caused by load changes; and the transient impact of the release and catch of the falling object, as well as the sudden disturbances caused by changes in load inertia during motorcycle movement, further amplify the trajectory tracking error.

[0030] Secondly, the impact error in the start-stop process stems from the mismatch between the acceleration step in the acceleration / deceleration command curve and the dynamic response characteristics of the transmission system, resulting in a step output of motor torque and causing transient vibration in the transmission system. This error causes torsional vibration of the motor shaft and vacuum drive shaft, which is transmitted to the steel belt drive mechanism, causing elastic vibration. Ultimately, this causes the actual start-stop motion of the trailer to lag behind the command curve, leading to speed fluctuations during the critical stage of separation and directly affecting the accuracy of gravity measurement results.

[0031] Both types of errors exist in the intermittent, periodic reciprocating motion of the system. Simply improving hardware precision cannot completely eliminate them. However, iterative learning control can rely on the strong periodicity of the system's motion characteristics and effectively suppress systematic errors by iteratively correcting the control input through multiple rounds of iteration.

[0032] To address this, this application designs an improved iterative learning control law that integrates feedback correction and error weight decay. In this improved iterative learning control law, a collaboratively optimized error index is defined as the iteration objective, denoted as the comprehensive error evaluation index; a convergence criterion is also defined.

[0033] In the error evaluation system, individual errors include: root mean square error of speed following and absolute error of speed integral. The comprehensive speed error index is a weighted integration of the above two types of errors to achieve dimensional normalization.

[0034] In some embodiments of this application, the velocity follows the root mean square error (RMSE). RMSE v This is used to quantify the overall level of speed deviation, and its expression is as follows: ; In the formula, , Indicates the first k Next iteration, time step t The speed tracking error is as follows, where, For the first k The ideal speed for the next iteration of the trolley For the first k The actual speed of the trolley in the next iteration T The time it takes for the motorcycle to complete one cycle of movement.

[0035] In some embodiments of this application, the velocity integral absolute error ( IAE v This is used to quantify the cumulative effect of errors over the entire cycle, and the expression is as follows: ; In the formula, T The time for one cycle of the motorcycle's movement, and , indicates the first k Next iteration, time step t The speed tracking error is as follows, among which For the first k The ideal speed for the next iteration of the trolley For the first k The actual speed of the trolley in the next iteration.

[0036] In some embodiments of this application, the comprehensive speed error index J(k) The above-mentioned root mean square error of speed tracking and absolute error of speed integral are summed with weights and their dimensions normalized. For example, each weight can be 0.5, and this value will be used for all subsequent explanations. The expression is as follows: ; In the formula, To average the absolute error of the integral, the dimensions of the two types of error indices are normalized, avoiding optimization bias caused by differences in dimensions. Specifically, T The time it takes for the motorcycle to complete one cycle of movement.

[0037] In some embodiments of this application, the convergence criterion is: when the comprehensive velocity error index J(k) If the change in the change is ≤0.001% and the condition is met for three consecutive iterations, the iteration is considered to have converged.

[0038] Improved learning law construction step S140: Based on the traditional PID-type iterative learning law, three improvement mechanisms are integrated: error normalization, real-time feedback correction, and error decay suppression, to construct an improved iterative learning control law.

[0039] The core of this application's improvement to the learning control law lies in simultaneously introducing error normalization processing, real-time feedback correction terms, and error attenuation terms. Specifically, in some embodiments of this application, the implementation logic for the improved learning control law includes: performing normalization processing based on the speed tracking deviation and the average command speed of the steady-speed segment, constructing a speed error weighting term to eliminate the influence of speed magnitude on the correction effect; performing discrete-domain PID learning law calculation based on the speed tracking deviation, constructing a feedback correction term to achieve real-time correction of single-cycle errors; adding an error attenuation coefficient to suppress random interference caused by measurement noise, load fluctuations, and guide rail friction fluctuations; and finally forming an improved iterative learning control law, which integrates the discrete-domain control law of closed-loop iterative learning and feedback correction to achieve synergy between multi-cycle iterative optimization and single-cycle real-time correction.

[0040] The following is a brief introduction to the classic PID iterative learning algorithm in existing technologies. The classic PID learning law integrates three types of information—proportional (P), integral (I), and derivative (D)—of the tracking error, simultaneously considering both steady-state tracking accuracy and dynamic response performance of the motorcycle trajectory. Its form is as follows: ; Where Γ p , Γ i , Γ d These are the proportional, integral, and derivative learning gains, respectively. The integral term effectively eliminates the steady-state tracking error of the system, while the derivative term suppresses error oscillations during the iteration process, making it the preferred learning law for the absolute instrument motor drive system.

[0041] While traditional iterative learning laws are simple in structure, they still have significant limitations in practical applications of absolute gravimeter drive control systems. These algorithms generally suffer from slow convergence speeds, making it difficult to quickly compensate for trajectory lag caused by system inertial delays. They also lack sufficient ability to suppress guide rail friction fluctuations, load disturbances, and measurement noise, and are prone to error oscillations during iteration, affecting the stability of the control process. More importantly, traditional iterative learning laws do not form a coordinated mechanism with the real-time closed-loop feedback of the servo system, failing to simultaneously address real-time error suppression within a single cycle and iterative optimization over multiple cycles. This makes them ill-suited to fully meet the high-precision and high-stability control requirements of absolute gravimeter drive systems.

[0042] This application addresses the shortcomings of traditional ILC (Iterative Learning Control) by making three improvements to the PID-type learning law: error normalization: dividing the speed tracking deviation by the average command speed of the steady-state segment to eliminate the influence of speed magnitude on the correction effect; introduction of a real-time feedback correction term: performing discrete-domain PID calculation on the speed deviation to achieve single-cycle real-time error suppression; and addition of an error attenuation term: introducing an attenuation coefficient to suppress iterative oscillations caused by measurement noise and random disturbances.

[0043] The final expression is as follows: ; In the formula, i,j : Discrete-time step index, the first step within a single iteration i , j Each sampling time, v cmd (k,i) : No. k The next iteration, the... i The ideal speed for a motorcycle at any given time v cmd (k+1,i) : No. k+1 The next iteration, the... i The ideal speed of the motorcycle is updated in real time. e (k,i) : No. k The next iteration, the... i Speed ​​tracking error at any given moment T s System sampling period K d Iterative learning of differential gain, Δ u pid (k,i) : No. k The next iteration, the... i The increment of the PID controller output at any given time, Γ p ,Γ i ,Γ d These are the proportional, integral, and differential learning gains of the iterative learning law, respectively. β These are the weighting coefficients for the feedback correction term, used to adjust the degree of influence of the speed loop feedback correction. α This is the error attenuation coefficient, with a value ranging from 0 to 1. i When it is 0, e (k,-1) The value is 0.

[0044] This improved iterative learning control law eliminates the influence of velocity magnitude on the correction effect through error normalization. The introduced real-time feedback correction term achieves the synergy between single-cycle error suppression and multi-cycle iterative optimization. The error attenuation term effectively suppresses the interference of random disturbances and measurement noise on the iterative process, and can better adapt to the high-precision control requirements of the absolute gravimeter drive control system.

[0045] The expression of the improved iterative learning control law provides the core update rule for the entire iterative optimization process. Based on the speed tracking error of the previous iteration, the control input correction is calculated by fusing proportional, integral, and differential information, combined with error normalization, real-time feedback correction, and error decay mechanisms. The correction is then applied to the vehicle speed command in the next cycle point by point. Through multi-cycle iteration, the trajectory tracking error is continuously converged, while iterative oscillations caused by measurement noise and random disturbances are suppressed, ultimately achieving high-precision tracking and stable operation of the vehicle's motion trajectory.

[0046] Iterative trajectory optimization step S150: Using the ideal trajectory of the motorcycle as the initial control command, multi-cycle iterative learning is performed through an improved iterative learning control law to output the optimal motorcycle speed motion command.

[0047] Using the ideal trajectory of the motorcycle as the initial command, and relying on the improved iterative learning control law, multi-cycle iterative learning is carried out to correct the trajectory control command cycle by cycle until the convergence criterion is met, and the optimal trajectory command is output to achieve high-precision and high-stability control of the motorcycle's periodic reciprocating motion.

[0048] Specifically, the ideal speed curve of the motorcycle is used as the initial control command to drive the motorcycle to perform periodic reciprocating motion; the actual motion speed data is collected and substituted into the error evaluation system to calculate the error index; the speed command curve of the next iteration cycle is corrected by using an improved iterative learning control law; the cycle is iterated until the preset convergence criterion is met, and the optimal speed command curve after convergence is output, so as to realize the high-precision and high-stability reciprocating motion control of the motorcycle.

[0049] In some embodiments of this application, preferred key experimental parameters are listed, and core algorithm parameters include, but are not limited to, the following parameters: proportional learning gain Γ. p =0.4, Integral learning gain Γ i =0.08, differential learning gain Γ d =0.05; Error attenuation coefficient α =0.85, weight of feedback correction term β =0.15; system sampling frequency 2000Hz, single motion period 0.3s.

[0050] Servo system tuning parameters include, but are not limited to, the following parameters: Current loop: C p =73、 C i =85, bandwidth 1800Hz; speed loop: V p =750、 V i =300, output filter 400Hz; Position loop: P p=300, velocity feedforward coefficient K vff =16384, acceleration feedforward coefficient K aff =50; Motor PID adjustment parameters: K p =2900, K i =50, K d =800.

[0051] The preferred iterative learning control parameters and servo system tuning parameters listed above have all been optimized and tuned through multiple rounds of simulation comparison tests and repeated trial runs of physical prototypes. By comparing the iterative convergence speed, trajectory tracking accuracy and running stability under different parameters, the optimal parameter combination was selected, ensuring the convergence, stability and engineering adaptability of the control algorithm.

[0052] To verify the actual control effect of the improved iterative learning control method of this application, numerical simulation and hardware prototype experiments were carried out sequentially using the same parameters. First, an identification model of the absolute gravimeter transmission control system was built in the simulation environment, and the iterative learning control parameters and servo system tuning parameters were configured. The system sampling frequency and the single-cycle motion duration of the trolley were set. Using the ideal speed trajectory as the initial command, the improved iterative learning control law of this application was used for multi-cycle iterative optimization. The root mean square error of speed following, the absolute error of speed integral, and the comprehensive error index were calculated in real time until the preset convergence criterion was met. The number of iterations and the error decay amplitude were statistically analyzed.

[0053] In the experimental verification, based on the effectiveness of the simulation verification, the optimized set of control parameters were directly imported into the absolute gravimeter hardware servo control system. The actual speed data of the trolley was collected in real time using a laser interferometer. The physical reciprocating motion test was carried out according to the same iterative process and error evaluation standard. The error index, convergence characteristics and trajectory tracking effect of the simulation and hardware test were compared to evaluate the improvement of the trolley's acceleration lag, deceleration overshoot and running stability, thus completing the feasibility and engineering practicality verification of the control strategy of this application.

[0054] Simulation results show that the algorithm can converge stably in 8 iterations, and the motorcycle speed... RMSE v , IAE v and comprehensive error J(k) The declines all exceeded 62%.

[0055] The physical test results of the hardware prototype showed a consistency of over 90% with the simulation results, with a comprehensive error consistency of 98.11%. After iterative optimization, the lag deviation during the acceleration phase of the motorcycle was significantly reduced, the deceleration overshoot was basically eliminated, and the motion stability was greatly improved.

[0056] In summary, by Figure 1 As can be seen from the method presented, firstly, the motor motion curve optimization method based on iterative learning proposed in this application is highly compatible with the strong periodic reciprocating motion characteristics of the laser interferometric absolute gravimeter trolley. It can fully utilize the multi-cycle repetitive operation pattern to effectively suppress the accumulation of multi-cycle errors caused by load disturbances, mechanical wear, and transmission elastic deformation, thereby fundamentally improving trajectory tracking deviation. Secondly, the motor motion curve optimization method based on iterative learning proposed in this application achieves organic synergy between single-cycle real-time error correction and multi-cycle iterative optimization. Compared with traditional iterative learning algorithms, it has a faster convergence speed, significantly improves trajectory tracking accuracy and motion stability, and can effectively reduce trolley acceleration lag and deceleration overshoot, as well as reduce mechanical shock and vibration of the transmission system. Thirdly, the numerical simulation results and hardware prototype experimental results of this application are in high agreement, fully verifying the feasibility and engineering practicality of the control strategy of this invention. It can be directly applied to the performance optimization of the servo control system of domestic absolute gravimeters, providing reliable technical support for improving the micro-gallon level gravity measurement accuracy of absolute gravimeters. Fourth, the improved iterative learning control law proposed in this application can converge stably within 8 iterations. The root mean square error, integral absolute error, and comprehensive error of the vehicle speed tracking are all reduced by more than 62%. The hardware experimental results and simulation results are in agreement of more than 90%, which verifies the engineering practicality of the strategy. It can significantly improve the tracking accuracy and dynamic stability of the vehicle motion trajectory, and provides core technical support for the accurate release and measurement accuracy of the absolute gravimeter.

[0057] Figure 2 A schematic diagram of a motor motion curve optimization device based on iterative learning according to an embodiment of this application is shown. Figure 2 It can be seen that the motor motion curve optimization device 200 based on iterative learning includes: System modeling unit 210 is used to perform system identification and modeling of the absolute gravimeter transmission control system and establish a transfer function model that can characterize the dynamic response characteristics of the system. The basic control architecture unit 220 is used to construct a three-level closed-loop control loop of current loop-speed loop-position loop, and introduces speed feedforward compensation and acceleration feedforward compensation to form a servo basic control architecture; Error evaluation construction unit 230 is used to define comprehensive error evaluation index and iterative convergence judgment criteria. The comprehensive error evaluation index includes: root mean square error of velocity following and absolute error of velocity integral. The improved learning law construction unit 240 is used to construct an improved iterative learning control law by integrating three improvement mechanisms—error normalization, real-time feedback correction, and error decay suppression—on the basis of the traditional PID-type iterative learning law. The iterative trajectory optimization unit 250 is used to take the ideal trajectory of the motorcycle as the initial control command, and perform multi-cycle iterative learning through an improved iterative learning control law to output the optimal motorcycle speed motion command.

[0058] In some embodiments of this application, in the above-described apparatus, the root mean square error of the speed follower is used to quantify the overall level of the speed deviation, as expressed below: ; In the formula, , Indicates the first k Next iteration, time step t The speed tracking error is as follows, where, For the first k The ideal speed for the next iteration of the trolley For the first k The actual speed of the trolley in the next iteration T The time it takes for the motorcycle to complete one cycle of movement.

[0059] The velocity integral absolute error is used to quantify the cumulative effect of the full-cycle error, and the expression is as follows: ; In the formula, T The time for one cycle of the motorcycle's movement, and , indicates the first k Next iteration, time step t The speed tracking error is as follows, among which For the first k The ideal speed for the next iteration of the trolley For the first k The actual speed of the trolley in the next iteration.

[0060] Comprehensive speed error index J(k) It is obtained by applying weights to the root mean square error of speed tracking and the absolute error of speed integral, summing them, and then normalizing the dimensions.

[0061] In some embodiments of this application, in the above-described apparatus, the iterative convergence criterion is: when the comprehensive velocity error index... J(k) If the change in the change is ≤0.001% and the condition is met for three consecutive iterations, the iteration is considered to have converged.

[0062] In some embodiments of this application, in the above-described apparatus, the improved learning law construction unit 240 is used to perform normalization processing based on the speed tracking deviation and the average command speed of the steady speed segment, construct a speed error weighting term to eliminate the influence of the speed magnitude on the correction effect; perform discrete domain PID learning law calculation based on the speed tracking deviation, construct a feedback correction term to achieve real-time correction of single-cycle error; and add an error attenuation coefficient to suppress random interference caused by measurement noise, load fluctuation and guide rail friction fluctuation, forming an improved iterative learning control law.

[0063] In some embodiments of this application, the expression of the improved iterative learning control law in the above-described apparatus is as follows: ; In the formula, i,j : Discrete-time step index, the first step within a single iteration i , j Each sampling time, v cmd (k,i) : No. k The next iteration, the... i The ideal speed for a motorcycle at any given time v cmd (k+1,i) : No. k+1 The next iteration, the... i The ideal speed of the motorcycle is updated in real time. e (k,i) : No. k The next iteration, the... i Speed ​​tracking error at any given moment T s System sampling period K d Iterative learning of differential gain, Δ u pid (k,i) : No. k The next iteration, the... i The increment of the PID controller output at any given time, Γ p ,Γ i ,Γ d These are the proportional, integral, and differential learning gains of the iterative learning law, respectively. β These are the weighting coefficients for the feedback correction term, used to adjust the degree of influence of the speed loop feedback correction. α This is the error attenuation coefficient, with a value ranging from 0 to 1. i When it is 0, e (k,-1) The value is 0.

[0064] In some embodiments of this application, the above-mentioned apparatus further includes: a verification unit, used to conduct numerical simulation experiments and hardware prototype physical experiments using the same iterative learning control parameters and servo system tuning parameters, respectively, to verify the actual control effect of the improved iterative learning control method.

[0065] In some embodiments of this application, the core algorithm parameters in the above-described apparatus include: proportional learning gain Γ. p =0.4, Integral learning gain Γ i =0.08, differential learning gain Γ d =0.05; Error attenuation coefficient α =0.85, weight of feedback correction term β =0.15; system sampling frequency 2000Hz, single motion period 0.3s.

[0066] In some embodiments of this application, the servo system tuning parameters in the above-described apparatus include: current loop: C p =73、 C i =85, bandwidth 1800Hz; speed loop: V p =750、 V i =300, output filter 400Hz; Position loop: P p =300, velocity feedforward coefficient K vff =16384, acceleration feedforward coefficient K aff =50; Motor PID adjustment parameters: K p =2900, K i =50, K d =800.

[0067] It should be noted that the aforementioned motor motion curve optimization device based on iterative learning can implement the aforementioned motor motion curve optimization method based on iterative learning. The implementation details will not be elaborated here.

[0068] Figure 3 This invention illustrates a schematic diagram of the structure of an electronic device according to an embodiment of the present application. Figure 3As shown, the electronic device includes a processor, memory, network interface, and database connected via a system bus. The processor provides computing and control capabilities. The memory includes non-volatile and / or volatile storage media and internal memory. The non-volatile storage media stores the operating system, computer programs, and database. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The network interface is used for communication with external devices via a network connection. When the computer program is executed by the processor, it implements the functions or steps of an iterative learning-based motor motion curve optimization method.

[0069] In one embodiment, the electronic device provided in this application includes a memory and a processor. The memory stores a database and a computer program that can run on the processor. When the processor executes the computer program, it implements the steps of the aforementioned motor motion curve optimization method based on iterative learning.

[0070] The above is as stated in this application. Figure 2 The method executed by the improved iterative learning control device for the laser interferometric absolute gravimeter cart disclosed in the illustrated embodiment can be applied to a processor or implemented by a processor. During implementation, each step of the above method can be completed by integrated logic circuits in the processor's hardware or by instructions in software form. The processor can be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it can also be a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. The steps of the method disclosed in the embodiments of this application can be directly embodied in the execution of a hardware decoding processor, or can be completed by a combination of hardware and software modules in the decoding processor. The software modules can reside in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. The storage medium is located in the memory. The processor reads the information in the memory and, in conjunction with its hardware, completes the steps of the above-mentioned motor motion curve optimization method based on iterative learning.

[0071] In one embodiment, a computer-readable storage medium is also provided, on which a computer program is stored, which, when executed by a processor, implements the steps of the aforementioned method for optimizing motor motion curves based on iterative learning.

[0072] It should be noted that the functions or steps that the above-mentioned electronic devices or computer-readable storage media can achieve can be referred to the relevant descriptions in the foregoing method embodiments. To avoid repetition, they will not be described one by one here.

[0073] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0074] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is used as an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the system can be divided into different functional units or modules to complete all or part of the functions described above.

[0075] The above-described embodiments are only used to illustrate the technical application of this application, and are not intended to limit it. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical applications described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical applications to deviate from the spirit and scope of the technical applications of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A method for optimizing motor motion curves based on iterative learning, characterized in that, include: System modeling steps: Perform system identification and modeling of the absolute gravimeter transmission control system, and establish a transfer function model that can characterize the dynamic response characteristics of the system; Basic control architecture construction: A three-level closed-loop control loop of current loop-speed loop-position loop is constructed, and speed feedforward compensation and acceleration feedforward compensation are introduced to form a servo basic control architecture; the servo basic control architecture serves as the underlying control foundation for vehicle trajectory tracking, providing a stable basic control layer for iterative learning and optimization; Error evaluation construction steps: Define the comprehensive error evaluation index and the iterative convergence judgment criterion. The comprehensive error evaluation index includes: root mean square error of velocity following and absolute error of velocity integral. Improved learning law construction steps: Based on the traditional PID-type iterative learning law, three improvement mechanisms are integrated: error normalization, real-time feedback correction, and error decay suppression, to construct an improved iterative learning control law; The expression for the improved iterative learning control law is as follows: ； In the formula, i,j : Discrete-time step index, the first step within a single iteration i , j Each sampling time, v cmd (k,i) : No. k The next iteration, the... i The ideal speed for a motorcycle at any given time v cmd (k+1,i) : No. k+1 The next iteration, the... i The ideal speed of the motorcycle is updated in real time. e(k, i) : No. k The next iteration, the... i Speed ​​tracking error at any given moment T s System sampling period K d Iterative learning of differential gain, Δu pid (k,i) : No. k The next iteration, the... i The increment of the PID controller output at any given time, Γ p ,Γ i These are the proportion and integral of the iterative learning law, respectively. β These are the weighting coefficients for the feedback correction term, used to adjust the degree of influence of the speed loop feedback correction. α This is the error attenuation coefficient, with a value ranging from 0 to 1. i When it is 0, e (k,-1) The value is 0; Iterative trajectory optimization steps: Using the ideal trajectory of the motorcycle as the initial control command, multi-cycle iterative learning is performed through an improved iterative learning control law. After each iteration, the comprehensive error evaluation index is calculated until the iterative convergence criterion is met, at which point the iteration terminates and the optimal motorcycle speed motion command is output.

2. The method according to claim 1, characterized in that, Speed ​​following root mean square error RMSE v The expression used to quantify the overall level of speed deviation is as follows: ； In the formula, , Indicates the first k Next iteration, time step t The speed tracking error is as follows, where, For the first k The ideal speed for the next iteration of the trolley For the first k The actual speed of the trolley in the next iteration T The time it takes for the motorcycle to complete one cycle of movement; absolute error of velocity integral IAE v The expression used to quantify the cumulative effect of errors over the entire period is as follows: ； Comprehensive speed error index J(k) It is obtained by weighting and summing the root mean square error of speed tracking and the absolute error of speed integral, and then normalizing the dimensions.

3. The method according to claim 1, characterized in that, The iterative convergence criterion is: when the comprehensive velocity error index... J(k) The change is ≤0.001% and the comprehensive velocity error index is met for three consecutive iterations. J(k) When the change is ≤0.001%, the iteration is considered to have converged.

4. The method according to claim 1, characterized in that, The specific steps for constructing the improved iterative learning control law include: Based on the speed tracking deviation and the average command speed of the steady speed segment, normalization is performed, and a speed error weighting term is constructed to eliminate the influence of speed magnitude on the correction effect. The discrete domain PID learning law is calculated based on the speed tracking deviation, and a feedback correction term is constructed to achieve real-time correction of single-cycle error. By adding an error attenuation coefficient, random disturbances caused by measurement noise, load fluctuations, and guide rail friction fluctuations are suppressed, forming an improved iterative learning control law.

5. The method according to claim 1, characterized in that, The method further includes: using the same iterative learning control parameters and servo system tuning parameters, conducting numerical simulation experiments and hardware prototype experiments respectively, to verify the actual control effect of the improved iterative learning control law.

6. The method according to claim 5, characterized in that, Iterative learning control parameters include: proportional learning gain Γ p =0.4, Integral learning gain Γ i =0.08, differential learning gain Γ d =0.05; Error attenuation coefficient α =0.85, weight of feedback correction term β =0.15; System sampling frequency 2000Hz, single motion cycle 0.3s; Servo system tuning parameters include: Current loop: C p =73、 C i =85, bandwidth 1800Hz; speed loop: V p =750、 V i =300, output filter 400Hz; Position loop: P p =300, velocity feedforward coefficient K vff =16384, acceleration feedforward coefficient K aff =50; Motor PID adjustment parameters: K p =2900, K i =50, K d =800.

7. A device for optimizing motor motion curves based on iterative learning, characterized in that, include: The system modeling unit is used to perform system identification and modeling of the absolute gravimeter transmission control system, and to establish a transfer function model that can characterize the dynamic response characteristics of the system. The basic control architecture unit is used to construct a three-level closed-loop control loop of current loop-speed loop-position loop, and introduces speed feedforward compensation and acceleration feedforward compensation to form a servo basic control architecture; the servo basic control architecture serves as the underlying control foundation for vehicle trajectory tracking, providing a stable basic control layer for iterative learning and optimization. The error evaluation construction unit is used to define the comprehensive error evaluation index and the iterative convergence judgment criterion. The comprehensive error evaluation index includes: the root mean square error of velocity following and the absolute error of velocity integral. An improved learning law construction unit is used to construct an improved iterative learning control law by integrating three improvement mechanisms—error normalization, real-time feedback correction, and error decay suppression—on the basis of the traditional PID-type iterative learning law. The expression of the improved iterative learning control law is as follows: ； In the formula, i,j : Discrete-time step index, the first step within a single iteration i , j Each sampling time, v cmd (k,i) : No. k The next iteration, the... i The ideal speed for a motorcycle at any given time v cmd (k+1,i) : No. k+1 The next iteration, the... i The ideal speed of the motorcycle is updated in real time. e(k, i) : No. k The next iteration, the... i Speed ​​tracking error at any given moment T s System sampling period K d Iterative learning of differential gain, Δu pid (k,i) : No. k The next iteration, the... i The increment of the PID controller output at any given time, Γ p ,Γ i These are the proportion and integral of the iterative learning law, respectively. β These are the weighting coefficients for the feedback correction term, used to adjust the degree of influence of the speed loop feedback correction. α This is the error attenuation coefficient, with a value ranging from 0 to 1. i When it is 0, e (k,-1) The value is 0; The iterative trajectory optimization unit is used to take the ideal trajectory of the motorcycle as the initial control command, and to perform multi-cycle iterative learning through an improved iterative learning control law. After each iteration, the comprehensive error evaluation index is calculated, and the iteration is terminated when the iterative convergence judgment criterion is met, and the optimal motorcycle speed motion command is output.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes a computer program, it implements the steps of the motor motion curve optimization method based on iterative learning as described in any one of claims 1 to 6.

9. A computer-readable storage medium storing a computer program, characterized in that, When a computer program is executed by a processor, it implements the steps of the motor motion curve optimization method based on iterative learning as described in any one of claims 1 to 6.

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