Expansion state observer control method and system based on airborne photoelectric tracking system

Abstract

The invention discloses an extended state observer control method and system based on an airborne photoelectric tracking system. Belongs to the technical field of servo control systems. The technical problem that the tracking precision is reduced due to the influence of attitude disturbance and high-frequency vibration in an airborne photoelectric tracking system is solved. Establishing a mathematical model of the airborne photoelectric tracking system; obtaining a state-space equation of the airborne photoelectric tracking system according to the mathematical model; introducing the differential equation of the first-order filter into the state-space equation of the airborne photoelectric tracking system, and reconstructing a fifth-order extended state observer; carrying out Lyapunov stability proving on the five-order extended state observer, solving a condition enabling the five-order extended state observer to have asymptotic stability, and adjusting the five-order extended state observer according to the condition; and designing a speed loop controller according to an expected frequency method, introducing the speed observed by the five-order extended state observer into the controller through feedback, and finally realizing a system closed loop.

Description

Technical Field

[0001] The present invention belongs to the technical field of servo control systems, and in particular relates to an extended state observer control method and system based on an airborne optoelectronic tracking system. Background Art

[0002] High-precision optoelectronic tracking systems offer significant application prospects in military fields such as laser communications and laser weapons, due to their advantages in precise pointing and stable tracking of targets. However, whether on airborne, satellite-borne, or missile-borne motion platforms, they are inevitably affected by reduced tracking accuracy caused by internal and external disturbances in the system. In closed-loop systems, current servo control algorithms are primarily based on PID control. However, in terms of disturbance rejection, traditional PID algorithms have difficulty effectively suppressing nonlinear disturbances of the controlled object. Among today's advanced control algorithms, the extended state observer (ESO) is widely used in various practical projects due to its strong disturbance rejection capabilities, lack of need for precise disturbance modeling, and simple parameter adjustment. Actual airborne platforms inevitably produce high-frequency vibrations, but the extended state observer's disturbance rejection capability is relatively poor when dealing with high-frequency signals. Summary of the Invention

[0003] In order to solve the technical problem that the tracking accuracy of an airborne optoelectronic tracking system is reduced due to the influence of attitude disturbance and high-frequency vibration, the present invention provides an extended state observer control method and system based on the airborne optoelectronic tracking system.

[0004] The method comprises the following steps: S1. Establish a mathematical model of the airborne optoelectronic tracking system; S2. deriving a state space equation of the airborne optoelectronic tracking system based on the mathematical model of step S1; S3. Introduce the differential equation of the first-order filter into the state space equation of the airborne electro-optical tracking system and reconstruct the fifth-order extended state observer; S4. Performing a Lyapunov stability proof on the fifth-order extended state observer constructed in step S3, solving a condition that makes the fifth-order extended state observer asymptotically stable, and adjusting the fifth-order extended state observer based on the condition to make it asymptotically stable; S5. Design a speed loop controller based on the expected frequency method, and introduce the speed observed by the fifth-order extended state observer into the speed loop controller through feedback, ultimately achieving overall closed-loop control including the speed loop controller, the fifth-order extended state observer, and the controlled object.

[0005] Furthermore, the mathematical model of the airborne optoelectronic tracking system is specifically as follows: ;in, From the current To speed The closed-loop transfer function of is the output speed; is the input current; is the proportionality coefficient; is the motor torque constant; is the integration coefficient; is the motor moment of inertia; is the winding inductance; is the Laplace variable; is the armature resistance; is the back electromotive force constant.

[0006] Furthermore, the state space equation of the airborne optoelectronic tracking system is specifically: ; in, 、 、 They represent velocity, acceleration, and jerk respectively; 、 、 Respectively 、 、 The derivative of ; ; ; ; is the equivalent current disturbance; is the derivative of the input current.

[0007] Further, step S3 is specifically as follows: S31, let the total disturbance inside and outside the system be , the expanded state space equation is established as: ;in, is the derivative of the total disturbance inside and outside the system; S32, according to the above formula, a fourth-order extended state observer is established, through Conduct; among them, is the output speed of the controlled object; 、 、 、 System status 、 、 and the total disturbance Observed values ​​of 、 、 Indicates velocity, acceleration, and jerk; 、 、 and is the observer gain to be designed; is the error between the observed speed and the actual speed; S33, introducing the differential equation of the first-order filter into the expanded state space, and re-obtaining the expanded state space equation of the new system; S34. Establish a fifth-order extended state observer based on the extended state space equation of the new system.

[0008] Furthermore, the condition for the fifth-order extended state observer to be asymptotically stable is: ,in, is the fifth-order extended state observer system matrix; is the output matrix of the fifth-order extended state observer; is the fifth-order extended state observer gain; is a symmetric matrix; is the unit diagonal matrix.

[0009] Furthermore, the transfer function of the speed loop controller is: ;in, is the speed loop controller gain; and is the time constant of the speed loop controller; is the time constant of the current loop closed-loop transfer function.

[0010] The system comprises: Module for building mathematical models of airborne electro-optical tracking systems; A module for deriving a state space equation of an airborne electro-optical tracking system according to the mathematical model; The differential equation of the first-order filter is introduced into the state space equation of the airborne electro-optical tracking system, and the module of the fifth-order extended state observer is reconstructed; A module for performing Lyapunov stability proof on the fifth-order extended state observer, solving a condition for making the fifth-order extended state observer asymptotically stable, and adjusting the fifth-order extended state observer based on the condition to make it asymptotically stable; The speed loop controller is designed according to the expected frequency method, and the speed observed by the fifth-order extended state observer is introduced into the speed loop controller through feedback. Finally, a module of overall closed-loop control including the speed loop controller, the fifth-order extended state observer and the controlled object is realized.

[0011] The beneficial effects of the method of the present invention are: Compared with the traditional PID algorithm, the present invention has better suppression capabilities for posture disturbances and high-frequency vibrations, and can effectively improve the tracking accuracy of the photoelectric tracking system.

[0012] The newly designed extended state observer can simultaneously resist low-frequency and high-frequency interference, is easy to adjust parameters and is applicable to various actual working conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 This is a flow chart of an extended state observer control method based on an airborne optoelectronic tracking system in an embodiment of the present invention; Figure 2 A diagram showing a torque motor model in an embodiment of the present invention; Figure 3 This is a model diagram of the controlled object in an embodiment of the present invention. DETAILED DESCRIPTION

[0014] The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0015] Example 1 This embodiment provides an extended state observer control method based on an airborne optoelectronic tracking system. The process of the method is as follows: Figure 1 As shown, specifically: Step 1: Establish a mathematical model of the photoelectric tracking system. The model is: ; in, From the current To speed The closed-loop transfer function of is the output speed; is the input current; is the proportionality coefficient; is the motor torque constant; is the integration coefficient; is the motor moment of inertia; is the winding inductance; is the Laplace variable; is the armature resistance; is the back electromotive force constant.

[0016] Step 2: Based on the mathematical model of step 1, the state space equation is: ; in, 、 、 They represent velocity, acceleration, and jerk respectively; 、 、 Denote their derivatives respectively; ; ; ; ; is the equivalent current disturbance; is the derivative of the input current.

[0017] Step 3: Introduce the differential equation of the first-order filter into the state space equation of the airborne electro-optical tracking system and reconstruct the fifth-order extended state observer.

[0018] Let the total disturbance inside and outside the system be , the expanded state space equation is established as: ;in, is the derivative of the total disturbance inside and outside the system; According to the above formula, the fourth-order extended state observer is established as: ; in, is the output speed of the controlled object; 、 、 Indicates speed, acceleration, jerk; output 、 、 、 They are 、 、 and the total disturbance Observed values ​​of 、 、 and is the observer gain to be designed; is the error between the observed speed and the actual speed; then the first-order filter is introduced into the state space equation of the original system to reconstruct the fifth-order extended state observer.

[0019] Step 4: Perform Lyapunov stability proof on the fifth-order extended state observer constructed in step S3, solve the conditions that make the fifth-order extended state observer asymptotically stable, and adjust the fifth-order extended state observer based on this condition to make it asymptotically stable.

[0020] Choose the Lyapunov function as: ;in, Indicates state error; represents a symmetric matrix. Apply the above formula (12) to time Taking the derivative we get: ; The error matrix of the observer is: ; in, is the fifth-order extended state observer system matrix; is the output matrix of the fifth-order extended state observer; is the gain of the fifth-order extended state observer; substituting the observer error matrix into formula (13) we can obtain: ; In order to ensure the asymptotic stability of the observer, To be negative definite, by reasonably adjusting the observation gain It can be achieved.

[0021] Step 5: Design the speed loop controller according to the expected frequency method, and introduce the speed observed by the extended state observer into the speed loop controller through feedback, finally realizing the closed loop of the system.

[0022] The closed-loop transfer function of the current loop can be equivalent to a first-order inertia link. The controlled object is corrected into a typical type II system using the expected frequency method. The transfer function of the speed loop controller is: ; in, is the controller gain; and is the controller time constant; is the time constant of the current loop closed-loop transfer function.

[0023] Compared with the traditional PID algorithm, the method of the present invention has better suppression capabilities for posture disturbances and high-frequency vibrations, and can effectively improve the tracking accuracy of the photoelectric tracking system.

[0024] The newly designed extended state observer can simultaneously resist low-frequency and high-frequency interference, is easy to adjust parameters and is applicable to various actual working conditions.

[0025] Example 2 This embodiment combines the attached Figure 2 and attached Figure 3 Further explanation of Example 1.

[0026] Step 1: According to the principle of DC torque motor: ; ; ; ; in: is the voltage across the armature; is the armature current, is the armature resistance; is the winding inductance; is the back electromotive force of the winding under the action of the magnetic field; is the motor output speed; is the back electromotive force constant; is the sum of the disturbance torques; is the motor moment of inertia, is the motor output torque; is the motor torque constant.

[0027] Perform Laplace transform on the above formulas (1) to (4) respectively, and obtain the model diagram of the torque motor system as shown below: Figure 2 As shown, on this basis, the current loop PI controller is introduced, as shown Figure 3 As shown, the final Mersenne gain formula can be obtained from the current To speed The closed-loop transfer function for: ; in, is the proportionality coefficient; is the integration coefficient.

[0028] Step 2, according to Figure 3 Perform system disturbance analysis, Figure 3 in is the sum of the motor torque disturbances, is the sum of the carrier disturbances, let , , we can get the following formula: ; ; ; Combining equations (7), (8) and (9), we can obtain: ; ; From formulas (9) and (10), it can be seen that whether it is a motor disturbance or a carrier disturbance, it can be equivalent to an equivalent current disturbance at the input end of the controlled object. At this time, by designing an observer By eliminating the disturbance, the disturbance can be suppressed, thereby improving the tracking accuracy of the optoelectronic system.

[0029] According to the third-order mathematical model of the optoelectronic tracking system (controlled object) obtained in step 1, it is converted into the state space equation as follows: ; in, 、 、 They represent velocity, acceleration, and jerk respectively; 、 、 Denote their derivatives respectively; ; ; ; ; is the equivalent current disturbance; is the derivative of the input current.

[0030] It can also be expressed as , represents the total disturbance inside and outside the system, where , For time.

[0031] Step 3: Based on the state space equation obtained in step 2, let the total disturbance inside and outside the system be , establish the expanded state space as: ;in, is the derivative of the total disturbance of the system; According to formula (12), the fourth-order extended state observer is established as: ; in, is the output speed of the controlled object; is the input current of the controlled object; 、 、 Indicates speed, acceleration, jerk; output 、 、 、 They are 、 、 and the total disturbance Observed values ​​of 、 、 and is the observer gain to be designed; is the error between the observed speed and the actual speed.

[0032] In the actual system, the high-speed flying body will inevitably produce high-frequency vibration, and this vibration is bound to affect the tracking accuracy of the optoelectronic tracking system. The observer gain of ESO is very large when it is designed. is the highest gain. Due to the existence of this gain, The high frequency components in the It will be passed to the remaining state variables in turn, and each state variable also contains Gain, high frequencies will be amplified, and the speed observed by the observer will be seriously affected by the high-frequency components.

[0033] In order to solve this problem, the differential equation of the first-order filter is introduced into the original state space. At this time, the composite system composed of the state equation of the original system and the differential equation of the filter is reconstructed into a fifth-order ESO to suppress high-frequency vibration.

[0034] The differential equation defining a first-order filter is as follows: ;in, represents the state variable after suppressing high-frequency components, The state variable representing the actual output of the system, , is the time constant of the first-order filter.

[0035] The state variable after suppressing high frequency components Expand to new state variables The equation used to describe the filter is introduced into the state space of the original system, and the state space equation of the entire new system is: ; According to the state space equation of formula (15), the fifth-order extended state observer is reconstructed as: ; in, It is the status Estimates, Yes Estimates, Yes Estimates, Yes Estimates, Yes estimates; is the gain of the fifth-order observer, which includes 、 、 、 and ; Using the state variable after suppressing high-frequency components As the output, the observer is corrected through feedback, and the observation gain can be obtained by the bandwidth method, which is as follows: ; ; in, is the system matrix; is the system matrix The characteristic value of is the observer bandwidth. According to this speed loop system, the gain can be flexibly adjusted under the premise of ensuring the order of magnitude relationship between the gains. , while satisfying the observer convergence and optimizing the tracking accuracy, the parameters are as follows: ; Step 4: Verify the stability of the observer and choose the Lyapunov function as: ; Apply the above formula (20) to time Taking the derivative we get: ; The error matrix of the observer is: ; in, is the system matrix; is the output matrix; substituting the observer error matrix into formula (21) we can get: ; In order to ensure the asymptotic stability of the observer, To be negative definite, we can take the unit diagonal matrix ,Right now , the observer gain Substitute this inequality and solve the symmetric matrix It is positive and satisfied While being positive is negative, indicating that by selecting the above gain , which ensures that the observer is asymptotically stable.

[0036] Step 5: Design the speed loop controller.

[0037] The closed-loop transfer function of the current loop can be equivalent to a first-order inertia link. The controlled object is corrected into a typical type II system using the expected frequency method. This system has the advantages of stable performance, simple implementation, and strong anti-interference ability. The open-loop transfer function of the typical type II system is: ; in, is the time constant of the speed loop controller; is the gain of the speed loop controller; from the frequency domain characteristics of the typical type II system, , , , where and is the turning frequency, is the cutoff frequency. The slope of If The controller designed by the present invention is: ; in, is the controller gain; and is the controller time constant; is the time constant of the current loop closed-loop transfer function.

Claims

1. An extended state observer control method based on an airborne optoelectronic tracking system is characterized in that: The method comprises the following steps: S1. Establish a mathematical model of the airborne optoelectronic tracking system; S2. deriving a state space equation of the airborne optoelectronic tracking system based on the mathematical model of step S1; S3. Introduce the differential equation of the first-order filter into the state space equation of the airborne electro-optical tracking system and reconstruct the fifth-order extended state observer; S4. Performing a Lyapunov stability proof on the fifth-order extended state observer constructed in step S3, solving a condition that makes the fifth-order extended state observer asymptotically stable, and adjusting the fifth-order extended state observer based on the condition to make it asymptotically stable; S5. Design a speed loop controller based on the expected frequency method, and introduce the speed observed by the fifth-order extended state observer into the speed loop controller through feedback, ultimately achieving overall closed-loop control including the speed loop controller, the fifth-order extended state observer, and the controlled object.

2. The extended state observer control method based on the airborne electro-optical tracking system according to claim 1, characterized in that: The mathematical model of the airborne optoelectronic tracking system is specifically: ;in, From the current To speed The closed-loop transfer function of is the output speed; is the input current; is the proportionality coefficient; is the motor torque constant; is the integration coefficient; is the motor moment of inertia; is the winding inductance; is the Laplace variable; is the armature resistance; is the back electromotive force constant.

3. The extended state observer control method based on the airborne electro-optical tracking system according to claim 2, characterized in that: The state space equation of the airborne optoelectronic tracking system is as follows: ； in, 、 、 They represent velocity, acceleration, and jerk respectively; 、 、 Respectively 、 、 The derivative of ; ; ; ; is the equivalent current disturbance; is the derivative of the input current.

4. The extended state observer control method based on the airborne electro-optical tracking system according to claim 3, characterized in that: Step S3 is specifically as follows: S31, let the total disturbance inside and outside the system be , the expanded state space equation is established as: ;in, is the derivative of the total disturbance inside and outside the system; S32, according to the above formula, a fourth-order extended state observer is established, through Conduct; among them, is the output speed of the controlled object; 、 、 、 System status 、 、 and the total disturbance Observed values ​​of 、 、 Indicates velocity, acceleration, and jerk; 、 、 and is the observer gain to be designed; is the error between the observed speed and the actual speed; S33, introducing the differential equation of the first-order filter into the expanded state space, and re-obtaining the expanded state space equation of the new system; S34. Establish a fifth-order extended state observer based on the extended state space equation of the new system.

5. The extended state observer control method based on the airborne electro-optical tracking system according to claim 4, characterized in that: The condition for the fifth-order extended state observer to be asymptotically stable is: ,in, is the fifth-order extended state observer system matrix; is the output matrix of the fifth-order extended state observer; is the fifth-order extended state observer gain; is a symmetric matrix; is the unit diagonal matrix.

6. The extended state observer control method based on the airborne electro-optical tracking system according to claim 5, characterized in that: The transfer function of the speed loop controller is: ;in, is the speed loop controller gain; and is the time constant of the speed loop controller; is the time constant of the current loop closed-loop transfer function.

7. An extended state observer control system based on an airborne optoelectronic tracking system, characterized in that: The system comprises: Module for building mathematical models of airborne electro-optical tracking systems; A module for deriving a state space equation of an airborne electro-optical tracking system according to the mathematical model; The differential equation of the first-order filter is introduced into the state space equation of the airborne electro-optical tracking system, and the module of the fifth-order extended state observer is reconstructed; A module for performing Lyapunov stability proof on the fifth-order extended state observer, solving a condition for making the fifth-order extended state observer asymptotically stable, and adjusting the fifth-order extended state observer according to the condition to make it asymptotically stable; The speed loop controller is designed according to the expected frequency method, and the speed observed by the fifth-order extended state observer is introduced into the speed loop controller through feedback. Finally, a module of overall closed-loop control including the speed loop controller, the fifth-order extended state observer and the controlled object is realized.

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