Laser communication coarse servo turntable low-speed friction disturbance compensation method and system based on linear active disturbance rejection control

Abstract

The invention discloses a laser communication coarse servo turntable low-speed friction disturbance compensation method based on linear active disturbance rejection control. Belongs to the technical field of laser communication tracking control. Aiming at the problems of crawling jitter, steady-state error increase and insufficient robustness under parameter perturbation caused by coupling of static friction, coulomb friction and viscous friction during low-speed operation of the laser communication coarse servo turntable, firstly, a Stribeck friction model is adopted to accurately describe the low-speed friction nonlinear characteristic of the turntable, and key parameters of the model are identified through experiments; designing a linear active disturbance rejection controller (LADRC) comprising a three-order linear extended state observer (LESO) and a linear error feedback control law (LSEF), estimating total disturbance formed by friction disturbance, parameter perturbation and external disturbance in real time by utilizing the LESO, and dynamically compensating to a control loop; and finally, a parameter setting process is simplified through a bandwidth method, optimization control can be realized only by configuring an observer bandwidth and a controller bandwidth, engineering realization is simple and convenient, and the design requirement of low complexity of laser communication coarse servo is met.

Description

Technical Field

[0001] This invention relates to the field of coarse servo control technology for laser communication, specifically to a method and system for compensating for low-speed frictional disturbances on a coarse servo turntable for laser communication based on linear active disturbance rejection control. Background Technology

[0002] Laser communication systems, with their advantages of high communication speed, large capacity, and strong anti-interference capabilities, are widely used in the field of space communication. The coarse servo turntable in laser communication is a core component of the tracking and aiming system. Its core function is to stabilize the captured target within the subsystem's field of view, providing a fundamental guarantee for the establishment of the fine tracking module and subsequent optical communication links. The coarse servo turntable is characterized by a large working range but relatively low bandwidth. Under low-speed tracking conditions, the frictional nonlinearity of the transmission mechanism becomes a key bottleneck restricting control accuracy.

[0003] This nonlinear friction is caused by the coupling of static friction, Coulomb friction, and viscous friction. Static friction can cause turntable startup lag, Coulomb friction can easily induce low-speed crawling jitter, and viscous friction can amplify position deviation. The combined effect of these three factors causes the turntable to experience tracking lag and steady-state fluctuations, which in severe cases can cause the target to leave the field of view and disrupt the stability of the laser link.

[0004] Existing compensation schemes for low-speed friction in coarse servo turntables have significant limitations: one type is based on PID improvement strategies such as parameter self-tuning and fuzzy PID, which significantly reduce robustness when temperature changes or wear of the mechanism cause perturbations in friction parameters, making it difficult to meet the long-term stable operation requirements of laser communication; the other type is complex nonlinear control strategies such as adaptive control and sliding mode control, which can suppress parameter changes, but require the design of complex adaptive laws or gain switching, and parameter tuning is cumbersome, which contradicts the low-complexity design requirements of the turntable. Summary of the Invention

[0005] To address the issues of creeping jitter, increased steady-state error, and insufficient robustness under parameter perturbations caused by low-speed frictional nonlinear disturbances in coarse servo turntables for laser communication, a low-speed frictional disturbance compensation method is proposed that balances accuracy, robustness, and engineering practicality. This method eliminates the need for a precise turntable model, simplifies parameter tuning, and ensures long-term stable operation of the turntable under complex working conditions, thus providing support for high-precision pointing in laser communication.

[0006] The method includes the following steps: S1. Construct a mathematical model of the controlled object of the laser communication coarse servo turntable system, and derive the state-space equation of the mathematical model. S2. Constructing a low-speed frictional disturbance model for a laser communication coarse servo turntable: The Stribeck friction model is used to describe the nonlinear characteristics of the coupling of static friction, Coulomb friction, and viscous friction in the turntable transmission mechanism. The mathematical expression of the Stribeck friction model is as follows: ; In the formula This represents the total frictional torque. The angular velocity of the turntable; It is a symbolic function; The frictional torque is the Coulomb friction torque. This is the static friction torque; It is the stribeck speed; It is the coefficient of viscous friction; It is an experience index; S3. Design a linear active disturbance rejection controller based on the Stribeck friction model. The linear active disturbance rejection controller includes a linear extended state observer and a linear error feedback control law. S4. The total disturbance of the laser communication coarse servo turntable is estimated in real time through the linear extended state observer. The total disturbance includes frictional disturbances described by the Stribeck friction model, parameter perturbations, and external disturbances. S5. Generate an ideal control quantity using the linear error feedback control law, and perform dynamic compensation by combining the total disturbance estimate output by the linear extended state observer to obtain the final control quantity. Input the final control quantity, i.e., the motor drive voltage, into the airborne photoelectric tracking turntable to achieve low-speed friction disturbance suppression.

[0007] Furthermore, in step S1, the mathematical model of the controlled object is a transfer function from voltage to the motor output angular velocity, and its form is: ; in, This is the open-loop transfer function from voltage to rotational speed; This is the motor drive voltage; For armature winding inductance; For armature winding resistance; It is the moment of inertia; The angular velocity of the turntable; It is the torque constant; It is the back electromotive force constant; For the Laplace operator.

[0008] Furthermore, in step S1, the state-space equation of the mathematical model is in the form of: ; in, For output speed, For acceleration, For the total disturbance estimate, The total disturbance inside and outside the system. For system gain The estimated value.

[0009] Furthermore, the parameters of the Stribeck friction model were obtained through experimental identification, specifically including: S21. Place the laser communication coarse servo turntable in speed closed-loop mode, send linearly increasing speed commands, record the current value when the turntable generates the first identifiable angular displacement, and calculate the static friction torque by combining it with the motor torque constant. ; S22. Set a series of constant angular velocity commands covering the low-speed region of the Stribeck effect and the region dominated by viscous friction. After the turntable speed stabilizes, record the steady-state current data and the actual average speed data, and calculate the Coulomb friction torque by combining the motor torque constant. ; S23. Based on measured friction torque data at different angular velocities, determine the Stribeck characteristic velocity through data fitting. Experience Index and coefficient of viscous friction .

[0010] Furthermore, in step S3, the linear extended state observer is a third-order extended state observer, and its state equation construction process is as follows: Define state variables ,in For the total disturbance, Let ω be the angular velocity of the turntable. Angular acceleration; Establish the state-space equations: ; in, This is the estimated value of the system gain; By establishing a third-order linear extended state observer for the system, we obtain: ; Among them, each level Corresponding to each order The estimated value; for Observed values; The observer gain matrix is... , This represents the observer bandwidth.

[0011] Furthermore, in step S3, the linear error feedback control law is a PD control law, the expression of which is: ; in, Based on the control quantity, Input the angular velocity command. For proportional gain, For differential gain, This refers to the controller bandwidth.

[0012] Furthermore, in step S5, the calculation expression for the final control quantity is: ; in, This is the total perturbation estimate output by the linearly extended state observer. The state variables corresponding to the third-order linear extended state observer The estimated value.

[0013] Furthermore, the parameters of the linear active disturbance rejection controller are tuned using the bandwidth method, specifically including: Set the observer bandwidth of the linearly extended state observer Controller bandwidth of linear error feedback control law ,in and The ratio ranges from 3 to 5; Based on the observer bandwidth Determine the gain matrix of the linear extended state observer Based on the controller bandwidth Determine the proportional gain of the PD control law and differential gain .

[0014] Furthermore, the experience index The value range is 1~2, and the observer bandwidth is... The value range is 200Hz~400Hz, and the controller bandwidth is... The value range is 50Hz~100Hz.

[0015] The beneficial effects of the method are as follows: This invention accurately characterizes the low-speed friction characteristics of the turntable using the Stribeck friction model, and combines it with a linear active disturbance rejection controller to estimate and compensate for the total disturbance in real time. This effectively eliminates low-speed crawling jitter and reduces steady-state error, without relying on a precise turntable model. It also exhibits strong robustness to friction parameter perturbations and external disturbances. Furthermore, the invention simplifies the parameter tuning process using the bandwidth method, making engineering implementation simple and adaptable to the low-complexity design requirements of the turntable. This improves the low-speed control accuracy and stability of the laser communication coarse servo turntable. Attached Figure Description

[0016] Figure 1 This is an overall flowchart of the method described in this invention; Figure 2 This is a model diagram of a torque motor; Figure 3 Scatter plot of the Stribeck friction model; Figure 4 This is a diagram of a linear active disturbance rejection control model. Detailed Implementation

[0017] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the protection scope of the present invention.

[0018] Example 1 This embodiment provides a linear active disturbance rejection control method based on a laser communication coarse servo system. The flow of the method is as follows: Figure 1 As shown, specifically: A mathematical model for a laser communication coarse servo system is established, and the model is as follows: ; in, This is the open-loop transfer function from voltage to rotational speed; This is the motor drive voltage; For armature winding inductance; For armature winding resistance; It is the moment of inertia; This refers to the angular velocity of the motor rotor. It is the torque constant; It is the back electromotive force constant; For the Laplace operator.

[0019] Based on the mathematical model, its state-space equation is: ; in, For output speed, For acceleration, For the total disturbance estimate, The total disturbance inside and outside the system. For system gain The estimated value, control the input voltage This is the motor drive voltage output by the linear active disturbance rejection control. Total perturbation is the core variable that the linear extended state observer needs to estimate in real time.

[0020] The Stribeck friction model parameter data were obtained through actual measurements, and the Stribeck friction mathematical model was obtained by fitting the data using the least squares method. ; In the formula This represents the total frictional torque. This refers to the angular velocity of the motor rotor. It is a symbolic function; The frictional torque is the Coulomb friction torque. This is the static friction torque; It is the stribeck speed; It is the coefficient of viscous friction; It is an experience index.

[0021] A linear active disturbance rejection controller (LADRC) is designed based on the Stribeck friction model. The LADRC includes a linear extended state observer (LESO) and a linear error feedback control law (LSEF).

[0022] Based on the state-space equation of the mathematical model, the observer equation of the Linear Extended State Observer (LESO) is constructed. They are respectively (observed values) ; in, For observer gain, This represents the error in angular velocity observation.

[0023] Design a PD-type linear error feedback control law (LSEF) to achieve compensation in conjunction with the disturbance estimation of a linear extended state observer: For the requirement of turntable angular velocity tracking, the PD control law expression is as follows: ; in, For the ideal control quantity, Input the angular velocity command. For proportional gain, This is the differential gain.

[0024] The input angular velocity signal is introduced into the linear error feedback control law. The input signal, the differential signal of the input signal, and the total disturbance are estimated by the linear extended state observer and fed back to the linear error feedback control law. The voltage signal calculated by the linear error feedback control law is subtracted from the total disturbance estimated by the linear extended state observer and then input into the controlled object to complete the closed-loop control.

[0025] Example 2 This embodiment will be combined with the appendix Figure 2 Appendix Figure 3 and attached Figure 4 Further explanation of Example 1.

[0026] Based on the working principle of the DC torque motor driving motor of the laser communication coarse servo turntable, the core physical equations are established: I. Voltage balance equation: (1) II. Torque Balance Equation: (2) III. Output Torque Equation: (3) IV. Back electromotive force equation: (4) in, This is the motor drive voltage; Armature current; For armature winding inductance; For armature winding resistance; It is the back electromotive force; It is the moment of inertia; This provides the output torque for the motor. For disturbance torque; This refers to the angular velocity of the motor rotor. It is the torque constant; It is the back electromotive force constant; This represents the motor speed.

[0027] Performing a Laplace transform on the above four equations yields the model diagram of the torque motor system as follows: Figure 2 As shown, the open-loop transfer function from the control voltage to the turntable angular velocity is derived: (5) The specific parameters of the turntable motor used in this embodiment are shown in Table 1.

[0028] Table 1:

[0029] Substituting the parameters into the transfer function, we obtain the actual open-loop transfer function: (6) The state-space equations are transformed into design requirements for adaptive linear active disturbance rejection control. The above transfer function is transformed into state-space equations, and the state variables are defined as follows: (7) Its state-space equations are obtained as follows: (8) in, For output speed, For acceleration, For total disturbance estimation, control input The motor drive voltage output by the linear active disturbance rejection control, and the total disturbance. It is the core variable that the linearly extended state observer needs to estimate in real time.

[0030] Stribeck friction model identification process: First is the static friction torque. Identify and place the coarse servo turntable in speed closed-loop mode. The host computer sends a linearly increasing speed command and synchronously records the motor armature current and the turntable angular displacement fed back by the encoder. When the encoder detects the first recognizable angular displacement, record the current at that moment. ; Record the current value of the encoder when it generates the first recognizable angular displacement through multiple tests, take the average value, and calculate: .

[0031] Secondly, there is the Coulomb friction torque. Identify and set multiple sets of constant angular velocity commands to control the turntable to run at a constant speed. After the speed stabilizes, record the steady-state current. ; Calculation: with For example, ,but .

[0032] Finally, the identification of the remaining parameters is based on... Figure 3 Multiple sets of angular velocity-friction torque data are used. The horizontal axis represents the turntable angular velocity, and the vertical axis represents the friction torque. The Stribeck model is fitted using the least squares method. (9) The final model is obtained: ; Design a third-order linear extended state observer for a second-order turntable system: Based on the state-space equations of the mathematical model, construct the observation equations for the linear extended state observer: (10) in, For observer gain, This is the error in angular velocity observation. They are respectively The observed values.

[0033] Set the observer bandwidth ; Pole placement: All three poles of the linearly extended state observer are placed at... That is, the characteristic equation: (11) Calculate the gain: .

[0034] Combination Figure 1A PD-type error feedback control law is designed to compensate for the disturbance estimation of a linear extended state observer. To address the requirement of rotary table angular velocity tracking, an ideal control variable is designed. The expression for the PD-type error feedback control law is: (12) in, Input the angular velocity command. For proportional gain, This is the differential gain.

[0035] Pole configuration is performed using the bandwidth method, and the controller bandwidth is set. ; Calculation parameters: .

[0036] Total perturbation estimated by combining linear extended state observer ,right Dynamic compensation is performed, ultimately driving the motor with the required voltage command: (13) Simplify by substituting parameters: .

[0037] The frictional torque output from the Stribeck friction model is introduced as a disturbance. Figure 2 middle At this point, the system output is acquired in real time by a linearly extended state observer, and the signal is obtained by observing the equations through the linearly extended state observer. The estimated values ​​are respectively and total disturbance ,Will Introduced into the PD-type error feedback control law, the uncompensated ideal control quantity is calculated. Then, using formula (13) to... and The final motor drive voltage was calculated. , The input is fed into the controlled object to drive the system, completing the closed-loop control. This process repeats continuously, achieving high-precision tracking and robust disturbance suppression. A complete system structure diagram is shown below. Figure 4 As shown.

Claims

1. A method for compensating low-speed friction disturbance of a coarse servo turntable in laser communication based on linear active disturbance rejection control, characterized in that, The method comprises the following steps: S1, constructing a mathematical model of a controlled object of a laser communication coarse servo turntable system, and deriving a state space equation of the mathematical model; S2, constructing a low-speed friction disturbance model of the laser communication coarse servo turntable: adopting a Stribeck friction model to describe the nonlinear characteristics of the coupling of static friction, Coulomb friction and viscous friction in the transmission mechanism of the turntable, and the mathematical expression of the Stribeck friction model is: wherein is the total friction torque; is the angular velocity of the turntable; is the sign function; is the coulomb friction torque; is the static friction torque; is the stribeck velocity; is the viscous friction coefficient; is the empirical exponent; S3, designing a linear active disturbance rejection controller based on the Stribeck friction model, the linear active disturbance rejection controller comprising a linear extended state observer and a linear error feedback control law; S4, estimating the total disturbance of the laser communication coarse servo turntable in real time through the linear extended state observer, the total disturbance comprising the friction disturbance described by the Stribeck friction model, parameter perturbation and external disturbance; S5, generating an ideal control quantity by using the linear error feedback control law, and dynamically compensating in combination with the estimated value of the total disturbance output by the linear extended state observer to obtain a final control quantity, inputting the final control quantity, i.e., motor driving voltage, into the airborne photoelectric tracking turntable, and realizing low-speed friction disturbance suppression.

2. The method of claim 1, wherein, In step S1, the mathematical model of the controlled object is a transfer function from voltage to motor output angular velocity, and its form is: ； wherein, is the open loop transfer function from voltage to speed; is the motor drive voltage; is the armature winding inductance; is the armature winding resistance; is the moment of inertia; is the trolley angular velocity; is the torque constant; is the back EMF constant; is the Laplace operator.

3. The method of claim 2, wherein, In step S1, the state space equation of the mathematical model, and its form is: ； where, is the output velocity, is the acceleration, is the total disturbance estimate, is the total disturbance within the system, is the system gain estimate.

4. The method of claim 3, wherein, In step S2, the parameters of the Stribeck friction model are obtained through experimental identification, and specifically include: S21. Put the laser communication coarse servo turntable into the speed closed loop mode, send the linearly increasing speed command, record the current value when the turntable produces the first recognizable angular displacement, and calculate the static friction torque in combination with the motor torque constant ; S22. Set a series of constant angular velocity instructions covering the Stribeck effect low speed area and the viscous friction dominant area, after the speed of the rotating table is stable, record the steady state current data and the actual average speed data, and calculate the Coulomb friction torque in combination with the motor torque constant ; S23. Based on the measured friction torque data at different angular velocities, the Stribeck characteristic velocity is determined by data fitting , the empirical exponent , and the viscous friction coefficient .

5. The method of claim 4, wherein, In step S3, the linear extended state observer is a third-order extended state observer, and its state equation construction process is: Defining state variables where is the total disturbance, is the turntable angular velocity, is the angular acceleration; The state space equation is established: ； wherein is a system gain estimate value; A third-order linear extended state observer is established for the system to obtain: ； wherein each order corresponding to each order of the estimate; is the observation value of is the observer gain matrix, , is the observer bandwidth.

6. The method of claim 5, wherein, In step S3, the linear error feedback control law is a PD control law, and its expression is: ； wherein, is a base control quantity, is an angular velocity command input, is a proportional gain, is a derivative gain, is a controller bandwidth.

7. The method of claim 6, wherein, In step S5, the calculation expression of the final control quantity is: ； wherein is the total disturbance estimate output by the linear extended state observer, is the estimate of the corresponding state variable of the third order linear extended state observer.

8. The method of claim 7, wherein, The parameters of the linear active disturbance rejection controller are set by a bandwidth method, and specifically include: Setting an observer bandwidth of a linear extended state observer and a controller bandwidth of a linear error feedback control law wherein and ranges from 3 to 5; based on the observer bandwidth determining a gain matrix of a linear extended state observer based on the controller bandwidth determining a proportional gain of a PD control law and a derivative gain .

9. The method of claim 8, wherein, Experience index is in the range of 1-2, the observer bandwidth is in the range of 200-400 Hz, the controller bandwidth is in the range of 50-100 Hz.

10. A low-speed friction disturbance compensation system for a laser communication coarse servo turntable based on linear active disturbance rejection control, characterized in that, including: The friction model construction module is used to adopt the Stribeck friction model to describe the low-speed friction disturbance characteristics of the turntable; The linear active disturbance rejection control module comprises a linear extended state observer and a linear error feedback control law, the linear extended state observer is used to estimate the total disturbance of the turntable in real time, and the linear error feedback control law is used to generate an ideal control quantity and dynamically compensate in combination with the estimated value of the total disturbance; the execution module is used to receive the final control quantity output by the linear active disturbance rejection control module, drive the turntable to run, and suppress the low-speed friction disturbance.

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