Servo control method of micro rudder based on variable gain extended state observer and backstepping control

Abstract

The application discloses a micro rudder servo control method based on a variable gain extended state observer and a backstepping control. First, a three-order nonlinear model of a rudder is established, and an extended state observer is designed, wherein the core lies in introducing a time-varying gain function L(t) to dynamically adjust the bandwidth of the observer. By fusing normalized flight speed, angle of attack, overload and rudder angular velocity information, a comprehensive working condition index s is constructed, and the hyperbolic tangent function is used to smoothly map s to L(t). Under a stable working condition, L(t) is automatically reduced to suppress noise amplification, and when a severe maneuver or disturbance occurs, L(t) is quickly raised to improve the estimation speed. Further, combined with a backstepping control law, the disturbance estimation value output by the observer is used for feedforward compensation, so that the accurate and robust tracking of the rudder angle is realized. The application solves the contradiction between the response lag and noise sensitivity of the fixed bandwidth observer, and significantly improves the control performance and reliability of the micro rudder in the whole flight envelope.

Description

Technical Field

[0001] This invention belongs to the field of high-precision servo control technology, specifically relating to a micro servo motor servo control method based on a combination of variable gain extended state observer and backstep control. Background Technology

[0002] As the core actuator of the control surface servo system of high-performance unmanned aerial vehicles (UAVs), the control performance of micro servos directly affects the control quality and flight safety of the aircraft. In practical applications, the load borne by micro servos not only changes with the flight state of the aircraft, such as uniform flight and maneuvering overload, but is also often superimposed with various disturbances such as atmospheric disturbances and inertial torque impacts caused by rapid deflection of control surfaces. These disturbances have time-varying, abrupt, and nonlinear characteristics, posing a severe challenge to the high-precision, high-dynamic tracking control of the servo system.

[0003] To improve system anti-interference capability, existing technologies typically employ model-based observers for online estimation and compensation of loads and disturbances, with extended state observers (ESOs) and sliding mode observers (SMOs) being common implementations. These methods are usually designed with fixed bandwidth, and their core idea is to achieve dynamic estimation of lumped disturbances by configuring a fixed observer gain (i.e., fixed bandwidth). However, the main problems exposed by fixed-bandwidth observers in practical applications are as follows:

[0004] (1) When the load of the servo motor or external interference changes rapidly, if the bandwidth of the observer is set too low, its dynamic response capability is insufficient and it cannot track the sudden signal in time, resulting in a significant increase in the estimation residual, a decrease in the transient tracking performance of the system, and a serious impact on the speed and accuracy of the servo motor during maneuvering.

[0005] (2) During the relatively stable phase of flight, external disturbances change slowly, but measurement noise is relatively significant. If the observer bandwidth is set too high, it will show a large gain on high-frequency measurement noise, causing the noise signal to be amplified by the observer and injected into the control loop, which in turn causes high-frequency jittering of the servo control input, oscillation of the output position, and may even threaten the stability of the closed-loop system.

[0006] To overcome the limitations of fixed bandwidth, some improvement schemes propose the design concept of variable bandwidth observers, typically by dynamically switching the observer bandwidth based on the magnitude of the control error. However, this type of method is essentially a "post-hoc" adjustment strategy, triggering bandwidth switching only after the tracking error has accumulated significantly, resulting in a noticeable response lag. This lag prevents the system from obtaining timely observation and compensation in the initial stage of sudden disturbances, making it difficult to meet the comprehensive performance requirements of micro servos for high precision, high bandwidth, and low noise sensitivity.

[0007] Therefore, existing technologies, whether using fixed-bandwidth observers or error-switching-based variable-bandwidth observers, suffer from a trade-off between response speed and noise suppression capability, failing to achieve a good balance between rapid disturbance estimation and smooth, low-noise operation across the entire flight operating range. To address the challenges of variable interference and high-frequency noise faced by micro servos in complex flight environments, there is an urgent need for a micro servo control method capable of smoothing and adaptively adjusting the observer gain based on real-time system operating information. This would improve the dynamic responsiveness, estimation accuracy, and robust stability of the servo control system. Summary of the Invention

[0008] To address the limitations of existing fixed or error-driven variable bandwidth observers, which suffer from estimation lag or noise amplification when faced with sudden changes in servo load and flight state, making it difficult to achieve high-precision, low-noise, and fast-response servo disturbance estimation, this invention proposes a micro servo control method that combines a variable-gain extended state observer based on flight state and servo control information with backstepping control. This method constructs a smooth and variable observer gain (bandwidth) scheduling function based on real-time flight state and servo control information to dynamically adjust the estimation performance of the extended state observer. Combined with a backstepping control law, it achieves real-time disturbance compensation and accurate tracking. This method ensures rapid tracking of rapidly changing loads and disturbances while suppressing high-frequency noise amplification under stable operating conditions, thus achieving high precision, high-speed response, and high robustness across the entire operating range, significantly improving the performance and reliability of the micro servo control system.

[0009] The technical solution of this invention is as follows:

[0010] A micro servo motor servo control method based on a combination of variable gain extended state observer and backstepping control includes the following steps:

[0011] Step 1: Establish a third-order nonlinear dynamic model of the micro servo motor electric drive system. The state variables of the model include the servo surface deflection angle, servo surface angular velocity and armature current. The mechanical side equivalent disturbance is modeled as the total disturbance acting on the system.

[0012] Step 2: Based on flight status information and servo control information, construct a time-smoothly varying observer variable gain function. ;

[0013] Step 3: Based on the mechanical acceleration equations containing total disturbance in the aforementioned dynamic model, design the gain as follows: An extended state observer is used to estimate the total disturbances acting on the system;

[0014] Step 4: Design a three-layer control law based on the backstepping method, and use the total disturbance value estimated by the extended state observer for feedforward compensation to generate the control input signal driving the micro servo motor. .

[0015] In a further preferred embodiment, in step 1, the dynamic model is as follows:

[0016]

[0017] in, The equivalent rotational inertia of the electric servo motor. The coefficient of viscous friction is... The torque constant of the electric servo motor is... The back electromotive force constant of the electric servo motor; The resistance of the armature winding of the electric servo motor. The inductance of the armature winding of the electric servo motor; This is the terminal voltage applied to the armature winding of the electric servo motor; This is the mechanical equivalent interference.

[0018] In a further preferred embodiment, step 2 involves constructing a time-smoothly varying observer variable gain function. The process is as follows:

[0019] Step 2.1: Select flight speed, angle of attack, vertical overload, and servo angular velocity as operating condition sensing variables and normalize them;

[0020] Step 2.2: Combine the normalized operating condition sensing variables into a unified operating condition index by weighting them according to their contribution to disturbances. , The value range is [0, 1];

[0021] Step 2.3: Based on operating condition indicators A time-smoothly varying observer gain function is constructed using a smooth mapping function. .

[0022] In a further preferred embodiment, the smoothing mapping function is a hyperbolic tangent function, and the observer's variable gain function changes smoothly over time. The format is as follows:

[0023]

[0024] in: This is the lower limit of the observer gain; This is the upper limit of the observer gain; To switch centers; This is the steepness parameter.

[0025] In a further preferred embodiment, the gain is The extended state observer is:

[0026]

[0027] in, This is an estimate of the angular velocity; This is an estimate of the load disturbance; The gain of the variable observer is dynamically determined by the system operating parameters. This represents the observer error.

[0028] In a further optimized approach, step 4 involves designing a three-layer control law based on the backstepping method as follows:

[0029] First, we introduce the systematic error variable:

[0030]

[0031] in, For the desired angle trajectory; These are the virtual control variables for the first and second layers, respectively. These are three layers of error variables, corresponding to angle, angular velocity, and current control errors, respectively.

[0032] The dynamic equation of the system error obtained from the dynamic model is:

[0033]

[0034] Regarding the angle error equation in the system error dynamics equation:

[0035]

[0036] Introducing virtual control laws:

[0037]

[0038] in Indicates control gain;

[0039] Regarding the angular velocity error equation in the system error dynamics equation:

[0040]

[0041] Design virtual control law for:

[0042]

[0043] In the formula, for The estimated value;

[0044] Regarding the current control error equation in the system error dynamics equation:

[0045]

[0046] Design the actual control law for:

[0047] .

[0048] Furthermore, the present invention also proposes an electronic device and a computer-readable storage medium:

[0049] An electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the aforementioned micro servo control method.

[0050] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-described micro servo motor servo control method.

[0051] Beneficial effects:

[0052] The beneficial effects of this invention are as follows:

[0053] 1. Compared to fixed-bandwidth observers, this method can adjust the observer gain in real time and smoothly according to the flight status and control parameters, enabling the system to quickly increase the estimated bandwidth to accelerate tracking when there are sudden changes in disturbances, and automatically reduce the bandwidth during stable flight to effectively suppress measurement noise amplification, thus fundamentally solving the contradiction faced by fixed-bandwidth design.

[0054] 2. Compared with variable bandwidth observers based on control error switching, this method directly uses multi-source operating condition information that characterizes the disturbance potential as the basis for gain scheduling, rather than passively waiting for control error accumulation. This enables the observer to respond in the early stages of disturbance occurrence or aggravation, significantly reducing estimation lag and improving the system's ability to cope with sudden disturbances.

[0055] 3. This method adopts a smooth gain scheduling mechanism based on the hyperbolic tangent function, which avoids control input chattering, output oscillation and transient impact problems that may be caused by sudden changes or frequent switching of bandwidth parameters, and is conducive to improving the operational stability and long-term reliability of the servo system.

[0056] 4. Under extreme flight conditions such as high angle of attack and strong maneuvering, this method can automatically adjust the observer gain to a high level, maintain high-precision estimation and compensation capability for severe disturbances, thereby ensuring the handling quality and flight safety of the unmanned aerial vehicle within the full envelope.

[0057] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0058] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0059] Figure 1 This is a schematic diagram of the mathematical model of a servo motor;

[0060] Figure 2 This is a simulation result diagram of the servo motor changing from no load to load with a fixed low gain when using MATLAB simulation experiment;

[0061] Figure 3 This is a simulation result diagram of the servo motor being switched from no load to load with a fixed high gain during a MATLAB simulation experiment.

[0062] Figure 4 This is a simulation result diagram of the variable gain of the servo motor when it is under no-load and under load using MATLAB simulation experiment. Detailed Implementation

[0063] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are for illustrative purposes only and do not constitute a limitation thereof.

[0064] This embodiment aims to overcome the inherent defects of existing fixed-bandwidth observers and error-switching-based variable-bandwidth observers when applied to micro servo motor control. Specifically, the technical problems to be solved include: 1) Fixed low-bandwidth observers experience tracking lag during rapid changes in load or disturbance, leading to a decrease in system transient performance; 2) Fixed high-bandwidth observers are overly sensitive to measurement noise under steady-state conditions, causing control input chattering and output oscillation, threatening system stability; 3) Existing error-driven variable-bandwidth methods rely on control errors for switching, resulting in a lag in response and an inability to promptly increase the estimated bandwidth in the initial stage of disturbance, making it difficult to meet the dual requirements of high dynamics and high accuracy.

[0065] To address the above issues, this embodiment provides a micro servo control method based on a combination of a variable gain extended state observer and backstepping control, enabling rapid and accurate tracking of control surface angles under complex flight conditions. The main process of this method is as follows: establishing a third-order motor system model, constructing operating condition indices based on flight state and control inputs, and generating a variable gain function online. Based on this, a variable gain observer was designed to achieve real-time disturbance estimation, and a three-layer backstepping control law was combined for disturbance compensation and closed-loop control to improve the robustness and control accuracy of the servo system. The specific steps are as follows:

[0066] Step 1: Establish a mathematical model for the electric servo motor;

[0067] First, a mathematical model of the micro servo motor electric drive system is established. For example... Figure 1 As shown, the micro servo motor electric drive system comprises two parts: mechanical dynamics and electrodynamics. Its typical model can be described as a third-order nonlinear system. The system state variable is defined as: rudder surface deflection angle. rudder surface angular velocity and armature current The system dynamics equation is then:

[0068]

[0069] in, The equivalent rotational inertia of the electric servo motor. The coefficient of viscous friction is... The torque constant of the electric servo motor is... The back electromotive force constant of the electric servo motor; The resistance of the armature winding of the electric servo motor. The inductance of the armature winding of the electric servo motor; The voltage applied to the armature winding of the electric servo motor is proportionally proportional and then enters the electrical circuit. The mechanical equivalent disturbances include aerodynamic disturbances, inertial impacts at hinges, and changes in gear meshing stiffness.

[0070] Step 2: Based on flight status and servo control information, construct a time-smoothly varying observer variable gain function. .

[0071] To achieve rapid estimation and stable observation of servo disturbances under various disturbance and noise environments, this invention designs a variable gain function based on flight state and servo control input. This method is used to dynamically adjust the gain of the extended state observer. It is based on a comprehensive index that integrates flight conditions and servo dynamics. The hyperbolic tangent function (tanh) is used to smoothly map this bandwidth to the observer bandwidth. This allows for maintaining a smaller bandwidth to suppress noise under steady-state conditions, while rapidly increasing the bandwidth under high maneuverability / large disturbance conditions, thereby improving estimation speed.

[0072] Step 2.1: To accurately characterize the current operating state of the system, the following key variables are selected as measures of disturbance intensity and normalized:

[0073]

[0074] in, For flight speed, For angle of attack, For vertical overload, For servo angular velocity, The maximum flight speed Design limit value for angle of attack, Design limit value for vertical overload, The maximum value of the servo motor's angular velocity, For normalized flight speed, For normalized angle of attack, For normalized vertical overload, To normalize the servo angular velocity, ensure that all normalized values ​​are within the range of [0, 1].

[0075] Step 2.2: Combine the normalized indices into a unified operating condition index by weighting them according to their contribution to the disturbance. :

[0076]

[0077] in: ω V ， ω α ， ω n Z ， ω ω m ∈[0 ， 1] These are weighting coefficients, reflecting the degree of influence of each indicator on the disturbance intensity; they satisfy the normalization condition: These weights can be set through simulation optimization, experimental calibration, or based on control sensitivity analysis. The value range is [0, 1]. A larger value indicates that there may be rapidly changing disturbances or maneuvers in the current system.

[0078] Step 2.3: Based on operating condition indicators Construct a time-smoothly varying observer gain function. The format is as follows:

[0079]

[0080] in: This is the lower limit of the observer gain (used for steady-state conditions). This is the upper limit of the observer gain (for severe operating conditions). This is the switching center, i.e., the intermediate operating point where the gain increases; For the steepness parameter, control gain from Transition to The rate.

[0081] This function has the following property: when hour, The gain approaches a low value. The observer exhibits low gain characteristics, effectively suppressing measurement noise; when hour, The gain is at the median. ;when hour, The gain increased to The observer exhibits high gain characteristics, enabling rapid tracking of disturbances. The entire change process is smooth and continuous, avoiding parameter jumps.

[0082] Using gain The dynamic adjustment can achieve a trade-off between estimation performance and noise suppression under different interference or noise scenarios.

[0083] Step 3: Based on the mechanical acceleration equations containing total disturbance in the aforementioned dynamic model, design the gain as follows: An extended state observer is used to estimate the total disturbances acting on the system.

[0084] In practical micro servo motor electric drive systems, external disturbances are frequently encountered. The impact of this disturbance source includes:

[0085] (1) Aerodynamic torque disturbance (affected by aerodynamic conditions such as flight speed and angle of attack);

[0086] (2) Uncertainties in mechanism transmission (such as gear meshing error, elastic deformation, etc.);

[0087] (3) Electromagnetic disturbances or inertial shocks, etc.

[0088] Since these disturbances are often difficult to describe accurately in physical modeling, this invention proposes the design concept of an extended state observer to dynamically estimate the disturbance online, thereby improving the compensation capability and overall robustness of the control system.

[0089] First, consider the actual kinematic expression of the mechanical acceleration relationship as follows:

[0090]

[0091] in It is the total equivalent disturbance input in the system, and its uncertainty directly affects the angular velocity. Precise control.

[0092] To The disturbance is estimated in real time using the following second-order extended state observer structure:

[0093]

[0094] in, This is an estimate of the angular velocity; This is an estimate of the load disturbance; The gain of the variable observer is dynamically determined by the system operating parameters. This represents the observer error. In this structure, the second-order extended state observer constructs a feedback channel through angular velocity measurement and estimation errors to address the disturbance term. Tracking.

[0095] Step 4: Design of a three-level backstepping control law and disturbance compensation based on a third-order model;

[0096] To ensure the servo system is functioning properly in the presence of disturbances Even under nonlinear coupling conditions, it can still accurately track the trajectory of the desired control surface angle. This invention employs a backstepping method to design a three-layer control law. Each layer of control is based on the error variable and Lyapunov function constructed in the previous layer. By introducing virtual control variables, nonlinearity and disturbance terms are eliminated step by step, ultimately outputting the control input. .

[0097] To construct a backstepping controller, we first introduce a system error variable:

[0098]

[0099] in, For the desired angle trajectory; These are the virtual control variables for the first and second layers, respectively. These are three layers of error variables, corresponding to angle, angular velocity, and current control errors, respectively.

[0100] The system error dynamic equation can be obtained from the third-order motor model as follows:

[0101]

[0102] Regarding the angle error equation in the system error dynamics equation:

[0103]

[0104] To suppress error Introducing a virtual control law:

[0105]

[0106] in Representing the control gain, we obtain Define Lyapunov functions. Differentiate it and apply the virtual control law Substitute and get .

[0107] Regarding the angular velocity error equation in the system error dynamics equation:

[0108]

[0109] Design virtual control law for:

[0110]

[0111] In the formula, for The estimated value, let To estimate the error, define the Lyapunov function. Differentiate it and apply the virtual control law Substitute, there is

[0112]

[0113] Regarding the current control error equation in the system error dynamics equation:

[0114]

[0115] Design the actual control law for:

[0116]

[0117] Define Lyapunov functions Differentiate it and apply the control law Substituting, we have:

[0118]

[0119] Based on Lyapunov's stability theory, it is proved that all error signals in the closed-loop system eventually become uniformly bounded, thus achieving stable and accurate tracking control.

[0120] To evaluate the effectiveness of the micro servo motor control method based on the combination of variable gain extended state observer and backstepping control designed in this invention, simulation was performed using MATLAB, with the given angle expectation value as follows: .

[0121] The physical parameters in the motor model are defined as follows:

[0122]

[0123] This embodiment adjusts the gain parameter of the controller. Simulation experiments were conducted under different control strategies, including:

[0124] 1. Low-gain control strategy: This indicates the use of a fixed low-gain observer;

[0125] 2. High-gain control strategy: This indicates the use of a fixed high-gain observer;

[0126] 3. Variable gain control strategy: This indicates that a variable gain observer based on changes in system state is enabled.

[0127] The control objective is to increase the angular displacement of the motor. Precisely track command signals The simulation time is set to 0 to 20 seconds.

[0128] Build a motor actuator control system model based on a variable gain extended state observer in MATLAB SIMULINK:

[0129] Figure 2 These are the actual and desired attitude angle values ​​when using a low-gain control strategy in a MATLAB simulation. Figure 3 These are the actual and desired attitude angle values ​​used in the MATLAB simulation employing a high-gain control strategy. Figure 4 The figures show the actual and desired attitude angles in the MATLAB simulation using a variable gain control strategy. It can be seen that under low gain, the motor response oscillates, exhibits significant tracking lag, and eventually diverges. Under high gain, the response speed is significantly improved, but the system experiences large oscillations during sudden load changes. Under variable gain control, the system has a high response speed in the initial stage, and automatically reduces the observer gain in the steady-state stage, thus achieving a comprehensive optimization of speed and stability.

[0130] This embodiment proposes a micro servo motor servo control method based on a combination of variable gain extended state observer and backstepping control, used for dynamically estimating disturbances and achieving precise rudder angle tracking. MATLAB simulation results show that, under external disturbances such as modeling uncertainties and sudden load changes, the constructed variable gain extended state observer control model can significantly improve the disturbance estimation accuracy, suppress output oscillations under high-gain control, and achieve rapid response, smooth transition, and high-precision tracking of the micro servo motor to the desired rudder angle trajectory.

[0131] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. A micro servo motor servo control method based on a combination of variable gain extended state observer and backstepping control, characterized in that: Includes the following steps: Step 1: Establish a third-order nonlinear dynamic model of the micro servo motor electric drive system. The state variables of the model include the servo surface deflection angle, servo surface angular velocity and armature current. The mechanical side equivalent disturbance is modeled as the total disturbance acting on the system. Step 2: Based on flight status information and servo control information, construct a time-smoothly varying observer variable gain function. The specific process is as follows: Step 2.1: Select flight speed, angle of attack, vertical overload, and servo angular velocity as operating condition sensing variables and normalize them; Step 2.2: Combine the normalized operating condition sensing variables into a unified operating condition index by weighting them according to their contribution to disturbances. , The value range is [0, 1]; Step 2.3: Based on operating condition indicators A time-smoothly varying observer gain function is constructed using a smooth mapping function. : The smoothing mapping function is a hyperbolic tangent function, and the observer's variable gain function changes smoothly over time. The format is as follows: in: This is the lower limit of the observer gain; This is the upper limit of the observer gain; To switch centers; This is the steepness parameter; Step 3: Based on the mechanical acceleration equations containing total disturbance in the aforementioned dynamic model, design the gain as follows: An extended state observer is used to estimate the total disturbances acting on the system; Step 4: Design a three-layer control law based on the backstepping method, and use the total disturbance value estimated by the extended state observer for feedforward compensation to generate the control input signal driving the micro servo motor. .

2. The micro servo motor control method based on a combination of variable gain extended state observer and backstepping control according to claim 1, characterized in that: In step 1, the dynamic model is as follows: in, The equivalent rotational inertia of the electric servo motor. The coefficient of viscous friction is... The torque constant of the electric servo motor is... The back electromotive force constant of the electric servo motor; The resistance of the armature winding of the electric servo motor. The inductance of the armature winding of the electric servo motor; This is the terminal voltage applied to the armature winding of the electric servo motor; This is the mechanical equivalent interference.

3. The micro servo motor control method based on a combination of variable gain extended state observer and backstepping control according to claim 1, characterized in that: The gain is The extended state observer is: in, This is an estimate of the angular velocity; This is an estimate of the load disturbance; The gain of the variable observer is dynamically determined by the system operating parameters. This represents the observer error.

4. The micro servo motor control method based on a combination of variable gain extended state observer and backstepping control according to claim 3, characterized in that: In step 4, the process of designing the three-layer control law based on the backstepping method is as follows: First, we introduce the systematic error variable: in, For the desired angle trajectory; These are the virtual control variables for the first and second layers, respectively. These are three layers of error variables, corresponding to angle, angular velocity, and current control errors, respectively. The dynamic equation of the system error obtained from the dynamic model is: Regarding the angle error equation in the system error dynamics equation: Introducing virtual control laws: in Indicates control gain; Regarding the angular velocity error equation in the system error dynamics equation: Design virtual control law for: In the formula, for The estimated value; Regarding the current control error equation in the system error dynamics equation: Design the actual control law for: 。 5. An electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, it implements the micro servo control method according to any one of claims 1 to 4.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by the processor, it implements the micro servo control method according to any one of claims 1 to 4.

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