A high-precision control method for a three-axis inertial stabilization platform based on an adaptive extended state observer and a global fast terminal sliding mode

Abstract

The application discloses a high-precision control method for a three-axis inertially stabilized platform based on an adaptive extended state observer and a global fast terminal sliding mode, and relates to a composite controller design of the adaptive extended state observer and the global fast terminal sliding mode. First, according to a state equation of the three-axis inertially stabilized platform, an adaptive extended state observer is constructed, unknown lumped disturbances are estimated in real time while rapidity, small overshoot and low noise are ensured through adaptive changes of an observer bandwidth and adaptive compensation of disturbance estimation deviation; second, a global fast terminal sliding mode controller is designed to process nonlinearity, in-frame and out-frame coupling and parameter uncertainty of the three-axis inertially stabilized platform, and combined with effective estimation of the adaptive extended state observer on the lumped disturbances, a high-order terminal function is replaced, chattering is reduced, and then high-precision control of the three-axis inertially stabilized platform under a complex environment is realized. The application has the advantages of good real-time performance, fast dynamic parameter response, strong adaptability to multi-source disturbances and the like, and can be used for high-precision control of the three-axis inertially stabilized platform under a complex multi-source disturbance environment.

Description

Technical Field

[0001] This invention relates to a high-precision control method for a three-axis inertial stabilization platform based on an adaptive extended state observer and a global fast terminal sliding mode, applicable to the field of high-precision control of aerial mapping stabilization platforms. Background Technology

[0002] The three-axis pod platform is fixed to the flight vehicle via a base, supporting and stabilizing the remote sensing payload. It improves the imaging quality of the remote sensing payload by isolating the non-ideal attitude motion of the flight vehicle from the line of sight of the remote sensing payload, and has broad application prospects.

[0003] As a complex multi-frame coupled system, the three-axis inertial stabilized platform is characterized by nonlinearity, strong coupling, and high control difficulty. Furthermore, during flight, the three-axis inertial stabilized platform experiences wind disturbances, angular motion disturbances caused by aircraft engine vibration, unbalanced torques due to the misalignment of the platform's center of mass and the rotating axis of the motion imaging load, coupling torques and frictional disturbances caused by imperfections in the platform's mechanical and electrical construction, and internal disturbances from the gyroscope and accelerometer measurement error systems. Therefore, high-precision control of the three-axis inertial stabilized platform under disturbances is one of the key technologies for surveying and mapping systems.

[0004] To improve performance, various control methods, such as PID control, robust control, intelligent control, and sliding mode control, are used for high-precision control of three-axis inertial stabilization platforms. PID controllers are simple in structure but have poor anti-interference capabilities, and the control performance of three-axis stabilization platforms is easily affected by external disturbances. Robust control can effectively eliminate inaccurate model parameters and external disturbances during flight, but it suffers from poor real-time performance and slow dynamic parameter response. Through extensive sample training, neural networks can achieve nonlinear adaptive control, overcoming model uncertainties and multi-source disturbances inherent in three-axis inertial stabilization platforms, and achieving high-precision attitude control. However, traditional neural networks require a large amount of sample data for training and suffer from poor real-time performance. Sliding mode variable structure control, by constructing a sliding surface, allows the system to move along a sliding mode according to predetermined rules. It is an effective control method for nonlinear problems with external disturbances and uncertainties, showing good control performance for systems with severe nonlinearity and external disturbances. However, the drawback of sliding mode control lies in its switching function, which may cause chattering when external disturbances are significant. Summary of the Invention

[0005] The technical problem solved by this invention is that the control performance of a three-axis inertial stabilization platform is easily affected by external disturbances when performing tasks. This invention proposes a high-precision control method for a three-axis inertial stabilization platform based on an adaptive extended state observer and a global fast terminal sliding mode controller. By designing an adaptive extended state observer to estimate unknown lumped disturbances in real time, a global fast terminal sliding mode controller is constructed to handle the nonlinearity, frame-internal and external coupling, and parameter uncertainties of the three-axis inertial stabilization platform. Furthermore, by combining the effective estimation of lumped disturbances by the adaptive extended state observer, the higher-order terminal function is replaced, reducing chattering, thereby achieving high-precision control of the three-axis inertial stabilization platform in complex environments.

[0006] The technical solution of this invention is as follows: First, for the dynamic model of a three-axis inertial stabilized platform, an adaptive extended state observer is designed. Utilizing the adaptive variation of the observer bandwidth and adaptive compensation for disturbance estimation bias, unknown lumped disturbances are estimated in real time while ensuring speed, small overshoot, and low noise. A global fast terminal sliding mode controller is designed to handle the nonlinearity, frame-internal and external coupling, and parameter uncertainties of the three-axis inertial stabilized platform. Combined with the effective estimation of lumped disturbances by the adaptive extended state observer, the higher-order terminal function is replaced, reducing chattering. The implementation steps are as follows:

[0007] (1) For the dynamic model of a three-axis inertial stable platform,

[0008]

[0009] Where ζ = r represents the roll channel, ζ = p represents the pitch channel, and ζ = a represents the yaw channel. dζ Let x be the desired angle along the ζ-axis. 1ζ =θ ζ x 2ζ =ω ζ These represent the actual angle and actual angular velocity along the ζ-axis, respectively. ζ b is the ζ-axis control voltage. ζ f is the gain of the ζ-axis control quantity. ζ Given a nonlinear function along the ζ-axis, D ζ The zeta-axis lumped disturbance, and its first derivative Bounded;

[0010] To reduce the impact of unknown disturbances on a three-axis inertial stabilized platform and improve control performance, an adaptive extended state observer is designed to estimate lumped disturbances online.

[0011] The ζ-axis adaptive extended state observer is defined as:

[0012]

[0013] in, These are the estimated values ​​for the ζ-axis angle, ζ-axis angular velocity, and ζ-axis lumped disturbance, respectively. 1ζ The actual angle θ of the ζ-axis ζ Angle estimate with ζ axis The error, ω Aζ This is the bandwidth of the ζ-axis observer, and its adaptive time-varying expression is as follows:

[0014]

[0015] In the formula, ω Ahζ ω is the upper bound of the bandwidth of the ζ-axis observer. Alζ δ is the lower bound of the bandwidth of the ζ-axis observer. 1ζ >0 represents the gain of the ζ-axis angle estimation bias, δ 2ζ >0 represents the gain of the zeta-axis angular velocity estimation bias;

[0016] ζ-axis observer bandwidth ω Aζ It makes full use of the angle and angular velocity information of the three-axis inertial stabilization platform to reduce the peak value of the observer's estimated curve and can introduce too much noise.

[0017] To further improve the estimation accuracy of the adaptive extended state observer for disturbances, an adaptive lumped disturbance estimation compensation for the ζ-axis is defined. Its adaptive law The expression is:

[0018]

[0019] in, It is an adaptive function for the ζ-axis, ε maxζ It is the upper boundary of the lumped disturbance estimation bias along the ζ-axis, ε minζ It is the lower boundary of the lumped disturbance estimation bias along the ζ-axis;

[0020] ζ-axis adaptive law Through the projection mapping relationship, not only is the adaptive lumped disturbance estimation compensation of the ζ-axis guaranteed. The adaptive real-time changes also ensure Always satisfied

[0021] (2) To address the nonlinearity, frame-internal and external coupling, and parameter uncertainty of the three-axis inertial stabilization platform, a global fast terminal sliding mode controller is designed. Combined with an adaptive extended state observer for effective estimation of lumped disturbances, the higher-order terminal function is replaced to reduce chattering and achieve high-precision control of the three-axis inertial stabilization platform in complex environments.

[0022] The expressions for the global fast terminal sliding mode on the ζ-axis, the ζ-axis control law based on the adaptive extended state observer and the global fast terminal sliding mode, and the ζ-axis adaptive function are as follows:

[0023]

[0024]

[0025]

[0026] Among them, s 1ζ For higher-order sliding modes along the ζ-axis, e ζ For the ζ-axis tracking error, k eζ >0 represents the tracking error gain along the ζ-axis, α 0ζ >0, β 0ζ >0, q 0ζ and p 0ζ All are positive odd numbers and satisfy p 0ζ >q 0ζ k sζ >0 represents the higher-order sliding mode gain along the ζ-axis, γ εζ It is the learning rate along the ζ-axis;

[0027] The ζ-axis is based on an adaptive extended state observer and a global fast terminal sliding mode control law u. ζ In the middle, higher-order terminal functions Replace with an adaptive extended state observer for estimating the lumped disturbance. This reduces chattering and improves the control accuracy of the three-axis inertial stabilization platform.

[0028] The advantages of this invention compared to the prior art are:

[0029] (1) This invention addresses the characteristics of a three-axis inertial stabilization platform system with strong model coupling and many unknown external disturbances. By designing an adaptive extended state observer, it estimates unknown lumped disturbances in real time. It utilizes a global fast terminal sliding mode controller to handle the nonlinearity, frame internal and external coupling, and parameter uncertainty of the three-axis inertial stabilization platform. Combined with the effective estimation of lumped disturbances by the adaptive extended state observer, it replaces the high-order terminal function, reduces chattering, and thus achieves high-precision control of the three-axis inertial stabilization platform in complex environments. It not only has the characteristics of simple structure and convenient control, but also has the characteristics of strong anti-interference ability.

[0030] (2) The adaptive extended state observer constructed in this invention inherits the advantages of both nonlinear and linear extended state observers and overcomes their disadvantages. Compared with the nonlinear extended state observer, the adaptive extended state observer is not only flexible in design but also achieves good observation performance. At the same time, the adaptive extended state observer has a good theoretical analysis form, which is also an advantage of the linear extended state observer. The designed control method has good real-time performance, fast dynamic parameter response, and strong anti-interference ability, which can meet the high-precision control requirements of the three-axis inertial stabilization platform.

[0031] (3) This invention adjusts the observation gain of the adaptive extended state observer by using adaptive observation bandwidth, makes full use of the angle and angular velocity information of the three-axis inertial stabilization platform to reduce the peak value of the observer estimation curve, and does not introduce too much noise. In addition, the adaptive lumped disturbance estimation compensation further improves the estimation accuracy of the adaptive extended state observer for lumped disturbance, thereby improving the robustness of the system to disturbances. Attached Figure Description

[0032] Figure 1 Control process for a three-axis inertial stabilization platform;

[0033] Figure 2 To demonstrate the pitch channel control effect of a three-axis inertial stabilized platform during flight experiments;

[0034] Figure 3 To demonstrate the roll channel control effect of a three-axis inertial stabilization platform during flight experiments;

[0035] Figure 4 The effect of the heading channel control of the three-axis inertial stabilization platform during flight experiments. Detailed Implementation

[0036] like Figure 1 As shown, the specific implementation of the present invention is as follows:

[0037] (1) Construct an adaptive extended state observer

[0038] Based on Newton-Euler theory, the dynamic equations of a three-axis inertial stable platform are expressed as follows:

[0039]

[0040] Where ζ = r represents the roll channel, ζ = p represents the pitch channel, and ζ = a represents the yaw channel. dζ Let x be the desired angle along the ζ-axis. 1ζ =θ ζ x 2ζ =ω ζ These represent the actual angle and actual angular velocity along the ζ-axis, respectively. ζ b is the ζ-axis control voltage. ζ f is the gain of the ζ-axis control quantity. ζ Given a nonlinear function along the ζ-axis, D ζ The zeta-axis lumped disturbance, and its first derivative Bounded;

[0041] To reduce the impact of unknown disturbances on the three-axis inertial stabilized platform and improve control performance, an adaptive extended state observer is introduced to estimate lumped disturbances online.

[0042] The ζ-axis adaptive extended state observer is established as follows:

[0043]

[0044] in, These are the estimated values ​​for the ζ-axis angle, ζ-axis angular velocity, and ζ-axis lumped disturbance, respectively. 1ζ The actual angle θ of the ζ-axis ζ Angle estimate with ζ axis The error, ω Aζ This is the bandwidth of the ζ-axis observer, and its adaptive time-varying expression is as follows:

[0045]

[0046] In the formula, ω Ahζ ω is the upper bound of the bandwidth of the ζ-axis observer. Alζ δ is the lower bound of the bandwidth of the ζ-axis observer. 1ζ >0 represents the gain of the ζ-axis angle estimation bias, δ 2ζ >0 represents the gain of the zeta-axis angular velocity estimation bias;

[0047] ζ-axis observer bandwidth ω Aζ It makes full use of the angle and angular velocity information of the three-axis inertial stabilization platform to reduce the peak value of the observer's estimated curve and can introduce too much noise.

[0048] To further improve the estimation accuracy of the adaptive extended state observer for disturbances, the ζ-axis lumped disturbance estimation bias is defined as follows:

[0049]

[0050] Wherein, the lumped disturbance estimation bias ε along the ζ-axis ζ It is a bounded constant variable with an unknown ζ-axis, satisfying ε minζ ≤ε ζ ≤ε maxζ , ε maxζ It is the upper boundary of the lumped disturbance estimation bias along the ζ-axis, ε minζ This is the lower boundary of the ζ-axis lumped disturbance estimation bias; to compensate for the estimation bias of the adaptive extended state observer on the lumped disturbance, the ζ-axis adaptive lumped disturbance estimation compensation is defined. It is the estimation bias ε of the lumped disturbance along the ζ-axis. ζ The estimated value, with an estimation error of Furthermore, adaptive lumped disturbance estimation compensation along the ζ-axis Adaptive law The expression is defined as:

[0051]

[0052] in, It is a ζ-axis adaptive function, and the ζ-axis adaptive law. Through the projection mapping relationship, not only is the adaptive lumped disturbance estimation compensation of the ζ-axis guaranteed. The adaptive real-time changes also ensure Always satisfied

[0053] (2) Constructing a global fast terminal sliding mode controller

[0054] To address the nonlinearity, frame-internal / external coupling, and parameter uncertainties of a three-axis inertial stabilization platform, a global fast terminal sliding mode controller is introduced to improve the platform's speed and tracking performance for desired angles. Furthermore, an adaptive extended state observer is used for effective estimation of lumped disturbances, replacing the higher-order terminal function to reduce chattering. The design of the global fast terminal sliding mode is as follows:

[0055]

[0056] Among them, s 1ζ For higher-order sliding modes along the ζ-axis, e ζ For the ζ-axis tracking error, k eζ >0 represents the tracking error gain along the ζ-axis, α 0ζ >0, β 0ζ >0, q 0ζ and p 0ζ All are positive odd numbers and satisfy p 0ζ >q 0ζ ;

[0057] When the higher-order sliding mode s of the ζ axis 1ζ When = 0, we have:

[0058]

[0059] When the ζ-axis tracking error e ζ When far from the equilibrium point, at this time It is a fast terminal attractor; when the ζ-axis tracking error e ζ Approaching equilibrium state e ζ When = 0, It is a linear sliding mode, and the ζ-axis tracking error e ζ It decays exponentially; therefore, the global fast terminal sliding mode introduces a fast terminal attractor, making the ζ-axis tracking error e ζ It achieves convergence in a finite time while retaining the fastness of the linear sliding mode near equilibrium, thus realizing the ζ-axis tracking error e. ζ It converges to an equilibrium state precisely and quickly;

[0060] higher-order sliding modes s along the ζ-axis 1ζ Find the first derivative:

[0061]

[0062] And define the adaptive function for the ζ-axis. expression:

[0063]

[0064] Where, γ εζ It is the learning rate along the ζ-axis.

[0065] Then the ζ-axis based on the adaptive extended state observer and the global fast terminal sliding mode control law is:

[0066]

[0067] Where, k sζ >0 represents the higher-order sliding mode gain along the ζ-axis, which is based on an adaptive extended state observer and a global fast terminal sliding mode control law u. ζ In the middle, higher-order terminal functions Replace with an adaptive extended state observer for estimating the lumped disturbance. This reduces chattering and improves the control accuracy of the three-axis inertial stabilization platform.

[0068] According to the actual control law u ζ The attitude angles of the three-axis inertial stabilized platform are asymptotically stable over a wide range, and the ζ-axis tracking error e ζ =0 is achievable within a finite time, therefore the actual angle θ of the three-axis inertial stabilized platform is... ζ It can track the desired angle θ dζ .

[0069] (3) Flight Examples

[0070] During flight, depending on the positional relationship between the drone and the target, the platform-mounted camera payload is required to maintain an altitude of 20 meters, taking images perpendicular to the ground at a forward flight speed of 8 meters per second. The pitch and roll channels are required to be maintained at 0 degrees, and the yaw channel at 90 degrees. The ground monitoring center will monitor the drone and platform in real time. The flight results of a particular experiment are as follows: Figure 2 , Figure 3 and Figure 4 As shown.

[0071] The inertial stabilization platform achieves high-precision and robust control against strong interference. Under severe environmental interference such as level 5 gusts, the root mean square error of the pitch channel is 0.3771 degrees, with a maximum deviation of 0.8567 degrees; the root mean square error of the roll channel is 0.2902 degrees, with a maximum deviation of 0.8504 degrees; and the root mean square error of the yaw channel is 0.0420 degrees, with a maximum deviation of 0.2048 degrees.

[0072] The high-precision control method for a three-axis inertial stabilization platform based on an adaptive extended state observer and global fast terminal sliding mode overcomes the shortcomings of existing control methods and can achieve high-precision control of the three-axis inertial stabilization platform in complex and multi-disturbance environments.

[0073] The contents not described in detail in this specification are existing technologies known to those skilled in the art.

Claims

1. A high-precision control method for a three-axis inertial stabilization platform based on an adaptive time-varying bandwidth observer, characterized in that... Implement the following steps: (1) For the dynamic model of a three-axis inertial stable platform, Where ζ = r represents the roll channel, ζ = p represents the pitch channel, and ζ = a represents the azimuth channel. dζ Let x be the desired angular position along the ζ-axis. 1ζ =θ ζ x 2ζ =ω ζ These represent the actual angular position and actual angular velocity along the ζ-axis, respectively. ζ b is the ζ-axis control voltage. ζ f represents the coefficient for the ζ-axis motor control in the platform state model. ζ The system's zeta-axis lumped disturbance, and its first derivative Bounded; A sliding mode variable structure control method based on the exponential reaching law is designed. The control command is generated through state error information to suppress the uncertainty and disturbance of the dynamic model parameters. The control law u of the sliding mode variable structure control method based on the exponential reaching law for the ζ-axis SMCζ Sliding surface s ζ And exponential convergence law They are respectively: Among them, e ζ The actual angular position θ of the ζ-axis ζ With the desired angular position θ dζ The error, c ζ >0 satisfies the conditions of Herwitz's theorem, k ζ >0, η ζ >|f ζ | is the estimated constant for the upper bound of the lumped disturbance along the system's ζ-axis, sat(s) ζ Let ) be a saturation function, and its expression is: In the formula, ξ ζ It is the ζ-axis boundary layer thickness; (2) To address the impact of chattering on control accuracy in sliding mode variable structure control, an observer with adaptive time-varying bandwidth is designed. Based on the sliding surface and its first derivative, the upper bound of the system's lumped disturbance error is estimated in real time, reducing the observer order and avoiding oscillation overshoot caused by high observer order. Furthermore, the observation gain varies with the observation bandwidth, which not only improves the observer's response speed but also balances the contradiction between speed and peak value, enabling high-precision control of a three-axis inertial stabilization platform in complex environments. The sliding mode variable structure control law based on the adaptive time-varying bandwidth observer for the ζ-axis, the adaptive time-varying bandwidth observer, and the observer gain are as follows: Among them, z 1ζ z 2ζ These are the estimated values ​​of the sliding surface along the ζ-axis and the lumped disturbance along the ζ-axis of the system, respectively. 1ζ The estimated value of the sliding surface z along the ζ-axis 1ζ With sliding surface s ζ The error, It is the nominal pole of the ζ-axis observer, ω oζ This is the bandwidth of the ζ-axis observer, generated by a third-order Butterworth filter, and its expression is as follows: In the formula, ω Bζ The bandwidth of the Butterworth filter along the ζ-axis is given by the filter, which determines ω. oζ How to follow the time-varying bandwidth command ω on the ζ-axis cζ ω cζ Defined as: T ωζ (||e ζ ||) represents ω cζ The time threshold is expressed as: In the formula, Δt ζ and Δθ ζ These represent the degree of change over time along the ζ-axis and the degree of attitude deviation, respectively. It is the ζ-axis ||e ζ ||From less than Δθ ζ to greater than or equal to Δθ ζ The timeline.

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