Compensation control method and system based on differential function observer and switching differentiator

Abstract

This invention relates to the field of UAV attitude disturbance rejection control technology, and provides a compensation control method and system based on a differential function observer and a switched differentiator. The method includes: designing a differential function observer for the nonlinear system based on Newton's dynamic equations according to a second-order nonlinear control model; employing a dual-channel architecture with a dual-integral type II differentiator (DID-II) and a dual-integral type I differentiator (DID-I) for parallel and independent computation, using the absolute value of the difference between the differential estimation outputs of the two channels as the switching criterion; constructing an output strategy for the switched dual-integral differentiator based on a preset empirical threshold and the switching criterion; constructing an active compensation term based on the output strategy of the switched dual-integral differentiator and the differential function observer, and combining it with feedback linearization control to construct an active disturbance rejection control law for UAV attitude compensation control. This invention provides a disturbance rejection control solution with stronger robustness and better transient and steady-state performance.

Description

Technical Field

[0001] This invention relates to the field of attitude disturbance rejection control technology for unmanned aerial vehicles (UAVs), and in particular to a compensation control method and system based on a differential function observer and a switching differential. Background Technology

[0002] The inherent dynamic modeling errors and unpredictable external environmental disturbances in the attitude system of unmanned aerial vehicles (UAVs) are the core factors restricting the achievement of high-performance control of their nonlinear attitude. Active observation compensation control strategies are an effective means to solve this problem. These strategies estimate the unknown function (lumped disturbance) by designing an observer and feed it forward to the control law for active compensation, achieving excellent anti-disturbance performance with relatively low computational cost. To this end, researchers have developed various observers, such as the Extended State Observer (ESO), Sliding Mode Observer (SMO), Disturbance Observer (DOB), and Compensation Function Observer (CFO), to estimate the system's uncertainties.

[0003] However, existing observer-based anti-interference control techniques have two major limitations. First, they heavily rely on high-gain mechanisms: to improve steady-state tracking performance, existing observers often require significantly increased gain parameters. This easily induces severe spikes or chattering in the initial stage of the system or during sudden disturbances, and significantly amplifies the wideband measurement noise of the sensors. The transient spikes of the estimated signal are easily amplified again in the control law through the feedback channel, leading to control oscillations or even system instability. Second, differential signal extraction faces an inherent contradiction between high accuracy and strong noise immunity: the estimation of the force function (disturbance) highly depends on the accurate reconstruction of the state differential, but existing mainstream differentiators are generally trapped in a technical deadlock where "steady-state tracking accuracy" and "transient noise immunity filtering" cannot be achieved simultaneously, easily leading to significant dynamic phase lag or high-frequency physical chattering. In practical engineering applications, such as the attitude control system of a quadcopter UAV, severe time-varying composite disturbances and extreme sensor measurement noise often coexist. Therefore, a novel observer and differentiator structure is needed that can fundamentally eliminate the dependence of unknown function estimation on high-gain mechanisms, while simultaneously achieving both high-precision differential extraction and extreme noise suppression at the architectural level. Summary of the Invention

[0004] This invention aims to at least solve one of the technical problems existing in related technologies. To this end, this invention provides a compensation control method and system based on a differential function observer and a switched differentiator. By transforming the estimation of the unknown function into a momentum error differential extraction problem, it eliminates the dependence of traditional observers on high-gain mechanisms. At the same time, it proposes a dynamically switched architecture for differentiator extraction of derivative signals, thereby balancing high-precision differential extraction with strong noise immunity, and providing a more robust disturbance rejection control solution with better transient and steady-state performance.

[0005] This invention provides a compensation control method based on a differential function observer and a switched differentiator, comprising: S1: Constructing a second-order nonlinear control model for the UAV attitude system based on Newton's dynamic equations; S2: Construct auxiliary state variables by integrating the control input of the UAV, and build a differential function observer for the nonlinear system based on the auxiliary state variables, the actual attitude angle acceleration error of the UAV, and the second-order nonlinear control model. S3: Construct a dual-integral type II differentiator and a dual-integral type I differentiator. Based on the dual-integral type II differentiator and the dual-integral type I differentiator, construct a switching dual-integral differentiator using a parallel and independent dual-channel architecture. The switching dual-integral differentiator uses the absolute value of the difference between the differential estimation outputs of the dual-integral type II differentiator and the dual-integral type I differentiator as the switching criterion. The output of the switching dual-integral differentiator is determined according to a preset empirical threshold and the switching criterion. When the switching criterion is greater than the preset empirical threshold, the output of the dual-integral differentiator is switched to the differential signal extracted by the dual-integral type I differentiator. When the switching criterion is less than or equal to the preset empirical threshold, the output of the dual-integral differentiator is switched to the differential signal extracted by the dual-integral type II differentiator. S4: Calculate the lumped disturbance estimate based on the differential function observer and the switching double integrator-differentiator, construct the active compensation term based on the lumped disturbance estimate, construct the active disturbance rejection control law based on the active compensation term and feedback linearization control theory, and perform compensation control on the UAV attitude system based on the active disturbance rejection control law.

[0006] Furthermore, the second-order nonlinear control model of the UAV attitude system is as follows: in, For the attitude angle of the drone, For attitude angular acceleration, for The derivative, for The derivative, For the nonlinear model of the system and the uncertainty of the model, For true gain, For the control input of the drone, for External disturbances to the drone at any given moment; The lumped uncertainty of unmodeled dynamics, parameter perturbations, and external disturbances is uniformly defined as lumped disturbance, and the calculation expression for lumped disturbance is as follows: in, For aggregated disturbances, This is the nominal control gain.

[0007] Furthermore, the computational expression for the differential function observer is: in, As auxiliary state variables, for The derivative, For the control input of the drone, The nominal control gain. This represents the actual attitude angular acceleration error of the drone. for The derivative, For attitude angular acceleration, This is an estimate of the lumped disturbance.

[0008] Furthermore, the state equation of the double-integral type II differentiator is: in, For tracking the state of the Type II differentiator system, for The derivative, This is the attitude angular acceleration tracking state for the Type II differentiator. for The derivative, This is the input error signal for the Type II differentiator. , For attitude angular acceleration, The first gain parameter of the type II differentiator. This is the second gain parameter of the type II differentiator. This is the differential signal extracted by the dual-integral type II differentiator.

[0009] Furthermore, the state equation of the double-integral type I differentiator is: in, For tracking the state of a Type I differentiator system, for The derivative, This is the attitude angular acceleration tracking state of the Type I differentiator. for The derivative, This is the first gain parameter of the Type I differentiator. For the input error signal of the Type I differentiator, , For the actual attitude angular acceleration, This is the second gain parameter of the Type I differentiator. This is the differential signal extracted by a dual-integral type I differentiator.

[0010] Furthermore, the output of the dual integrator-differentiator is switched as follows: in, This is an estimate of the lumped disturbance. For dynamically switching criteria, The differential signal extracted by the dual-integral type I differentiator. The differential signal extracted by the dual-integral type II differentiator. This is a preset empirical threshold.

[0011] Furthermore, step S4 includes: Calculate the tracking error of the system based on the expected trajectory tracking signal; The tracking error of the system is differentiated to obtain the dynamic equation of the system error; Construct an active disturbance rejection control law based on the feedback linearization control concept; Substituting the active disturbance rejection control law into the error dynamics equation, we obtain the closed-loop error dynamic equation. The attitude control of the UAV is compensated by using a closed-loop error dynamic equation.

[0012] Furthermore, the calculation expression for the active disturbance rejection control law is as follows: in, The nominal control gain. For the control input of the drone, The desired trajectory tracking signal for the system. for The second derivative, The first gain parameter of the control law. This is the second gain parameter of the control law. For attitude angular acceleration tracking error, For position tracking error, This is an estimate of the lumped disturbance.

[0013] Furthermore, the calculation expression for the closed-loop error dynamic equation is as follows: in, for The derivative, Estimate the residuals for the observer's perturbation. This is a lumped disturbance.

[0014] The present invention also provides a compensation control system based on a differential function observer and a switched differentiator, for executing the above-described compensation control method based on a differential function observer and a switched differentiator, comprising: A control model construction module is used to construct a second-order nonlinear control model of the UAV attitude system based on Newton's equations of motion. The differential function observer construction module is used to construct auxiliary state variables by integrating the control input of the UAV, and to construct the differential function observer of the nonlinear system based on the auxiliary state variables, the actual attitude angle acceleration error of the UAV, and the second-order nonlinear control model. A switching dual-integral-differentiator construction module is used to construct a dual-integral-type II differentiator and a dual-integral-type I differentiator. Based on the dual-integral-type II differentiator and the dual-integral-type I differentiator, a dual-channel architecture with parallel and independent calculation is used to construct a switching dual-integral-differentiator. The switching dual-integral-differentiator uses the absolute value of the difference between the differential estimation outputs of the dual-integral-type II differentiator and the dual-integral-type I differentiator as the switching criterion. The output of the switching dual-integral-differentiator is determined according to a preset empirical threshold and the switching criterion. When the switching criterion is greater than the preset empirical threshold, the output of the dual-integral differentiator is switched to the differential signal extracted by the dual-integral type I differentiator. When the switching criterion is less than or equal to the preset empirical threshold, the output of the dual-integral differentiator is switched to the differential signal extracted by the dual-integral type II differentiator. The compensation control module is used to calculate the lumped disturbance estimate based on the differential function observer and the switching double integrator, construct an active compensation term based on the lumped disturbance estimate, construct an active disturbance rejection control law based on the active compensation term and feedback linearization control theory, and perform compensation control on the UAV attitude system based on the active disturbance rejection control law.

[0015] The above-described one or more technical solutions in the embodiments of the present invention have at least one of the following technical effects: This invention, based on Newton's second law, transforms the estimation of an unknown function (perturbation) into an equivalent problem of momentum error differential extraction. By integrating the control quantity and differentiating the error, the estimation of the unknown function no longer relies on a high-gain mechanism, thus fundamentally avoiding peak phenomena and sensitivity to noise. This invention designs a Double-Integral Differentiator with Type-I (DID-I) and a Double-Integrator Differentiator with Type-II (DID-II). DID-I is used to effectively suppress high-frequency noise and transient overshoot, while DID-II ensures high-precision differential extraction in the steady-state phase. A Switch Double Integrator Differentiator (SDID) is constructed, employing parallel dual-channel and residual evaluation logic. It dynamically switches to DID-I during disturbed transients and smoothly switches back to DID-II in steady state. This mechanism achieves both high-precision differential extraction and strong noise resistance at the architecture level, greatly reducing the difficulty of system parameter tuning.

[0016] 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

[0017] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0018] Figure 1 This is a flowchart illustrating a compensation control method based on a differential function observer and a switching differential, provided by the present invention.

[0019] Figure 2 This is a block diagram of the differential function observer provided by the present invention.

[0020] Figure 3 The structural block diagram of the dual-integral type II differentiator provided by the present invention.

[0021] Figure 4 The structural block diagram of the dual-integral type I differentiator provided by the present invention.

[0022] Figure 5 The block diagram of the switching dual integrator-differentiator implementation provided by the present invention is shown.

[0023] Figure 6 This is a comparison chart of the tracking performance of DID-I, DID-II, SDID, and ID under parabolic signal conditions. Figure 6 Figure (a) shows a comparison of system state tracking for DID-I, DID-II, SDID, and ID under the parabolic signal condition. Figure 6 Figure (b) shows a comparison of the tracking errors of DID-I, DID-II, SDID, and ID under the parabolic signal condition.

[0024] Figure 7 This is a comparison chart of the tracking performance of STD, URED, FO-STD, and SDID under parabolic signal conditions. Figure 7 Figure (a) shows a comparison of system state tracking for STD, URED, FO-STD, and SDID under parabolic signal conditions. Figure 7 Figure (b) in the figure is a comparison of the tracking errors of STD, URED, FO-STD and SDID under the parabolic signal condition.

[0025] Figure 8 This is a comparison chart of the tracking performance of DID-I, DID-II, SDID, and ID under high-frequency smooth time-varying signals in an embodiment of the present invention. Figure 8 Figure (a) shows a comparison of system state tracking for DID-I, DID-II, SDID, and ID under high-frequency smooth time-varying signals. Figure 8 Figure (b) in the figure is a comparison of the tracking errors of DID-I, DID-II, SDID and ID under high-frequency smooth time-varying signals.

[0026] Figure 9 This is a comparison chart of the tracking performance of STD, URED, FO-STD, and SDID under high-frequency smooth time-varying signals. Figure 9 Figure (a) shows a comparison of system state tracking for STD, URED, FO-STD, and SDID under high-frequency smoothed time-varying signals. Figure 9 Figure (b) in the figure is a comparison of the tracking errors of STD, URED, FO-STD and SDID under high-frequency smooth time-varying signals.

[0027] Figure 10 This is a comparison chart of the tracking performance of ID and DID-II, and DID-I and SDID under a composite signal of strong noise pollution and step change. Figure 10 Figure (a) in the figure shows a comparison of the tracking performance of traditional ID and DID-II under the combined signal of strong noise pollution and step change; Figure 10 Figure (b) shows a comparison of the tracking performance of DID-I and SDID under a composite signal of strong noise pollution and step change.

[0028] Figure 11 This is a comparison chart of the tracking performance of URED and FO-STD, STD and SDID under a composite signal of strong noise pollution and step abrupt change. Figure 11 Figure (a) shows a comparison of the tracking performance of URED and FO-STD under a composite signal of strong noise pollution and step abrupt change. Figure 11 Figure (b) in the figure shows a comparison of the tracking performance of STD and SDID under the combined signal of strong noise pollution and step change.

[0029] Figure 12 This is a comparison chart of the estimation and estimation error of the lumped disturbance in the UAV pitch channel by each observer, where... Figure 12 Figure (a) in the figure shows a comparison of the estimates of the lumped disturbance in the pitch channel of the UAV by various observers. Figure 12 Figure (b) in the figure is a comparison of the estimation errors of each observer for the lumped disturbance of the UAV pitch channel.

[0030] Figure 13 This is a comparison of the estimation and estimation error of the lumped disturbance in the UAV pitch channel by a high-order sliding mode observer, where... Figure 13 Figure (a) shows a comparison of estimations of lumped disturbances in the pitch channel of the UAV by a higher-order sliding mode observer. Figure 13 Figure (b) in the figure is a comparison of the estimation errors of the high-order sliding mode observer for the lumped disturbance of the UAV pitch channel.

[0031] Figure 14 This is a comparison chart of the system output roll angle and roll angle tracking error under different observer control in the roll channel of this invention embodiment. Figure 14 Figure (a) in the figure is a comparison of the system output roll angle under different observer control in the roll channel. Figure 14 Figure (b) in the figure is a comparison of the tracking error of the system output roll angle under different observer control in the roll channel.

[0032] Figure 15 This is a comparison chart of the system output pitch angle and pitch angle tracking error under different observer control in the pitch channel of this invention embodiment. Figure 15 Figure (a) shows a comparison of the system output pitch angles under different observer control in the pitch channel. Figure 15 Figure (b) in the figure is a comparison of the tracking error of the system output pitch angle under different observer control of the pitch channel.

[0033] Figure 16 This invention provides a schematic diagram of a compensation control system based on a differential function observer and a switching differential.

[0034] Figure label: 101. Control model construction module; 102. Differential function observer construction module; 103. Switching double integrator and differentiator construction module; 104. Compensation control module. Detailed Implementation

[0035] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention. The following embodiments are used to illustrate this invention but cannot be used to limit the scope of this invention.

[0036] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0037] The following is combined Figures 1 to 16 This invention describes a compensation control method and system based on a differential function observer and a switching differential.

[0038] like Figure 1 As shown, a compensation control method based on a differential function observer and a switching differentiator includes: S1: Constructing a second-order nonlinear control model for the UAV attitude system based on Newton's dynamic equations; Based on Newton's equations of motion, the attitude dynamics model of the UAV is expressed as follows: in, The roll angle of the drone. The pitch angle of the drone. The yaw angle of the drone. The angular velocity along the X-axis in the body coordinate system. The angular velocity along the Y-axis in the body coordinate system. The angular velocity along the Z-axis in the body coordinate system. Let X be the moment of inertia along the X-axis. The moment of inertia is the rotation along the Y-axis. Let Z be the moment of inertia along the rotational axis. For roll control torque, For pitch control torque, For yaw control torque, For the rotor's moment of inertia, The rotational speed of the first rotor. This is the rotational speed of the second rotor. The rotational speed of the third rotor. The rotational speed of the fourth rotor. The roll aerodynamic damping coefficient is... This is the pitch aerodynamic damping coefficient. This is the aerodynamic damping coefficient. The magnitude of the body's angular velocity vector; This represents the total external disturbance experienced by the roll channel. This represents the total external disturbance experienced by the pitch channel. This represents the total external disturbance experienced by the yaw channel; for The second derivative, for The first derivative, for The second derivative, for The first derivative, for The second derivative, for The first derivative; Based on the above mechanisms and nonlinear coupling characteristics, under the small-angle assumption, the second-order nonlinear control model of the UAV attitude system can be expressed as: in, For the attitude angle of the drone, For attitude angular acceleration, for The derivative, for The derivative, For the nonlinear model of the system and the uncertainty of the model, For true gain, For the control input of the drone, for External disturbances to the drone at any given moment; The lumped uncertainty of unmodeled dynamics, parameter perturbations, and external disturbances is uniformly defined as lumped disturbance, and the calculation expression for lumped disturbance is as follows: in, For aggregated disturbances, This is the nominal control gain; It can be explicitly expressed as the difference between the rate of change of momentum and the known control input of the UAV, and the calculation expression is: It is usually unknown, and an observer needs to be designed to estimate it, transforming the problem of observing unknown functions into the problem of extracting momentum differential signals.

[0039] The second-order nonlinear control model is equivalent to: .

[0040] S2: Construct auxiliary state variables by integrating the control input of the UAV, and build a differential function observer for the nonlinear system based on the auxiliary state variables, the actual attitude angle acceleration error of the UAV, and the second-order nonlinear control model. Directly obtain Dependent on the control input of the drone and To eliminate the influence of the UAV's control input, an integrator is designed to store the UAV's control input in the integrator, i.e.: in, As auxiliary state variables, for The derivative, For the control input of the drone, This is the nominal control gain; The difference between the attitude angular acceleration and the auxiliary state variable is defined as the error of the UAV's true attitude angular acceleration, and its calculation expression is: in, Let $\frac{ ... in, for The derivative of .

[0041] This eliminates the direct algebraic coupling between the UAV's control input u and the lumped disturbance to be estimated, by solving... The lumped disturbance can then be solved. .

[0042] At this point, the function estimation problem has been transformed into a problem of momentum error differential or error acceleration. Designed for The disturbance estimate is used to obtain the complete DFO observer, such as Figure 2 As shown, the calculation expression is: in, As auxiliary state variables, for The derivative, For the control input of the drone, The nominal control gain. This represents the actual attitude angular acceleration error of the drone. for The derivative, For attitude angular acceleration, This is an estimate of the lumped disturbance. Figure 2 middle This indicates that the signal is integrated.

[0043] The DFO contains an integrator and a differentiator. Only the parameters of its embedded differentiator need to be configured, which avoids the spike contradictions caused by the high-gain mechanism, greatly simplifies the complexity of the observer design, and eliminates the need for complex observer and controller parameter co-tuning.

[0044] S3: Construct a dual-integral type II differentiator and a dual-integral type I differentiator. Based on the dual-integral type II differentiator and the dual-integral type I differentiator, construct a switching dual-integral differentiator using a parallel and independent dual-channel architecture. The switching dual-integral differentiator uses the absolute value of the difference between the differential estimation outputs of the dual-integral type II differentiator and the dual-integral type I differentiator as the switching criterion. The output of the switching dual-integral differentiator is determined according to a preset empirical threshold and the switching criterion. When the switching criterion is greater than the preset empirical threshold, the output of the dual-integral differentiator is switched to the differential signal extracted by the dual-integral type I differentiator. When the switching criterion is less than or equal to the preset empirical threshold, the output of the dual-integral differentiator is switched to the differential signal extracted by the dual-integral type II differentiator. Traditional differentiators are generally caught in a technical impasse where "high accuracy" and "strong filtering" are mutually exclusive. This invention equates the differential estimation problem to a signal tracking problem, where the type of tracking system directly determines the tracking accuracy. By designing a dual-channel solution architecture, the requirements for steady-state high accuracy and transient strong filtering are met respectively.

[0045] To ensure high-precision differential extraction during the steady-state phase, a block diagram of a dual-integral type II differentiator is designed as follows: Figure 3 As shown, the state equation of the double-integral type II differentiator is: in, For tracking the state of the Type II differentiator system, for The derivative, This is the attitude angular acceleration tracking state for the Type II differentiator. for The derivative, This is the input error signal for the Type II differentiator. , This represents the actual attitude angular acceleration error of the drone. The first gain parameter of the type II differentiator. This is the second gain parameter of the type II differentiator. This is the differential signal extracted by the dual-integral type II differentiator.

[0046] Frequency domain analysis of DID-II, its input signal To differential output The transfer function is: in, For the complex frequency variable of the Laplace transform; Characteristic Analysis (High Precision and Weak Filtering): The DID-II represents a significant improvement over traditional first-order differentiators, achieving steady-state, zero-steady-state-error extraction of differentiated ramp signals and effectively suppressing dynamic phase lag. However, its transfer function reveals that the numerator and denominator of the closed-loop transfer function are of the same order, resulting in a constant high-frequency gain and a lack of high-frequency filtering capability. Furthermore, constrained by the forward zero, it exhibits inherent response overshoot in transient processes. Therefore, the DID-II is primarily used for extracting signals under extremely high-precision steady-state conditions.

[0047] To compensate for the lack of high-frequency filtering capability of the DID-II under harsh operating conditions and to effectively suppress high-frequency noise amplification and transient overshoot, a dual-integral type-I differentiator is designed. The DID-I possesses strong filtering and no overshoot characteristics. Its block diagram is shown below. Figure 4 As shown, the state equation of the double-integral type I differentiator is: in, For tracking the state of a Type I differentiator system, for The derivative, This is the attitude angular acceleration tracking state of the Type I differentiator. for The derivative, This is the first gain parameter of the Type I differentiator. For the input error signal of the Type I differentiator, , This represents the actual attitude angular acceleration error of the drone. This is the second gain parameter of the Type I differentiator. This is the differential signal extracted by a dual-integral type I differentiator.

[0048] Frequency domain analysis of DID-I is performed, which analyzes the input signal... To differential output The closed-loop transfer function is: Characteristic Analysis (Low Precision and Strong Filtering): The DID-I is essentially a typical Type I tracking system. While its steady-state accuracy is lower than that of a Type II system, it offers significant advantages in transient response and high-frequency noise immunity. Because its closed-loop transfer function has no forward zeros, in practical applications, only critical damping is needed to completely eliminate step response overshoot. Simultaneously, its differential operator possesses a low-pass characteristic with a relative order of 1, effectively blocking the amplification path of high-frequency measurement noise from its mathematical origin.

[0049] Traditional differentiators typically employ internal parameter or structural switching mechanisms to address the trade-off between high precision and strong filtering. However, the internal dynamics of a differentiator are persistent, and such switching can easily trigger discontinuous jumps in the state derivative, leading to numerical chattering and state delays in the closed-loop system. To fundamentally overcome this inherent topological contradiction, the SDID of this invention abandons the traditional internal switching mechanism and adopts a fully parallel dual-channel solution architecture with two differentiators, performing routing switching at the output end.

[0050] Let DID-I and DID-II be solved independently in a fully parallel dual-channel manner. The error-driven dynamic switching criterion is as follows: in, For dynamically switching criteria, The differential signal extracted by the dual-integral type I differentiator. This is the differential signal extracted by the dual-integral type II differentiator.

[0051] It can accurately characterize the transient severity and high-frequency noise pollution level of a system in real time. Its design is based on the fact that when the system faces signal step changes or strong noise interference, the high-frequency pass-through characteristics of DID-II contrast sharply with the low-pass attenuation characteristics of DID-I, leading to differences in their outputs. The amplitude increases rapidly and significantly; conversely, when the system is in a stable tracking phase, both channels can track the signal well, and the estimated outputs tend to be consistent. It approaches zero.

[0052] use Given the significant amplitude variations under different operating conditions, an empirical threshold is introduced. The output of SDID is constructed, and the structure diagram of SDID is as follows. Figure 5 As shown, the calculation expression is: in, This is an estimate of the lumped disturbance. This is a preset empirical threshold.

[0053] When the system is in a disturbed transient or high-noise condition ( When the system is in a steady-state smooth condition, the output automatically switches to DID-I to effectively cut off the amplification path of sudden changes or noise; when the system is in a steady-state smooth condition ( When the output is switched back to DID-II, it is smooth to ensure extremely high steady-state differential extraction accuracy.

[0054] In a fully parallel solution architecture, the internal integral states of each subsystem are always updated independently and continuously in real time. This mechanism avoids the risks of state derivative jumps, closed-loop numerical chattering, and state delays caused by traditional gain switching and structure switching from a mathematical perspective. At the architectural level, it successfully overcomes the topological limitations that make it difficult to balance response bandwidth and noise robustness.

[0055] Finally, the SDID output is highly fidelity and smooth. As the output of DFO. If the high smoothness of the input signal is known a priori, the system can be deployed with DID-II alone to pursue ultimate accuracy.

[0056] S4: Calculate the lumped disturbance estimate based on the differential function observer and the switching double integrator, construct the active compensation term based on the lumped disturbance estimate, construct the active disturbance rejection control law based on the active compensation term and the feedback linearization control theory, and perform compensation control on the UAV attitude system based on the active disturbance rejection control law; Utilizing the aforementioned high-precision observation information, a closed-loop control law combining active feedforward compensation and feedback regulation is constructed to effectively suppress multi-source disturbances in the system. For systems with lumped disturbances, the desired trajectory tracking signal is defined as... The set control objective is: to control the UAV... Under its influence, the system state can overcome internal nonlinearity and external disturbances, and gradually and accurately track the desired signal. S41: Calculate the system's tracking error based on the system's desired trajectory tracking signal; the system's tracking error includes position error and momentum error, and the calculation expression is as follows: in, For attitude angular acceleration tracking error, For position tracking error, The desired trajectory tracking signal for the system. for The derivative; S42: Differentiate the tracking error of the system to obtain the system error dynamic equation. The calculation expression is as follows: in, for The derivative, for The derivative, for The second derivative; S43: Construct an active disturbance rejection control law based on the feedback linearization control concept. The calculation expression is as follows: in, The nominal control gain. For the control input of the drone, The desired trajectory tracking signal for the system. for The second derivative, The first gain parameter of the control law. This is the second gain parameter of the control law. This is an estimate of the lumped disturbance.

[0057] First derivative of the expected trajectory and second derivative It can be obtained through a higher-order differentiator (HOD). , Let be the positive real numbers to be selected. This is a linear error feedback term used to ensure the asymptotic stability of the system. It is the lumped disturbance estimate extracted in real time from DFO and SDID, which is used as an active compensation term to offset the actual system lumped disturbance. .

[0058] S44: Substituting the active disturbance rejection control law into the error dynamics equation, we obtain the closed-loop error dynamic equation, and its calculation expression is: in, for The derivative, Estimate the residuals for the observer's perturbation. This is a lumped disturbance.

[0059] The closed-loop error dynamic equation intuitively reveals the endogenous coupling relationship between the observation residual and the control performance.

[0060] S45: Compensation control of the UAV attitude system is achieved through closed-loop error dynamic equations.

[0061] Because the DFO combined with SDID used in this invention breaks the limitations of traditional high-gain mechanisms, it can balance high-precision differential extraction and strong noise-resistant filtering, thereby reducing the observer's disturbance estimation residual. The stability constraint is within a very small bounded range. Finally, reasonable differentiator parameters and switching thresholds are selected to ensure the accuracy of differential extraction, while also selecting... Furthermore, based on Lyapunov stability theory, the proposed control law, as the control input of the UAV, can effectively block the feedback amplification path of high-frequency noise from the observer to the controller. The output channel of the controlled system can effectively avoid the influence of unmodeled dynamics and external lumped uncertainties, ultimately ensuring that the tracking error state of the entire closed-loop system is semi-globally consistent and eventually bounded (SGUUB), achieving high-precision robust disturbance-resistant tracking.

[0062] To demonstrate that the SDID differentiator proposed in this invention can eliminate the influence of different dynamic frequencies and strong noise pollution on system signal extraction, parabolic differential signals, high-frequency smooth time-varying signals, and strong noise composite abrupt change signals were designed for testing. In-depth comparisons were also made with traditional differentiators with inertial elements (ID), standard superspiral differentiators (STD), uniform robust differentiators (URED), and fractional superspiral differentiators (FO-STD).

[0063] Figures 6 to 11 middle The input signal of the differentiator. for The derivative of . Figure 6 and Figure 7 The tracking performance of different differentiators under parabolic signal conditions is demonstrated. Figure 6 Figure (a) shows a comparison of system state tracking for DID-I, DID-II, SDID, and ID under the parabolic signal condition. Figure 6 Figure (b) shows a comparison of the tracking errors of DID-I, DID-II, SDID, and ID under the parabolic signal condition. Figure 7 Figure (a) shows a comparison of system state tracking for STD, URED, FO-STD, and SDID under parabolic signal conditions. Figure 7 Figure (b) in the figure is a comparison of the tracking errors of STD, URED, FO-STD and SDID under the parabolic signal condition.

[0064] As a Type I system, ID exhibits significant steady-state hysteresis; however, the SDID proposed in this invention inherits the high-precision Type II characteristics of DID-II, compressing the steady-state error to a theoretical constant, and achieving near coincidence with the theoretical differential signal.

[0065] Figure 8 and Figure 9The graph shows a comparison of the tracking performance of different differentiators under high-frequency smooth time-varying signals. Figure 8 Figure (a) shows a comparison of system state tracking for DID-I, DID-II, SDID, and ID under high-frequency smooth time-varying signals. Figure 8 Figure (b) in the figure is a comparison of the tracking errors of DID-I, DID-II, SDID and ID under high-frequency smooth time-varying signals.

[0066] Figure 9 Figure (a) shows a comparison of system state tracking for STD, URED, FO-STD, and SDID under high-frequency smoothed time-varying signals. Figure 9 Figure (b) in the figure is a comparison of the tracking errors of STD, URED, FO-STD and SDID under high-frequency smooth time-varying signals.

[0067] In practical tuning, the standard superspiral differentiator (STD) exhibits singularly high gain near the origin, making it highly sensitive to parameters and prone to triggering severe chattering that contaminates experimental images. After multiple experimental compromises, this simulation was conducted to avoid chattering. Under the impact of high-frequency continuous dynamic signals, while the nonlinear differentiators FO-STD and URED can track smoothly, they still retain varying degrees of dynamic phase lag. SDID, on the other hand, consistently maintains extremely small tracking errors, minimizing dynamic phase lag.

[0068] Figure 10 and Figure 11 The graph shows a comparison of the tracking performance of different differentiators under a composite signal of strong noise pollution and step abrupt change. Figure 10 Figure (a) in the figure shows a comparison of the tracking performance of traditional ID and DID-II under the combined signal of strong noise pollution and step change; Figure 10 Figure (b) shows a comparison of the tracking performance of DID-I and SDID under a composite signal of strong noise pollution and step change. Figure 11 Figure (a) shows a comparison of the tracking performance of URED and FO-STD under a composite signal of strong noise pollution and step abrupt change. Figure 11 Figure (b) in the figure shows a comparison of the tracking performance of STD and SDID under the combined signal of strong noise pollution and step change.

[0069] Under these extremely harsh operating conditions, traditional ID and DID-II, lacking high-frequency suppression mechanisms, are extremely sensitive to noise, resulting in significant differential output jitter; URED induces extreme peak overshoot in the initial stage of signal abrupt changes; while FO-STD can filter, it comes at the cost of significant steady-state error. In contrast, the SDID of this invention, through parallel residual criteria, effectively filters signal abrupt changes and strong noise during sudden changes (…). The system accurately switched to DID-I, successfully achieving strong noise immunity and overshoot-free response; during the stable tracking phase ( It then seamlessly switches back to DID-II, regaining ultimate differentiation accuracy. This successfully breaks through the topological limitation of traditional differentiators where "filtering smoothing" and "phase following" are mutually exclusive.

[0070] For a general system model, the control objective is to require the system output to be... Able to stably and progressively track the desired given signal And effectively suppress multi-source composite disturbances. The effect. Taking the derivative twice with respect to the system output yields... The tracking error state of the system is defined as follows: and The disturbance rejection control law based on DFO feedforward compensation and feedback linearization (FLC) is designed as follows: in, Estimated jointly by DFO and SDID, this serves as an active compensation term for uncertainty; the control gain parameter is selected. This ensures that the closed-loop system satisfies the Hurwitz stability condition, achieving semi-globally consistent eventual boundedness (SGUUB).

[0071] To further highlight the superior performance of the closed-loop control in this invention, control strategies based on Extended State Observer (ESO), Compensated Function Observer (CFO), and Higher-Order Sliding Mode Observer (HSMO) were also designed as a control group. A composite time-varying disturbance, including constant bias, low-frequency airflow fluctuations, and high-frequency noise, was injected into the system during operation.

[0072] Figure 12 The graph shows a comparison of the estimates and estimation errors of the lumped disturbance of the UAV attitude system by each observer. Figure 12 Figure (a) in the figure shows a comparison of the estimates of the lumped disturbance of the UAV attitude system by each observer. Figure 12 Figure (b) in the figure is a comparison of the estimation errors of each observer for the lumped disturbance of the UAV attitude system.

[0073] Figure 13 A graph showing the estimation of lumped perturbations in the UAV attitude system by a high-order sliding mode observer and the comparison of estimation errors is presented. Figure 13 Figure (a) shows a comparison of estimations of the lumped disturbance of the UAV attitude system by a higher-order sliding mode observer. Figure 13 Figure (b) in the figure is a comparison of the estimation errors of the high-order sliding mode observer for the lumped disturbance of the UAV attitude system.

[0074] At the moment of abrupt change in disturbance, traditional high-gain ESOs, due to their inherently low topology, excite huge transient overshoot distortion and error spikes; CFOs also exhibit significant transient overshoot and convergence hysteresis at the abrupt change; HSMOs reveal significant dynamic phase lag accompanied by high-frequency physical chattering. The DFO proposed in this invention, based on a momentum integral decoupling architecture, not only achieves accurate tracking with extremely low latency at the spikes, but also greatly reduces oscillations and phase lag in the steady-state phase, rapidly and smoothly converging the estimation error to a minimal neighborhood.

[0075] Figure 14 The graph shows a comparison of the system output roll angle and roll angle tracking error under different observer control in the roll channel. Figure 14 Figure (a) in the figure is a comparison of the system output roll angle under different observer control in the roll channel. Figure 14 Figure (b) in the figure is a comparison of the tracking error of the system output roll angle under different observer control in the roll channel.

[0076] Figure 15 The graph shows a comparison of the system output pitch angle and pitch tracking error under different observer control in the pitch channel. Figure 15 Figure (a) shows a comparison of the system output pitch angles under different observer control in the pitch channel. Figure 15 Figure (b) in the figure is a comparison of the tracking error of the system output pitch angle under different observer control of the pitch channel.

[0077] All four types of controllers can ultimately enable the system output to asymptotically converge to a given desired trajectory. However, based on local magnification and error curve comparison, it can be seen that the control effect of DFO based on this invention is significantly better than the ESO, CFO, and HSMO control groups. Specifically, under complex disturbances and sudden shocks, the control method of this invention has the shortest settling time, the strongest resistance to shock distortion, and the steady-state tracking error is compressed to an extremely small order of magnitude. The accuracy is significantly improved compared with traditional methods, and there are no high-frequency numerical oscillations throughout the process, demonstrating extremely high transient safety and steady-state fidelity.

[0078] like Figure 16 As shown, a compensation control system based on a differential function observer and a switched differentiator, used to execute the aforementioned compensation control method based on a differential function observer and a switched differentiator, includes: Control model construction module 101 is used to construct a second-order nonlinear control model of the UAV attitude system based on Newton's dynamic equations; The differential function observer construction module 102 is used to construct auxiliary state variables by integrating the control input of the UAV, and to construct the differential function observer of the nonlinear system based on the auxiliary state variables, the actual attitude angle acceleration error of the UAV and the second-order nonlinear control model. The switching dual-integral differentiator construction module 103 is used to construct a dual-integral type II differentiator and a dual-integral type I differentiator. Based on the dual-integral type II differentiator and the dual-integral type I differentiator, a dual-channel architecture with parallel independent calculation is used to construct a switching dual-integral differentiator. The switching dual-integral differentiator uses the absolute value of the difference between the differential estimation outputs of the dual-integral type II differentiator and the dual-integral type I differentiator as the switching criterion. The output of the switching dual-integral differentiator is determined according to the preset empirical threshold and the switching criterion. When the switching criterion is greater than the preset empirical threshold, the output of the dual-integral differentiator is switched to the differential signal extracted by the dual-integral type I differentiator. When the switching criterion is less than or equal to the preset empirical threshold, the output of the dual-integral differentiator is switched to the differential signal extracted by the dual-integral type II differentiator. The compensation control module 104 is used to calculate the lumped disturbance estimate based on the differential function observer and the switching double integrator, construct an active compensation term based on the lumped disturbance estimate, construct an active disturbance rejection control law based on the active compensation term and feedback linearization control theory, and perform compensation control on the UAV attitude system based on the active disturbance rejection control law.

[0079] Through the collaborative work of the aforementioned modules, based on Newton's second law, the estimation of the unknown function (lumped disturbance) is equivalently transformed into a momentum error differential extraction problem. By integrating the UAV's control input and differentiating the error, the estimation of the unknown function no longer relies on a high-gain mechanism, thus fundamentally avoiding peak phenomena and sensitivity to noise. Dual-integral type I and type II differentiators (DID-I and DID-II) were designed. The dual-integral type I differentiator (DID-I) is used to effectively suppress high-frequency noise and transient overshoot, while the dual-integral type II differentiator (DID-II) is used to ensure high-precision differential extraction in the steady-state phase. Switching between the dual-integral differentiators (SDID) employs parallel dual-channel and residual evaluation logic, dynamically switching to DID-I during disturbed transients and smoothly switching back to DID-II in steady state. This mechanism achieves both high-precision differential extraction and strong noise immunity at the architectural level, greatly reducing the difficulty of system parameter tuning.

[0080] When DFO and SDID are applied to attitude tracking control of a quadcopter UAV with multi-source time-varying uncertainties, numerical simulation results show that, compared with the compared observer methods, the present invention has better performance in terms of differential extraction fidelity, peak noise error suppression, and attitude tracking control performance.

[0081] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A compensation control method based on a differential function observer and a switched differentiator, characterized in that, include: S1: Constructing a second-order nonlinear control model for the UAV attitude system based on Newton's dynamic equations; S2: Construct auxiliary state variables by integrating the control input of the UAV, and build a differential function observer for the nonlinear system based on the auxiliary state variables, the actual attitude angle acceleration error of the UAV, and the second-order nonlinear control model. S3: Construct a dual-integral type II differentiator and a dual-integral type I differentiator. Based on the dual-integral type II differentiator and the dual-integral type I differentiator, construct a switching dual-integral differentiator using a parallel and independent dual-channel architecture. The switching dual-integral differentiator uses the absolute value of the difference between the differential estimation outputs of the dual-integral type II differentiator and the dual-integral type I differentiator as the switching criterion. The output of the switching dual-integral differentiator is determined according to a preset empirical threshold and the switching criterion. When the switching criterion is greater than the preset empirical threshold, the output of the dual-integral differentiator is switched to the differential signal extracted by the dual-integral type I differentiator. When the switching criterion is less than or equal to the preset empirical threshold, the output of the dual-integral differentiator is switched to the differential signal extracted by the dual-integral type II differentiator. S4: Calculate the lumped disturbance estimate based on the differential function observer and the switching double integrator-differentiator, construct the active compensation term based on the lumped disturbance estimate, construct the active disturbance rejection control law based on the active compensation term and feedback linearization control theory, and perform compensation control on the UAV attitude system based on the active disturbance rejection control law.

2. The compensation control method based on a differential function observer and a switching differentiator according to claim 1, characterized in that, The second-order nonlinear control model of the UAV attitude system is as follows: in, For the attitude angle of the drone, For attitude angular acceleration, for The derivative of for The derivative of For the system's nonlinear model and model uncertainty, For true gain, For the control input of the drone, for External disturbances to the drone at any given moment; The lumped uncertainty of unmodeled dynamics, parameter perturbations, and external disturbances is uniformly defined as lumped disturbance, and the calculation expression for lumped disturbance is as follows: in, For aggregated disturbances, This is the nominal control gain.

3. The compensation control method based on a differential function observer and a switching differentiator according to claim 1, characterized in that, The computational expression for the differential function observer is: in, As auxiliary state variables, for The derivative of For the control input of the drone, The nominal control gain. This represents the actual attitude angular acceleration error of the drone. for The derivative of For attitude angular acceleration, This is an estimate of the lumped disturbance.

4. The compensation control method based on a differential function observer and a switching differentiator according to claim 1, characterized in that, The state equation of the dual-integral type II differentiator is: in, For tracking the state of the Type II differentiator system, for The derivative of This is the attitude angular acceleration tracking state for the Type II differentiator. for The derivative of This is the input error signal for the Type II differentiator. , This represents the actual attitude angular acceleration error of the drone. The first gain parameter of the type II differentiator. This is the second gain parameter of the type II differentiator. This is the differential signal extracted by the dual-integral type II differentiator.

5. The compensation control method based on a differential function observer and a switching differentiator according to claim 1, characterized in that, The state equation of the double-integral type I differentiator is: in, For tracking the state of a Type I differentiator system, for The derivative of This is the attitude angular acceleration tracking state of the Type I differentiator. for The derivative of This is the first gain parameter of the Type I differentiator. For the input error signal of the Type I differentiator, , This represents the actual attitude angular acceleration error of the drone. This is the second gain parameter of the Type I differentiator. This is the differential signal extracted by a dual-integral type I differentiator.

6. The compensation control method based on a differential function observer and a switching differentiator according to claim 1, characterized in that, The output of the dual integrator-differentiator is switched to: in, This is an estimate of the lumped disturbance. For dynamically switching criteria, The differential signal extracted by the dual-integral type I differentiator. The differential signal extracted by the dual-integral type II differentiator. This is a preset empirical threshold.

7. The compensation control method based on a differential function observer and a switching differentiator according to claim 1, characterized in that, Step S4 includes: Calculate the tracking error of the system based on the expected trajectory tracking signal; The tracking error of the system is differentiated to obtain the dynamic equation of the system error; Construct an active disturbance rejection control law based on the feedback linearization control concept; Substituting the active disturbance rejection control law into the error dynamics equation, we obtain the closed-loop error dynamic equation. The attitude control of the UAV is compensated by using a closed-loop error dynamic equation.

8. The compensation control method based on a differential function observer and a switching differentiator according to claim 7, characterized in that, The calculation expression for the active disturbance rejection control law is: in, The nominal control gain. For the control input of the drone, The desired trajectory tracking signal for the system. for The second derivative, The first gain parameter of the control law. This is the second gain parameter of the control law. For attitude angular acceleration tracking error, For position tracking error, This is an estimate of the lumped disturbance.

9. A compensation control method based on a differential function observer and a switching differentiator according to claim 8, characterized in that, The expression for calculating the dynamic equation of the closed-loop error is as follows: in, for The derivative of Estimate the residuals for the observer's perturbation. This is a lumped disturbance.

10. A compensation control system based on a differential function observer and a switched differentiator, characterized in that, To execute a compensation control method based on a differential function observer and a switching differential as described in any one of claims 1 to 9, comprising: A control model construction module is used to construct a second-order nonlinear control model of the UAV attitude system based on Newton's equations of motion. The differential function observer construction module is used to construct auxiliary state variables by integrating the control input of the UAV, and to construct the differential function observer of the nonlinear system based on the auxiliary state variables, the actual attitude angle acceleration error of the UAV, and the second-order nonlinear control model. A switching dual-integral-differentiator construction module is used to construct a dual-integral-type II differentiator and a dual-integral-type I differentiator. Based on the dual-integral-type II differentiator and the dual-integral-type I differentiator, a dual-channel architecture with parallel and independent calculation is used to construct a switching dual-integral-differentiator. The switching dual-integral-differentiator uses the absolute value of the difference between the differential estimation outputs of the dual-integral-type II differentiator and the dual-integral-type I differentiator as the switching criterion. The output of the switching dual-integral-differentiator is determined according to a preset empirical threshold and the switching criterion. When the switching criterion is greater than the preset empirical threshold, the output of the dual-integral differentiator is switched to the differential signal extracted by the dual-integral type I differentiator. When the switching criterion is less than or equal to the preset empirical threshold, the output of the dual-integral differentiator is switched to the differential signal extracted by the dual-integral type II differentiator. The compensation control module is used to calculate the lumped disturbance estimate based on the differential function observer and the switching double integrator, construct an active compensation term based on the lumped disturbance estimate, construct an active disturbance rejection control law based on the active compensation term and feedback linearization control theory, and perform compensation control on the UAV attitude system based on the active disturbance rejection control law.

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