Turntable motion control method based on time-varying disturbance compensation and predictive control

Abstract

A turntable motion control method based on time-varying disturbance compensation and predictive control belongs to the field of turntable control technology. This invention addresses the problem that existing turntable control methods, when incorporating disturbance observers and model predictive control, struggle to balance control accuracy and system robustness. The method includes: establishing a nonlinear dynamic model based on the relationship between the actual values ​​of the turntable pitch and yaw angles and the actual value of the disturbance vector; obtaining the disturbance vector estimate by solving the time-domain equation relationship between the actual and estimated values ​​of the time-varying disturbance vector; adjusting the nominal control constraint range based on the disturbance vector estimate, establishing a cost function, and calculating the current nominal control signal with the objective of minimizing pitch and yaw tracking errors; and finally, combining the disturbance vector estimate to obtain the turntable control torque. This invention is applicable to scenarios requiring high-precision pointing control, such as space communication and target surveillance.

Description

Technical Field

[0001] This invention relates to a turntable motion control method based on time-varying disturbance compensation and predictive control, belonging to the field of turntable control technology. Background Technology

[0002] In industrial production and high-end equipment manufacturing, turntables, as core components for achieving precise positioning and motion tracking, are widely used in scenarios such as satellite communication antenna pointing, radar target tracking, laser cutting, and precision instrument testing. These applications place stringent demands on the control performance of turntables: for example, in satellite communication, the turntable must drive the antenna to achieve a pointing accuracy within 0.1° under strong airflow interference; otherwise, signal transmission will be interrupted. However, in practical engineering, the control effect of turntables is often constrained by two major practical problems, severely affecting the actual servo accuracy:

[0003] First, interference in complex environments is difficult to eliminate. Turntables encounter various unpredictable interference factors during operation: gear backlash and bearing friction in mechanical transmissions change with temperature; outdoor turntables are subject to wind and vibration; and electromagnetic interference from the motor itself during high-speed rotation affects control accuracy. While traditional proportional-integral-derivative (PI-DI) control and control based on linear quadratic regulators can achieve basic control in ideal environments, they often face the dilemma of "difficult parameter tuning" when dealing with such time-varying disturbances—overly aggressive parameters easily lead to oscillations, while overly conservative parameters cannot offset the disturbances, resulting in a significant decrease in actual motion accuracy. Practical turntable systems urgently need robust control designs for time-varying disturbance compensation to ensure the instantaneous and steady-state accuracy of turntable operation.

[0004] Secondly, the physical saturation constraints of the actuators limit their performance. Actuators such as the turntable's drive motor and reducer have clearly defined output limits. For example, the motor's maximum torque cannot exceed the design value, otherwise the coil will burn out; the reducer's speed exceeding a critical value will cause resonance. To avoid actuator overload, traditional control strategies typically limit the input amplitude of the control signal, especially in situations with interference. The original control input range is further narrowed to account for the amplitude of interference compensation, resulting in an overly "conservative" servo strategy. While this approach ensures equipment safety, it sacrifices control performance: in scenarios requiring rapid attitude adjustments (such as a missile tracking turntable responding to target maneuvers), the limited control signal leads to response lag and missed tracking; while in situations with minimal interference, overly tight constraints cause the turntable to move stiffly, failing to fully utilize the actuator's performance.

[0005] In recent years, the engineering community has attempted to address these issues by introducing disturbance observers and model predictive control (MDC). Disturbance observers, by estimating disturbances and generating compensation signals, can effectively counteract the effects of friction, wind, and other factors. MDC, on the other hand, can consider actuator constraints in real time during the control process, avoiding overload. However, combining the two introduces new contradictions: if the maximum output of the actuator is directly used as the upper limit of MDC (an aggressive strategy), the total control signal will exceed the actuator's capacity when the disturbance estimated by the disturbance observer suddenly increases, leading to motor saturation. Conversely, if the control range of MDC is significantly reduced to allow sufficient safety margin (a conservative strategy), the performance bottleneck of traditional control will reappear. In practical engineering applications, how to ensure equipment safety and maximize performance of the turntable under the dual constraints of complex disturbances and actuator constraints has become a pressing problem. Existing control schemes either lack reliability due to neglecting actual operating conditions or sacrifice accuracy due to excessive conservatism, failing to meet the "high precision, high reliability, and fast response" requirements of high-end equipment for turntable control.

[0006] Therefore, there is an urgent need for a turntable motion control method that can maximize control performance while handling constraints and disturbances. Summary of the Invention

[0007] To address the problem that existing turntable control methods, when incorporating disturbance observers and model predictive control, struggle to balance control accuracy and system robustness, this invention provides a turntable motion control method based on time-varying disturbance compensation and predictive control.

[0008] The present invention provides a turntable motion control method based on time-varying disturbance compensation and predictive control, comprising:

[0009] Based on the actual value of the turntable's pitch angle and actual yaw angle A nonlinear dynamic model is established based on the relationship between the actual value of the disturbance vector and the model, and then linearized to obtain the corresponding linear model.

[0010] Then, establish the temporal filtering relationship between the actual value and the estimated value of the interference vector, and based on the actual value of the pitch angle. and actual yaw angle Obtain the interference estimate for the corresponding channel;

[0011] Adjust the nominal control constraint range based on the interference vector estimate, establish a cost function, calculate the current nominal control signal with the goal of minimizing the pitch and yaw tracking errors, and then obtain the turntable control torque by combining the interference vector estimate.

[0012] According to the turntable motion control method based on time-varying disturbance compensation and predictive control of the present invention, the nonlinear dynamic model includes:

[0013] Pitch angle dynamics model:

[0014] ;

[0015] Yaw angle dynamics model:

[0016] ;

[0017] In the formula For pitch rotation inertia, For yaw moment of inertia, For the quality of the turntable, Let be the distance from the center of mass of the turntable to the axis of rotation. This is the pitch damping coefficient. This is the yaw damping coefficient. It is the acceleration due to gravity. For pitch input torque, For yaw input torque, This represents the actual value of pitch interference. This represents the actual value of yaw interference.

[0018] The turntable motion control method based on time-varying disturbance compensation and predictive control according to the present invention uses a first-order linear approximation and ignores small terms. The pitch angle linear model and yaw angle linear model are obtained:

[0019] ,

[0020] ,

[0021] In the formula These are the linearization coefficients.

[0022] According to the turntable motion control method based on time-varying disturbance compensation and predictive control of the present invention, a system state-space model is established:

[0023] ,

[0024] In the formula For state variables, , For time, Here is the state transition matrix. For the input matrix, For turntable control torque, ; For interference vectors, ;

[0025] ;

[0026] Turntable control torque Satisfy actuator saturation constraints:

[0027] ,

[0028] In the formula For the actuator saturation constraint set, For the set of real numbers, For maximum input torque, , This is the maximum input torque for pitch. This is the maximum input torque for yaw.

[0029] According to the turntable motion control method based on time-varying disturbance compensation and predictive control of the present invention, the time-domain filtering relationship between the actual value of the disturbance vector and the estimated value of the disturbance vector is as follows:

[0030] ,

[0031] In the formula It is a bounded time-varying function. , This is the estimated value for pitch interference;

[0032] Combining the pitch angle linear model, we obtain:

[0033] ,

[0034] In the formula For pitch nominal control signal;

[0035] By using the integration by parts method, the implementation form of the pitch channel time-varying uncertainty and disturbance estimator is obtained:

[0036] ,

[0037] The formula is for Integral variable within the interval;

[0038] Similarly, the implementation of the time-varying uncertainty and disturbance estimator for the yaw channel is obtained:

[0039] ,

[0040] In the formula This is an estimate of the yaw interference. This is the nominal yaw control signal.

[0041] According to the turntable motion control method based on time-varying disturbance compensation and predictive control of the present invention, the nominal control constraint range is adjusted according to the disturbance vector estimate:

[0042] ,

[0043] In the formula For the nominal control constraint set, For nominal control signals, , For the interference estimation vector, , A constant vector, , The pitch contraction constant, is the yaw contraction constant.

[0044] According to the turntable motion control method based on time-varying disturbance compensation and predictive control of the present invention, a cost function is established. :

[0045] ,

[0046] In the formula To track errors, , The expected value of the pitch angle. This is the expected value of the yaw angle. To predict duration, Let the process cost function be... For the terminal penalty function: To predict time variables in the time domain, ;

[0047] , ,

[0048] In the formula Here is the error weight matrix. For the input weight matrix, This is the terminal weight matrix.

[0049] According to the turntable motion control method based on time-varying disturbance compensation and predictive control of the present invention, the nominal control signal is calculated. The optimization problem is expressed as:

[0050] ,

[0051] In the formula State variables The predicted value, For robust terminal regions.

[0052] According to the turntable motion control method based on time-varying disturbance compensation and predictive control of the present invention, the turntable control torque... for:

[0053] .

[0054] The beneficial effects of this invention are as follows: This invention constructs a two-degree-of-freedom control framework comprising a time-varying uncertainty and disturbance estimator and a model predictive control with flexible constraints. By using the time-varying uncertainty and disturbance estimator to estimate and compensate for disturbances in real time, transient peak phenomena are avoided, ensuring the reliability of disturbance estimation. The flexible constraint mechanism dynamically adjusts the nominal input range of the model predictive control based on the output of the time-varying uncertainty and disturbance estimator, ensuring that actuator constraints are satisfied while avoiding performance degradation caused by excessively tight offline constraints. This invention enables high-precision motion control of a turntable even in the presence of disturbances and actuator saturation constraints, improving the system's robustness and control accuracy. It can be widely applied in scenarios requiring high-precision pointing control, such as space communication and target surveillance.

[0055] The method of this invention is applicable to equipment that requires high-precision motion control, such as pointing turntables, target tracking turntables, and laser processing turntables in space optical communication. Attached Figure Description

[0056] Figure 1 This is a flowchart of the turntable motion control method based on time-varying disturbance compensation and predictive control as described in this invention. Detailed Implementation

[0057] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0058] Specific Implementation Method 1: Combination Figure 1 As shown, this invention provides a turntable motion control method based on time-varying disturbance compensation and predictive control, comprising:

[0059] Based on the actual value of the turntable's pitch angle and actual yaw angle A nonlinear dynamic model is established based on the relationship between the actual value of the disturbance vector and the model, and then linearized to obtain the corresponding linear model.

[0060] Then, establish the temporal filtering relationship between the actual value and the estimated value of the interference vector, and based on the actual value of the pitch angle. and actual yaw angle Obtain the interference estimate for the corresponding channel;

[0061] Adjust the nominal control constraint range based on the interference vector estimate, establish a cost function, calculate the current nominal control signal with the goal of minimizing the pitch and yaw tracking errors, and then obtain the turntable control torque by combining the interference vector estimate.

[0062] This implementation addresses the challenge of balancing control accuracy and system robustness when the system simultaneously faces actuator constraints and various uncertainties and disturbances. A robust predictive control framework based on an uncertainty and disturbance estimator is designed to address this issue. Furthermore, to ensure the control input signal satisfies actuator constraints, a safe and flexible predictive control constraint is designed to adjust the amplitude of the input signal.

[0063] This implementation is based on a time-varying disturbance estimator and robust predictive control with a flexible mechanism. Its flexible mechanism eliminates the use of commonly determined offline tightening boundaries, preventing actuator saturation while generating a more reasonable range for nominal control. The time-varying disturbance estimator provides reliable disturbance estimation and compensation without adverse transient responses, helping to determine the reasonable range of predictive control and reducing the risk of constraint violations. Its flexible two-degree-of-freedom structure enables the predictive control component to achieve high-precision servo control under constraints, with the estimator ensuring active estimation and suppression of disturbances. This achieves the highest possible servo accuracy under different disturbance conditions, exhibiting excellent performance in turntable motion control.

[0064] In practical implementation, the motion input signals from the host computer, including reference attitude and velocity, are first acquired as the system input for the inner loop controller. Measurement data from the turntable's onboard sensors are received, including encoder angle measurements and angular velocities acquired by the microelectromechanical inertial measurement unit (MEMS). In the time-varying interference estimation stage, a time-varying uncertainty and interference estimator is designed based on an estimation model with clear bandwidth characteristics in the frequency domain to estimate the interference experienced by the turntable. In the constraint control step, the constraint range of the nominal control is dynamically adjusted according to the interference estimate. In the model predictive control step, model predictive control is designed based on flexible time-varying elastic constraints to obtain the nominal control signal. In the control signal generation step, the total control signal is generated based on the nominal control and interference estimates to achieve motion control of the turntable. The details are as follows:

[0065] Command Reception and Target Parsing. First, motion commands are received from the host computer or external control source. These commands contain key information such as target position, velocity, and acceleration. The commands are then parsed to clarify the motion target state that the turntable needs to achieve, providing a basis for the subsequent development of control strategies.

[0066] Model building and state estimation. Based on the mechanical structure and motor characteristics of the turntable, an accurate mathematical model is established, covering the dynamics and kinematics of the turntable. Simultaneously, using sensor feedback (such as angles and speeds measured by encoders), combined with the model, the current actual state of the turntable is estimated in real time, providing accurate system state information for the control algorithm.

[0067] Furthermore, the nonlinear dynamic model includes:

[0068] Pitch angle dynamics model:

[0069] ;

[0070] Yaw angle dynamics model:

[0071] ;

[0072] In the formula For pitch rotation inertia, For yaw moment of inertia, For the quality of the turntable, Let be the distance from the center of mass of the turntable to the axis of rotation. This is the pitch damping coefficient. This is the yaw damping coefficient. It is the acceleration due to gravity. For pitch input torque, For yaw input torque, This represents the actual value of pitch interference. This represents the actual value of yaw interference. and The lumped disturbances include external disturbances, residual higher-order errors from linearization, and uncertainties caused by changes in the operating point.

[0073] By using a first-order linear approximation and ignoring small terms The pitch angle linear model and yaw angle linear model are obtained:

[0074] ,

[0075] ,

[0076] In the formula These are the linearization coefficients.

[0077] Establish the system state-space model:

[0078] ,

[0079] In the formula For state variables, , For time, Here is the state transition matrix. For the input matrix, For turntable control torque, ; For interference vectors, ;

[0080] ;

[0081] Turntable control torque Satisfy actuator saturation constraints:

[0082] ,

[0083] In the formula For the actuator saturation constraint set, For the set of real numbers, For maximum input torque, , This is the maximum input torque for pitch. This is the maximum input torque for yaw.

[0084] Disturbance estimation and compensation calculation. A time-varying uncertainty and disturbance estimator is used to estimate various disturbances (including external environmental disturbances, friction, etc.) in the control system in real time. Based on the estimation results, the amount of disturbance requiring compensation is calculated for subsequent control signal correction to counteract the impact of disturbances on the turntable motion.

[0085] Furthermore, a time-varying uncertainty and interference estimator is designed to avoid transient peak phenomena and ensure reliable interference estimation. For the pitch channel, the time-domain filtering relationship between the actual value of the interference vector and the estimated value of the interference vector is as follows:

[0086] ,

[0087] In the formula It is a bounded time-varying function. , This is the estimated value for pitch interference;

[0088] Combining the pitch angle linear model, we obtain:

[0089] ,

[0090] In the formula For pitch nominal control signal;

[0091] By using the integration by parts method, the implementation form of the pitch channel time-varying uncertainty and disturbance estimator is obtained:

[0092] ,

[0093] The formula is for The integral variable within the interval is used to calculate Points earned during the period;

[0094] Similarly, the implementation of the time-varying uncertainty and disturbance estimator for the yaw channel is obtained:

[0095] ,

[0096] In the formula This is an estimate of the yaw interference. This is the nominal yaw control signal.

[0097] Elastic constraint boundary generation. To ensure that the total control signal satisfies the input, the predictive control boundary needs to adapt to the output of the disturbance estimator. Therefore, this implementation calculates a predictive control boundary that does not violate the system input constraints based on the real-time output of the disturbance estimator. This boundary will be used in subsequent predictive control signal generation, providing robust boundary guarantees for the predictive control optimization problem.

[0098] Based on the time-varying uncertainty and the output of the disturbance estimator, the nominal control range is dynamically adjusted to satisfy actuator constraints. The nominal control constraint range is adjusted according to the disturbance vector estimate as follows:

[0099] ,

[0100] In the formula For the nominal control constraint set, For nominal control signals, , For the interference estimation vector, , This is a constant vector used to ensure the recursive feasibility of model predictive control. , The pitch contraction constant, is the yaw contraction constant.

[0101] Predictive control signal generation. Model predictive control with flexible constraints generates a nominal control signal that satisfies actuator constraints and system performance requirements based on the target state, the current estimated system state, and disturbance compensation. Based on the predicted future motion state of the turntable, an optimization algorithm solves for the optimal control input sequence, from which the control signal for the current moment is selected for output.

[0102] Furthermore, a model predictive control based on flexible time-varying elastic constraints is designed to maximize the overall performance of the nominal closed-loop system. A cost function is established. :

[0103] ,

[0104] In the formula To track errors, , The expected value of the pitch angle. This is the expected value of the yaw angle. To predict duration, Let the process cost function be... For the terminal penalty function: To predict time variables in the time domain, ;

[0105] , ,

[0106] In the formula Here is the error weight matrix. For the input weight matrix, This is the terminal weight matrix.

[0107] Calculate the nominal control signal The optimization problem is expressed as:

[0108] ,

[0109] In the formula State variables The predicted value, For robust terminal regions.

[0110] Signal synthesis and drive output. The nominal signal generated by predictive control and the interference compensation signal calculated by the interference estimator are synthesized to obtain the final total control signal acting on the turntable actuator (such as a motor driver). The actuator drives the turntable motor according to the total control signal, causing the turntable to move according to the predetermined target.

[0111] Turntable control torque for:

[0112] .

[0113] Control torque of the turntable The input is fed into the actual system to achieve motion control response of the turntable.

[0114] Feedback monitoring and adjustment. During the turntable's movement, sensors continuously acquire feedback on the turntable's actual motion status, such as position and speed. This feedback information is compared with the target state. If a deviation is detected, the system returns to the disturbance estimation and compensation calculation step to adjust the control strategy, ensuring the turntable always moves towards the target state, thus achieving closed-loop control.

[0115] While the invention has been described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the invention. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that different dependent claims and features described herein can be combined in ways different from those described in the original claims. It is also understood that features described in conjunction with individual embodiments can be used in other described embodiments.

Claims

1. A method for motion control of a turntable based on time-varying disturbance compensation and predictive control, characterized in that, include: According to the actual value of the tilt angle of the turntable and the actual value of the yaw angle A nonlinear dynamic model is established according to the relationship between the actual value of the interference vector and the actual value of the tilt angle of the turntable, and linearization is performed to obtain the corresponding linear model; Then, establish the temporal filtering relationship between the actual value and the estimated value of the interference vector, and based on the actual value of the pitch angle. and actual yaw angle Obtain the interference estimate for the corresponding channel; Adjust the nominal control constraint range based on the interference vector estimate, establish a cost function, calculate the current nominal control signal with the goal of minimizing the pitch and yaw tracking errors, and then obtain the turntable control torque by combining the interference vector estimate. Adjust the nominal control constraint range based on the disturbance vector estimate: ， In the formula For the nominal control constraint set, For nominal control signals, , For pitch nominal control signal, This is the nominal yaw control signal; For maximum input torque, For the interference estimation vector, , This is the estimated value for pitch disturbance. This is an estimate of the yaw interference. A constant vector, , The pitch contraction constant, is the yaw contraction constant.

2. The turntable motion control method based on time-varying disturbance compensation and predictive control according to claim 1, characterized in that, Nonlinear dynamic models include: Pitch angle dynamics model: ； Yaw angle dynamics model: ； In the formula For pitch rotation inertia, For yaw moment of inertia, For the quality of the turntable, Let be the distance from the center of mass of the turntable to the axis of rotation. This is the pitch damping coefficient. This is the yaw damping coefficient. It is the acceleration due to gravity. For pitch input torque, For yaw input torque, This represents the actual value of pitch interference. This represents the actual value of yaw interference.

3. The turntable motion control method based on time-varying disturbance compensation and predictive control according to claim 2, characterized in that, By using a first-order linear approximation and ignoring small terms The pitch angle linear model and yaw angle linear model are obtained: ， ， In the formula These are the linearization coefficients.

4. The turntable motion control method based on time-varying disturbance compensation and predictive control according to claim 3, characterized in that, Establish the system state-space model: ， In the formula For state variables, , For time, Here is the state transition matrix. For the input matrix, For turntable control torque, ; For interference vectors, ; ； Turntable control torque Satisfy actuator saturation constraints: ， In the formula For the actuator saturation constraint set, For the set of real numbers, , This is the maximum input torque for pitch. This is the maximum input torque for yaw.

5. The turntable motion control method based on time-varying disturbance compensation and predictive control according to claim 4, characterized in that, The time-domain filtering relationship between the actual value and the estimated value of the interference vector is as follows: ， In the formula It is a bounded time-varying function. ; Combining the pitch angle linear model, we obtain: ； By using the integration by parts method, the implementation form of the pitch channel time-varying uncertainty and disturbance estimator is obtained: ， The formula is For Integral variable within the interval Similarly, the implementation of the time-varying uncertainty and disturbance estimator for the yaw channel is obtained: 。 6. The turntable motion control method based on time-varying disturbance compensation and predictive control according to claim 5, characterized in that, establishing a cost function : ， In the formula To track errors, , The expected value of the pitch angle. This is the expected value of the yaw angle. To predict duration, Let the process cost function be... For the terminal penalty function: To predict time variables in the time domain, ; ， ， In the formula Here is the error weight matrix. For the input weight matrix, This is the terminal weight matrix.

7. The turntable motion control method based on time-varying disturbance compensation and predictive control according to claim 6, characterized in that, The calculation of the nominal control signal The optimization problem is formulated as: ， In the formula State variables The predicted value, For robust terminal regions.

8. The turntable motion control method based on time-varying disturbance compensation and predictive control according to claim 7, characterized in that, Turret control torque Is: 。

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