A method and device for active disturbance rejection control for dynamic trajectory tracking

Abstract

This invention belongs to the field of automatic control related technology. It discloses an active disturbance rejection control method and device for dynamic trajectory tracking. (1) Calculate the system tracking error between the output signal of the controlled object and the reference trajectory, and establish the error dynamic equation of the system tracking error; (2) Reconstruct the error dynamic equation into the integrator cascade canonical form through composite lumped disturbance, and regard the composite lumped disturbance as the extended state to be estimated in the integrator cascade canonical form; (3) Design a tracking-oriented extended state observer. The tracking-oriented extended state observer takes the system tracking error and the control input signal as input, estimates the extended state vector in real time, and outputs the corresponding estimated value; (4) Design a compensation control law based on the obtained estimated value to generate the control input signal, and use the control input signal to stabilize the error system corresponding to the integrator cascade canonical form. This invention fundamentally solves the problem of "objective non-equivalence".

Description

Technical Field

[0001] This invention belongs to the field of automatic control technology, and more specifically, relates to an active disturbance rejection control method and device for dynamic trajectory tracking. Background Technology

[0002] In precision motion control fields such as high-end manufacturing, medical surgical robotics, and aerospace, control systems must simultaneously meet stringent requirements for trajectory tracking accuracy and robustness. However, real-world physical systems, such as multi-degree-of-freedom robotic arms, generally exhibit strong nonlinearity, time-varying coupled dynamics, model uncertainties (such as load variations and friction), and external environmental disturbances. These factors severely limit the improvement of control performance. Therefore, designing advanced control strategies with both high accuracy and strong robustness for uncertain nonlinear systems has always been a core research topic in control theory and engineering applications.

[0003] Currently, mainstream control strategies each have their limitations. Proportional-Integral-Derivative (PID) control is widely used due to its simple structure, but its linear characteristics make it difficult to effectively handle complex nonlinear dynamics, and parameter tuning often requires a trade-off between response speed and stability. Model-based control methods, such as computational torque control (CTC), are highly dependent on accurate dynamic models; their robustness drops sharply if the dynamic model is mismatched or unmodeled dynamics exist. Sliding mode control (SMC), while theoretically perfectly robust to matching uncertainties, suffers from chattering due to its inherent discontinuous switching characteristics, damaging actuators and affecting control accuracy. Furthermore, data-driven methods, such as neural networks (NN) and reinforcement learning (RL), while theoretically approximating arbitrary nonlinearities, are highly dependent on the quantity and quality of training data, have limited generalization ability, and generally lack rigorous stability and safety guarantees, limiting their application in safety-critical fields.

[0004] As a cutting-edge control technique that does not rely on precise models, Active Disturbance Rejection Control (ADRC) offers a highly attractive framework for addressing the aforementioned challenges. The core idea of ​​ADRC is to treat all unmodeled dynamics, parameter perturbations, and external disturbances within the system as a single "total disturbance." In modern control theory, this concept is more accurately termed "lumped disturbance." ADRC utilizes its core component—the Extended State Observer (ESO)—to estimate this lumped disturbance in real time, and then actively compensates for it using a control law. In this way, ADRC can transform a complex, uncertain system into a simple integrator-cascaded system, thereby greatly simplifying controller design while endowing the system with strong disturbance rejection capabilities.

[0005] Thanks to the aforementioned advantages, ADRC has achieved great success in stabilizing control problems (i.e., requiring the system output to remain stable at a certain constant value). However, when the application scenario shifts from stabilizing to high dynamic trajectory tracking (i.e., requiring the system output to accurately follow a rapidly time-varying reference trajectory), the classic ADRC (hereinafter referred to as C-ADRC) framework exposes a fundamental and long-standing structural flaw.

[0006] This defect is defined as "objective non-equivalence".

[0007] The essence of the problem is that, within the C-ADRC framework, the design goals of the observer and the final performance goals of the control system are not mathematically equivalent. Specifically: 1. The design goal of the observer is to make its estimated state (including the position, velocity and other conventional states of the controlled object, as well as the "lumped disturbance" as an extended state) approximate the true state of the system as quickly and accurately as possible by adjusting the observer's parameters; the object of its optimization is the state estimation error.

[0008] 2. The ultimate performance goal of a control system is to make the actual output of the controlled object follow the given reference trajectory as accurately as possible; the object of optimization is the system tracking error.

[0009] In the C-ADRC structure, minimizing the state estimation error is not equivalent to minimizing the system tracking error. This profound structural contradiction can be rigorously revealed through analysis of the dynamic equation of the closed-loop tracking error in C-ADRC. Taking a typical second-order uncertain system as an example, its dynamics can be expressed as follows: ,in For system output, To control the input, Let be an unknown function, which incorporates the system's unmodeled dynamics, parameter perturbations, and external environmental disturbances. Under the classic ADRC framework, its closed-loop tracking error... The dynamic evolution is determined by the following formula:

[0010] in, For reference trajectory, For controller gain, and These represent the estimation errors of the extended state observer for the system's position, velocity, and lumped disturbance, respectively.

[0011] This equation clearly shows that the driving tracking error The dynamically evolving "forcing term" (right side of the equation) consists of two parts: one part is the error in ESO estimation. The other part consists of terms related to the dynamics of the reference trajectory itself, namely the acceleration of the reference trajectory. .

[0012] This structure leads to two unavoidable performance bottlenecks: First, it neglects the structural aspects of trajectory dynamics. In the C-ADRC framework, the "lumped disturbance" as an extended state is typically defined as... This definition structurally only includes unmodeled dynamics within the system, parameter perturbations, external disturbances, and uncertainties related to the control input; it completely excludes any information about the reference trajectory. Therefore, the core component of C-ADRC—the Extended State Observer (ESO)—was designed solely to estimate the aforementioned "lumped disturbances" caused by the system's own characteristics and the external environment.

[0013] Second, suboptimal performance and coupled amplification effects. Due to the aforementioned structural defects, a better-performing ESO (i.e., one with smaller estimation errors) is... This does not necessarily lead to better tracking performance (i.e., smaller tracking error). In multiple-input multiple-output (MIMO) systems such as robotic arms, the strong dynamic coupling between joints makes the "lumped perturbation" of each joint exceptionally complex and severe. This further degrades the estimation performance of ESO, thus amplifying the impact of... Term and estimation error The tracking performance degradation is caused by both factors.

[0014] To overcome this deficiency, existing technologies mainly improve the system along two paths. The first path focuses on enhancing the performance of the ESO itself, such as by employing cascaded structures and adaptive gain. However, these methods do not fundamentally change the dynamic structure of the closed-loop error, and the "objective non-equivalence" problem persists. The second path introduces feedforward compensation, forming feedforward ADRC (F-ADRC), which attempts to pre-calculate... This is then directly subtracted from the control law. However, this method has performance limitations in practice because online differentiation of noisy signals inherently involves a trade-off between "speed" and "noise resistance," which contradicts the core principle of ADRC's pursuit of robustness.

[0015] In summary, the classic ADRC and its mainstream improvements in the existing technology fail to fundamentally solve the structural defect of "target non-equivalence". Therefore, when facing high dynamic and high-precision trajectory tracking tasks, their performance is structurally limited and cannot reach the theoretical optimal level. Summary of the Invention

[0016] In view of the above-mentioned defects or improvement needs of the existing technology, the present invention provides an active disturbance rejection control method and device for dynamic trajectory tracking, which aims to solve the performance limitation problem caused by the inherent structural defect of "target non-equivalence" in the existing active disturbance rejection control (ADRC) technology when dealing with high dynamic trajectory tracking tasks.

[0017] To achieve the above objectives, according to one aspect of the present invention, an active disturbance rejection control method for dynamic trajectory tracking is provided, comprising the following steps: (1) Calculate the system tracking error between the output signal of the controlled object and the reference trajectory, and establish the error dynamic equation of the system tracking error; (2) The error dynamic equation is reconstructed into the integrator cascade canonical form by the composite lumped disturbance, and the composite lumped disturbance is regarded as an extended state to be estimated of the integrator cascade canonical form; wherein, the composite lumped disturbance includes the total disturbance of the controlled object and the dynamic characteristics of the reference trajectory; (3) For the integrator cascaded standard type, a tracking-guided extended state observer (TO-ESO) is designed. The tracking-guided extended state observer takes the system tracking error and control input signal as input, and performs real-time estimation of an extended state vector containing the system tracking error, its derivative and composite lumped disturbance and outputs the corresponding estimated value. (4) Design a compensation control law based on the obtained estimate to generate the control input signal, and use the control input signal to stabilize the error system corresponding to the integrator cascade standard type.

[0018] Furthermore, the composite lumped disturbance includes the unmodeled dynamics of the controlled object, parameter perturbations, external physical disturbances, and the dynamic characteristics of the reference trajectory signal itself.

[0019] Furthermore, for a controlled object of order n, its dynamic representation is as follows: ,in The nth derivative of the output signal. For the total disturbance, For control input; the composite lumped disturbance is specifically defined as: ,in Let be the nth derivative of the reference trajectory signal.

[0020] Furthermore, the total disturbance The composition methods include: When a portion of the model of the controlled object is known, the total disturbance is offset by feedback linearization after the known dynamics are canceled. It incorporates model uncertainties, unmodeled dynamics, and external disturbances; When the model of the controlled object is completely unknown, the total disturbance It incorporates all internal dynamics and external disturbances of the controlled object.

[0021] Furthermore, the extended state vector of TO-ESO is defined as ,in The system tracking error, Its i-th derivative, This refers to the composite lumped disturbance.

[0022] Furthermore, the compensation control law includes two functional terms: (a) a disturbance compensation term: actively compensating for the composite lumped disturbance using the estimated value of the composite lumped disturbance; and (b) an error feedback control term: stabilizing the error system described by the cascaded canonical form of the compensated integrator based on the estimated value of the TO-ESO for an extended state vector containing the system tracking error, its derivative, and the composite lumped disturbance.

[0023] Furthermore, the steps for generating the compensation control law are as follows: (a) Based on the TO-ESO estimates of the system tracking error and its derivative, determine an error feedback control term. ; (b) The error feedback control item The estimated value of the composite lumped disturbance These are combined to form an intermediate control signal, which is used to counteract the effects of the composite lumped disturbance; (c) The intermediate control signal is transmitted through the nominal control gain of the controlled object. Scaling is performed to generate the final compensated control law. .

[0024] Furthermore, the error feedback control term is generated by a feedback controller; the tracking-guided extended state observer employs an observer structure.

[0025] The present invention also provides an active disturbance rejection control system for dynamic trajectory tracking, the system including a memory and a processor, the memory storing a computer program, and the processor executing the computer program to perform the active disturbance rejection control method for dynamic trajectory tracking as described above.

[0026] The present invention also provides a computer-readable storage medium storing machine-executable instructions, which, when invoked and executed by a processor, cause the processor to implement the active disturbance rejection control method for dynamic trajectory tracking as described above.

[0027] In summary, compared with the prior art, the active disturbance rejection control method and device for dynamic trajectory tracking provided by the present invention have the following advantages: 1. This invention fundamentally solves the problem of "objective non-equivalence" and achieves structural causal determinism. By reconstructing the control problem into a direct stabilization of the system tracking error dynamics, this invention makes the observer's design objective and the final performance objective of the control system mathematically equivalent. Specifically, the forced terms of the closed-loop tracking error dynamics (as shown in Equation (11)) in existing technologies (such as C-ADRC) simultaneously include the observer's estimated error. Related terms and structural deviation terms related to the dynamics of the reference trajectory In contrast, the closed-loop tracking error dynamic equation constructed in this invention (as shown in equation (18)) has a forcing term derived solely from the estimation error of the tracking-guided extended state observer (TO-ESO) proposed in this invention. This structure structurally eliminates the direct influence of the reference trajectory dynamics. This structure establishes a clear and deterministic causal relationship: any improvement in TO-ESO estimation performance will directly and predictably translate into an improvement in system tracking performance. Thus, a coupled optimization problem that requires balancing "observer performance" and "trajectory dynamic compensation" is decomposed into a single objective function (i.e., minimizing the observer estimation error) with structural determinism.

[0028] 2. Systematically improved dynamic trajectory tracking performance. This invention structurally upgrades the tracking type of an nth-order system from the nth type of traditional ADRC to the n+1th type by intrinsically including the dynamic information of the reference trajectory in the "composite lumped disturbance" and actively compensating for it. For example, for a typical second-order system, this invention upgrades its tracking type from type II to type III, achieving zero steady-state error tracking of a constant acceleration trajectory and significantly improving the tracking fidelity of the system.

[0029] 3. Enhanced robustness of the controller to noisy reference trajectories. This invention eliminates the need for feedforward compensation of the reference trajectory, structurally avoiding the requirement for online numerical differentiation of the signal. By transforming the signal's "differentiation problem" into a standard "estimation problem," it resolves the inherent contradiction between "speed" and "noise resistance" in online differentiation, significantly enhancing the controller's robustness to noisy reference trajectories.

[0030] 4. Simplified control architecture and reduced implementation complexity. Classical ADRC typically requires a separate tracking differentiator (TD) to obtain the derivatives of the reference trajectory for feedback control, resulting in three core components: the TD, the extended state observer (ESO), and the nonlinear feedback control law (NLSEF). This invention, by reconstructing the error dynamics, internalizes the requirement for the reference trajectory derivatives into the estimation of the composite lumped disturbance, thus eliminating the need for a separate tracking differentiator in typical applications. This simplifies the control architecture from three parts to two (TO-ESO and the control law), reducing the number of parameters requiring tuning and lowering the computational burden and engineering implementation complexity.

[0031] 5. A decoupled, scalable, modular control platform is provided. This invention constructs a functionally decoupled two-layer control architecture by achieving "objective equivalence." (a) Lower layer (robust foundation layer): This layer consists of the Tracking-Guided Extended State Observer (TO-ESO) proposed in this invention, whose function is to estimate and compensate for "composite lumped disturbances" in real time. Through this compensation, the original nonlinear uncertainty error dynamics of the controlled object (as shown in equation (13) are reduced). The online equivalent transformation is to a known, approximately ideal linear time-invariant (LTI) nominal model, which takes the form of: (b) Upper layer (performance synthesis layer): This layer addresses the simplified LTI nominal model created by the lower layer. To design nominal control laws The advantage of this architecture lies in the fact that the designer of the upper-level nominal control law does not need to deal with the original unmodeled dynamics of the controlled object, parameter perturbations, and external disturbances (i.e., ), and there is no need to consider the dynamics of the reference trajectory (i.e. This is because these uncertainties and dynamic characteristics have been treated as "composite lumped disturbances" by the lower layers. A portion of the estimation and active compensation is made transparent. This decoupling significantly reduces the design complexity and implementation threshold of integrating advanced control algorithms such as sliding mode control (SMC), model predictive control (MPC), and reinforcement learning (RL) with uncertain nonlinear systems. Therefore, this invention elevates TO-ADRC from a single controller to an open control platform, providing a systematic and scalable solution for solving complex industrial control problems.

[0032] 6. This invention unifies the stabilization and tracking problems and is compatible with existing theoretical frameworks. The TO-ADRC framework proposed in this invention treats the stabilization problem as a special case of the tracking problem, unifying it under a single "composite lumped disturbance suppression" framework. Simultaneously, the "structural isomorphism" between its core component, TO-ESO, and the classical ESO ensures that all mature ESO analysis theories and parameter tuning methods can be seamlessly inherited and directly applied, greatly reducing the theoretical analysis and engineering application threshold of the new framework. Attached Figure Description

[0033] Figure 1 These are comparative diagrams of control framework structures according to an embodiment of the present invention; (a) shows the framework structure of the classical active disturbance rejection control (C-ADRC) in the prior art; (b) shows the framework structure of the tracking-guided active disturbance rejection control (TO-ADRC) proposed in the present invention.

[0034] Figure 2 The following are comparison diagrams of tracking errors for joint 2: (a) is a comparison diagram of tracking errors under ideal signal conditions; (b) is a comparison diagram of tracking errors under noisy signal conditions.

[0035] Figure 3 The diagram shows the perturbation estimation performance comparison for joint 2. (a) shows the C-ADRC estimate for the total perturbation. The estimate, (b) is the TO-ADRC of the present invention for the composite lumped disturbance. The estimate.

[0036] Figure 4 The experimental verification diagram for the "target equivalence" principle of this invention shows a high degree of consistency between the tracking error and the composite lumped disturbance estimation error.

[0037] Figure 5 This is a comparison chart showing the tracking errors of C-ADRC and the TO-ADRC of the present invention on a 2-DOF robotic arm for a constant acceleration trajectory.

[0038] Figure 6 Lumped perturbation of joint 2 in the robotic arm experiment The waveform diagram.

[0039] Figure 7 This is a comparison chart showing the tracking errors of the C-ADRC and the TO-ADRC of the present invention on an ideal dual integrator for a constant acceleration trajectory.

[0040] Figure 8 This is a comparison chart of the tracking errors of SMC, C-ADRC-SMC and the TO-ADRC-SMC of the present invention under noisy conditions.

[0041] Figure 9This is a comparison chart of the control torque output of SMC, C-ADRC-SMC and the TO-ADRC-SMC of the present invention under noisy conditions.

[0042] Figure 10 This is a flowchart of an active disturbance rejection control method for dynamic trajectory tracking provided by the present invention. Detailed Implementation

[0043] 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 merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0044] This invention provides an active disturbance rejection control (ADRC) method for dynamic trajectory tracking. It structurally eliminates the inequivalence between the observer design objective and the final performance objective of the control system in traditional ADRC, thereby achieving high-fidelity and robust tracking of dynamic reference trajectories simultaneously without relying on accurate models and explicit signal feedforward. By dynamically incorporating the reference trajectory into the disturbance model for integrated estimation and compensation, this invention simplifies the controller structure. It significantly improves the tracking accuracy and robustness of the control system for complex dynamic trajectories, and reduces the complexity of system design and parameter tuning, typically eliminating the need for a tracking differentiator (TD).

[0045] Please see Figure 10 The control method mainly includes the following steps: Step 1: Calculate the system tracking error between the output signal of the controlled object and the reference trajectory, and establish the error dynamic equation of the system tracking error based on the dynamic model of the controlled object.

[0046] Step 2: Reconstruct the error dynamic equation through the composite lumped disturbance, so that the error dynamic equation is equivalent to a canonical form of a cascaded integrator with the composite lumped disturbance as the only unknown input; and regard the composite lumped disturbance as an extended state to be estimated of the canonical form of the cascaded integrator; wherein, the composite lumped disturbance includes the total disturbance of the controlled object and the dynamic characteristics of the reference trajectory.

[0047] The composite lumped disturbance includes the unmodeled dynamics of the controlled object, parameter perturbations, external physical disturbances, and the dynamic characteristics of the reference trajectory signal itself.

[0048] For an n-order controlled object, its dynamics can be represented as follows: ,in The nth derivative of the output signal. For the total disturbance, For control input; the composite lumped disturbance is specifically defined as: ,in Let be the nth derivative of the reference trajectory signal.

[0049] The total disturbance The composition includes at least one of the following: When a portion of the model of the controlled object is known, the total disturbance is offset by feedback linearization after the known dynamics are canceled. It incorporates model uncertainties, unmodeled dynamics, and external disturbances; When the model of the controlled object is completely unknown, the total disturbance It incorporates all internal dynamics and external disturbances of the controlled object.

[0050] Step 3: Design a tracking-guided extended state observer (TO-ESO) for the standard type of integrator cascade. The tracking-guided extended state observer takes the system tracking error and control input signal as input, performs real-time estimation of an extended state vector that includes the system tracking error, its derivative and composite lumped disturbance, and outputs the corresponding estimated value.

[0051] The extended state vector of TO-ESO is defined as ,in The system tracking error, Its i-th derivative, This refers to the composite lumped disturbance.

[0052] The Tracking Guided Extended State Observer (TO-ESO) employs an observer architecture selected from a group that includes: linear extended state observers, high-gain extended state observers, cascaded extended state observers, variable bandwidth extended state observers, sliding mode extended state observers, nonlinear extended state observers, disturbance observers (DOB), and neural network-based extended state observers.

[0053] Step four: Design a compensation control law based on the obtained estimate to generate the control input signal, and use the control input signal to stabilize the error system corresponding to the integrator cascade standard type.

[0054] Based on the separation principle, this control law is designed, specifically including two functional items: (a) Disturbance compensation item: Actively compensates for the composite lumped disturbance using the estimated value of the composite lumped disturbance. Specifically, it actively and fully compensates for the composite lumped disturbance at the control input using the estimated value of the composite lumped disturbance output by the TO-ESO step. (b) Error feedback control item: Stabilizes the error system described by the cascaded integrator standard form after compensation based on the estimated value of the system tracking error and its derivative by the TO-ESO. Specifically, after compensation, the original cascaded integrator standard form is functionally equivalent to a known, approximately ideal nominal model (e.g., an integrator series system); a feedback controller (e.g., a PD controller) is designed for this nominal model to drive the system tracking error and its derivative to converge rapidly to zero.

[0055] The steps for generating the compensation control law are as follows: (a) Based on the TO-ESO estimates of the system tracking error and its derivative, determine an error feedback control term. ; (b) The error feedback control item The estimated value of the composite lumped disturbance These are combined to form an intermediate control signal, which is used to counteract the effects of the composite lumped disturbance; (c) The intermediate control signal is transmitted through the nominal control gain of the controlled object. Scaling is performed to generate the final compensated control law. .

[0056] Furthermore, the control method does not require a separate tracking differentiator to obtain the derivatives of the reference trajectory during implementation.

[0057] The error feedback control term is generated by a feedback controller selected from a group that includes: proportional-derivative (PD) controllers, sliding mode control (SMC), model predictive control (MPC), linear quadratic regulators (LQR), iterative learning control (ILC), reinforcement learning (RL), backstepping, passive-based control, fuzzy logic control, adaptive controllers, and... Controller.

[0058] The present invention also provides an active disturbance rejection control system for dynamic trajectory tracking, the system including a memory and a processor, the memory storing a computer program, and the processor executing the computer program to perform the active disturbance rejection control method for dynamic trajectory tracking as described above.

[0059] The present invention also provides a computer-readable storage medium storing machine-executable instructions, which, when invoked and executed by a processor, cause the processor to implement the active disturbance rejection control method for dynamic trajectory tracking as described above.

[0060] The present invention will be further described in detail below with reference to specific embodiments, comparative examples and experimental verification.

[0061] Example 1: Robot Control In this embodiment 1, a... As a typical controlled object, the dynamic equations of a rigid body robotic arm with degrees of freedom (DOF) can be expressed as follows: (1) in, These are the joint's position, velocity, and acceleration vectors, respectively. It is a symmetric positive definite inertial matrix; It is the matrix of Coriolis force and centrifugal force; It is the gravity vector; It is the friction vector; It is the external disturbance vector; It is the control torque input vector. Specifically, it includes the following steps: Model Reconstruction for Active Disturbance Rejection (ADRROR): To apply the ADRROR control framework, the complex nonlinear system (corresponding to formula (1)) needs to be reconstructed as follows: A unified form. Depending on the level of understanding of the model's prior knowledge, this reconstruction can be achieved through the following two approaches.

[0062] Preferred solution: Reconstruction based on partially known models When the nominal model of the system Given the information, the following control torque can be designed. To counteract the main nonlinear dynamics: (2) Substituting equation (2) into equation (1) and rearranging, the system can be reconstructed as follows: (3) In this form, the nominal control gain is the identity matrix. Total disturbance This encompasses all the uncertainties caused by model inaccuracies:

[0063] Here It represents the difference between the actual value and the nominal value.

[0064] Basic Solution: Reconstruction under the condition of completely unknown model When the model is completely unknown, a constant diagonal positive definite matrix selected by the designer can be introduced. As the nominal control gain, a simple control torque is designed as follows: (5) Substituting equation (5) into equation (1) and rearranging, the system is reconstructed as follows: (6) At this point, the total disturbance This encompasses all internal nonlinear dynamics and external disturbances: (7) Unified integrator cascade standard form: The reconstruction of both of the above schemes derives The unified form. Due to the nominal control gain matrix It is diagonal (in the preferred solution) This multiple-input multiple-output (MIMO) system can be decomposed into Each is a separate single-input single-output (SISO) subsystem. For the first... The scalar dynamics of each joint can be uniformly described as follows: (8) in, It is the corresponding scalar total disturbance (i.e. or The (each component). To achieve control over the total disturbance. Real-time estimation and compensation can be defined as an extended state of the system, and an extended state observer can be constructed accordingly to estimate it.

[0065] Existing technology: Classical Active Disturbance Rejection Control (C-ADRC) framework Reference Figure 1 In (a), the C-ADRC framework revolves around the state of the controlled object. Estimation and control are performed. An extended state vector is established for the subsystem defined in equation (8). And a linear extended state observer (LESO) was designed to obtain its estimate. Its control law is in the form of:

[0066] in It is a PD controller that generates a nominal control signal based on the deviation between the reference trajectory and the estimated state. (10) Substituting equations (9) and (10) into (8), we can obtain the closed-loop tracking error. The dynamic equation is: (11) in The estimation error of LESO is defined as follows: (estimated value) (True value). The forced terms of this equation contain a term related to the acceleration of the reference trajectory. This is a structural defect of C-ADRC.

[0067] Tracking-guided active disturbance rejection control (TO-ADRC) framework To address the aforementioned problems, this invention proposes a tracking-guided active disturbance rejection control (TO-ADRC) framework. (Refer to...) Figure 1 In (b), TO-ADRC revolves around the system tracking error. To remain calm in the face of dynamic situations, specifically: Error dynamic reconstruction and composite lumped disturbance Tracking error The second-order dynamics are:

[0068] The embodiments of the present invention define a composite lumped disturbance. : (12) Through this definition, the tracking error dynamics are precisely reconstructed into a state where... The standard form for a unique, unknown input: (13) TO-ADRC control structure For the error system corresponding to the stabilization formula (13), this invention constructs an extended state vector for it. And design the corresponding tracking-guided extended state observer (TO-ESO) and control law.

[0069] TO-ESO: (14) in, For the error state vector Real-time estimation.

[0070] Control Law:

[0071] in, It is a PD controller that directly stabilizes the estimated error state: (16) The final TO-ADRC control law is:

[0072] This invention features target equivalence, structural isomorphism, and unity in stabilization and tracking problems.

[0073] The core advantage of this invention stems from its unique error dynamic reconstruction method, which fundamentally solves the "objective non-equivalence" problem of classical ADRC. This property can be expressed as follows: for the error system described by equation (13), after adopting the TO-ADRC control law proposed in this invention, the forcing term of its final closed-loop tracking error dynamic equation is composed only of the estimated error of TO-ESO.

[0074] The derivation process is as follows: Substituting the control law of TO-ADRC, i.e., equation (17), into the reconstructed error system dynamic equation, i.e., equation (13), we can obtain:

[0075]

[0076] The estimation error of TO-ESO is defined as follows: (i.e., estimated value) (True value). Therefore, the estimated state can be expressed as , ,as well as Substituting these relationships into the above equation and rearranging, we obtain the final dynamic equation for the closed-loop tracking error: (18) Compared with the error dynamics of C-ADRC (11), the forced terms under the framework of this invention no longer contain structural deviation terms. The right-hand side of equation (18) consists entirely of the estimation error terms of TO-ESO. Therefore, the estimation is valid if and only if the observer achieves perfect estimation (i.e., all...). When the tracking error is... It will converge to zero.

[0077] This "target equivalence" is the fundamental advantage of this invention. It transforms the key factor determining tracking performance from the coupling of two independent factors, "observer performance" and "trajectory dynamics," in C-ADRC, to being determined solely by the single factor of "TO-ESO estimation performance."

[0078] Structural isomorphism: TO-ESO(14) designed for the error system has the same error dynamic system matrix as LESO of C-ADRC designed for the original system.

[0079] By deriving the estimation error dynamic equations for LESO and TO-ESO respectively, it can be found that both can be written as... In the form of, These are the derivatives of the total disturbance or the composite lumped disturbance, respectively. Both share the exact same error dynamic system matrix. :

[0080] Therefore, they share the same characteristic equation and are structurally isomorphic. This property ensures that all theoretical results and engineering experience regarding LESO (such as parameter tuning methods) can be directly applied to the TO-ESO of this invention.

[0081] Unity of Stabilization and Tracking Problems: The TO-ADRC framework proposed in this invention provides a more general perspective than C-ADRC. In stabilization tasks, the reference signal... It is a constant, which means Under these conditions, the composite lumped disturbance defined in equation (12) Mathematically, it is related to the total disturbance. Equivalent. Therefore, C-ADRC can be considered a special case of the TO-ADRC of the present invention in the context of stabilization problems. Closed-loop stability and performance analysis The TO-ADRC closed-loop error system constructed by this invention is input-state stable (ISS), and all error states are globally consistent and ultimately bounded (GUUB). Specifically: 1. Construct a 5th-order augmented error state vector that includes the tracking error dynamics and the TO-ESO estimation error dynamics. .

[0082] 2. Derive the dynamic equations of the augmented system. The system matrix It's by Hurwitz. It is related to the derivative of the composite lumped perturbation.

[0083] 3. The ISS and GUUB properties of the system can be proved using Lyapunov analysis.

[0084] The TO-ADRC closed-loop system of this invention is a Type III tracking system and a Type I disturbance suppression system. Steady-state performance analysis is performed to determine the system type, specifically: 1. Perform a Laplace transform on the closed-loop error dynamics (18) to derive the result from the reference input. To tracking error The transfer function, and from the total disturbance To tracking error The transfer function.

[0085] 2. Analyze the transfer function in The properties at the origin are as follows: It can be observed that the transfer function from the reference input to the tracking error has a third-order zero at the origin, proving that the system is a Type III tracking system. The transfer function from the total disturbance to the tracking error has a first-order zero at the origin, proving that the system is a Type I disturbance suppression system.

[0086] Table 1 Comparison of System Types

[0087] As shown in Table 1, the Type III tracking capability enables TO-ADRC to track a trajectory with constant acceleration without steady-state error, which is something that the Type II system C-ADRC cannot achieve.

[0088] Example 2 Generalized nth-order system This invention is universal and can be directly extended to general applications. The dynamics of a SISO controlled object can be represented as follows: (19) Type restrictions of classic ADRC (C-ADRC): n-type rule Within the C-ADRC framework, closed-loop tracking error The dynamic equations can ultimately be simplified to:

[0089] in It is the observer pair of The estimation error of the first derivative. Forcing term. The continued existence of this determines that the tracking system type of C-ADRC is structurally restricted to type n.

[0090] The Type Upgrading of this Invention (TO-ADRC): The n+1 Type Rule This invention defines a composite lumped disturbance. The closed-loop error is dynamically reconstructed as follows:

[0091] in It is TO-ESO of The estimation error of the first derivative. It can be proven that from the reference input... To tracking error The numerator of the transfer function must contain This demonstrates that the TO-ADRC framework of this invention can structurally elevate the tracking type of the system to type n+1. This analysis clearly reveals the fundamental structural advantages of TO-ADRC in dynamic tracking performance. The comparison results of the generalized n-order system types are shown in Table 2.

[0092] Table 2 Comparison of Types of Generalized nth-Order Systems

[0093] Example 3: TO-ADRC as a Modular Synthetic Framework The TO-ADRC framework proposed in this invention can be viewed as a modular integrated framework, providing a scalable and functionally decoupled architecture for integrating advanced control theory. Traditional classical active disturbance rejection control (C-ADRC) suffers from an inherent "objective non-equivalence" defect, resulting in undesirable coupling between the disturbance estimation layer and the feedback control layer, which fundamentally limits its utility as a modular platform.

[0094] This invention establishes a deterministic causal relationship between the estimation error of TO-ESO and the tracking error of the system (as shown in Equation (18)) by achieving "target equivalence," thereby forming a functionally completely decoupled modular architecture. This architecture allows engineers to systematically and predictably improve system performance through the following two independent and orthogonal aspects: Firstly, improve the estimation performance of the robust base layer. This aspect aims to optimize the robust base layer composed of TO-ESO groups. Thanks to the "structural isomorphism" revealed in this invention, various advanced variants developed from standard ESOs can be directly and seamlessly ported to construct the TO-ESO of this invention, further improving its estimation performance. This porting can be achieved by simply replacing the linear error feedback structure within the TO-ESO without changing its tracking-oriented core framework. These advanced variants include, but are not limited to, high-gain ESOs, cascaded ESOs, variable bandwidth ESOs, sliding mode ESOs, nonlinear ESOs, traditional interference observers (DOBs), and neural network-based intelligent ESOs. Due to the fundamental guarantee of "target equivalence" in this invention, the improvement in estimation accuracy brought about by adopting these advanced observers will directly and predictably translate into an improvement in the final system tracking performance.

[0095] Secondly, optimize the nominal control law of the performance synthesis layer. In the first aspect, it provides an approximately ideal linear time-invariant (LTI) platform for the system. Following this, this aspect aims to design an advanced nominal controller for the performance synthesis layer. To achieve the final performance metrics. In addition to the detailed examples below, the principles of this invention are also applicable to combinations with other control strategies, such as backstepping, passivity-based control, and fuzzy logic control. In these combinations, the framework of this invention uniformly plays a fundamental role in simplifying design and enhancing robustness. These examples are intended to illustrate the broad applicability of this invention but do not constitute a limitation on its scope of protection. 1. Enhanced Robustness and Precision Control: TO-ADRC fundamentally simplifies the design of robust controllers by actively compensating for lumped disturbances. Its significant compression of disturbance boundaries makes it suitable as a... Sliding mode control (SMC) requires only a small switching gain to structurally suppress chattering while maintaining robustness. Simultaneously, this framework transforms the complex nonlinear control problem into a stabilization problem for nominal LTI systems and bounded estimation errors, thus providing a basis for... The application of linear robust technologies such as control creates ideal conditions, making it easy to systematically guarantee preset performance indicators.

[0096] 2. Simplified Design of Optimal and Constraint Control: Directly applying LQR or MPC to the original nonlinear system typically relies on local linearization that is only effective in a small range, or solving nonlinear programming (NLP) problems that are difficult to satisfy in real time. TO-ADRC provides a globally effective approximate LTI platform by actively compensating for nonlinear terms, thus fundamentally solving this dilemma. This allows the optimal state feedback law of LQR to be directly designed and applied to the entire workspace; at the same time, it simplifies the online optimization problem of MPC from NLP to a quadratic programming (QP) problem that can be solved efficiently, making it possible to systematically handle complex constraints while meeting real-time requirements.

[0097] Empowering Adaptive and Learning Control Systems: TO-ADRC provides structural security and efficiency improvements for data-driven methods, addressing their core challenges in physical system deployment. For adaptive control, it compensates for disturbances caused by unstructured dynamics and parameter variations, enabling adaptive laws to focus on a few key physical parameters, thus simplifying design and accelerating convergence. For Iterative Learning Control (ILC), it provides a stable operating environment for the learning process by actively suppressing non-repetitive disturbances that change during iteration; simultaneously, it compensates for repetitive disturbances in real time during each iteration, significantly reducing initial errors and enabling ILC to achieve higher convergence accuracy with fewer iterations. Finally, it provides triple structural support for reinforcement learning (RL), fundamentally addressing its core challenges in physical system deployment: (a) Security guaranteed by Input-State Stability (ISS): The framework of this invention guarantees that the closed-loop system is input-state stable for bounded lumped disturbances and estimation errors. This means that even if the RL agent generates unreasonable or dangerous action commands during the exploration process, TO-ADRC can still treat it as an internal disturbance and actively compensate for it, thereby constraining the system state within a safe boundary and providing an unprecedented safe exploration environment for RL. (b) High sample efficiency brought about by model simplification: TO-ADRC transforms the complex, nonlinear controlled object dynamics into an approximate, globally effective linear time-invariant system. This allows the RL agent to focus on learning higher-level task policies instead of consuming a large number of samples to learn and identify the complex dynamics of the underlying system (such as friction, variable load, etc.), thus greatly improving sample efficiency. (c) "Simulation to Reality" migration achieved through disturbance compensation: The main obstacle to "simulation to reality" lies in the difference between the simulation model and physical reality. The core function of TO-ADRC is to estimate and compensate for this model uncertainty in real time. Therefore, an RL policy trained in a simplified simulation environment can be directly deployed to the physical system. TO-ADRC will actively handle unmodeled dynamics and external disturbances in the real world, thereby bridging the "simulation to reality" gap to the greatest extent and achieving smooth and reliable technology migration.

[0098] Example 4: Comparative Experiment and Performance Verification To provide rigorous experimental verification of the aforementioned theoretical framework and performance assertions, comprehensive numerical simulations are presented below. Employing simulation as a verification method aims to achieve clear causal attribution, ensuring that observed performance differences are uniquely attributed to the algorithm's intrinsic structure, thus providing direct and unambiguous evidence for the theoretical advantages of the framework proposed in this invention.

[0099] Simulation settings: To ensure the reproducibility of the research and the fairness of the comparison, all simulations were conducted in the MATLAB / Simulink (R2024b) environment using a fixed step size. The ode4 solver for ) . Controlled object: The controlled object in the simulation is a two-degree-of-freedom (2-DOF) planar rigid manipulator, whose actual dynamics are described by equation (1). The nominal model parameters used in the controller design ( There is a 20% systematic deviation compared to the actual physical parameters. The physical control torque of all controllers... All calculations are performed using the following feedback linearization framework: (twenty two) in It is an auxiliary control law generated by various comparison algorithms.

[0100] Comparison Algorithms: To comprehensively evaluate this invention, seven control algorithms were selected for comparison. The auxiliary control laws of each algorithm are as follows: The definition is as follows: 1. PID controller:

[0101] 2. Classic ADRC (C-ADRC): (twenty four) 3. Feedforward ADRC (F-ADRC): (25) 4. This invention (TO-ADRC): (26) 5. Sliding Mode Control (SMC): (27) in, . 6. C-ADRC-SMC: (28) in, . 7. This invention (TO-ADRC-SMC): (29) in, .

[0102] Parameter Configuration: To ensure fair comparison, all controllers share the same bandwidth parameters. The controller bandwidth is set to... The observer bandwidth is set to The main parameter settings are as follows: PD gain: , PID integral gain: ;ESO / TO-ESO gain: , , SMC sliding surface: SMC switching gain: ; .

[0103] Reference signal derivative processing: Two experimental conditions were set to evaluate the theoretical performance and practical robustness of the algorithm: Ideal derivative: Direct use The analytic derivative. The noisy derivative: in the reference trajectory. Gaussian white noise is injected. At this point, the controller requiring derivatives (PID, C-ADRC, F-ADRC, SMC, C-ADRC-SMC) uses a tracking differentiator (TD) to estimate its derivatives online. Specifically, the C-ADRC controller requiring first-order derivatives uses a second-order TD. ); while PID, F-ADRC, SMC, and C-ADRC-SMC, which require first and second derivatives, employ cascaded TD ( ; The TO-ADRC and its SMC integration scheme of the present invention do not require obtaining any external derivatives of the reference trajectory due to their structural characteristics.

[0104] To quantitatively evaluate each control strategy, the following five key performance indicators (KPIs) are used: 1. Integral Absolute Error (IAE): 1. Measures overall tracking accuracy. 2. Integral Squared Error (ISE): More sensitive to large errors. 3. Maximum absolute error (MaxAE): 4. Control Energy (CE): Measure the worst-case transient performance. 5. Quantify energy consumption. Steady-state tracking error ( ): for Used to verify the steady-state performance of the system.

[0105] In summary, the dynamics of joint 2 not only include its own inertia and gravity terms, but also bear the strongly coupled dynamics originating from the motion of joint 1, which constitutes a complex lumped disturbance. Therefore, it can serve as a representative benchmark for evaluating the overall performance of the controller.

[0106] The tracking accuracy and noise robustness of this invention were verified. Experimental setup: Scenario 1 (ideal) using a reference trajectory Scenario 2 (with noise) is further enhanced by adding Gaussian white noise with a mean of 0 and a standard deviation of 0.01. Both scenarios are... Apply time to joint 2 The step disturbance.

[0107] Tracking performance and robustness analysis: In scenario one (ideal signal), F-ADRC achieved the highest tracking accuracy, with its IAE and ISE indices (Table 3) significantly outperforming other methods. TO-ADRC performed second best, but achieved the best MaxAE, demonstrating stronger transient suppression capability. Figure 2 (a)). In scenario two (noisy signal), the performance ranking is fundamentally reversed. For example... Figure 2 As shown in (b), the performance of PID, C-ADRC, and F-ADRC, which rely on TD to obtain the derivative, all showed a significant decline, with F-ADRC experiencing the most severe error deterioration. In contrast, TO-ADRC exhibited superior robustness, with its tracking and error curves almost identical to those of the ideal scenario under noisy conditions. The data in Table 3 quantifies this advantage: TO-ADRC significantly outperformed PID, C-ADRC, and F-ADRC across all accuracy metrics in Scenario 2, with its ISE metrics being only 8.8%, 7.8%, and 4.9% of those of PID, C-ADRC, and F-ADRC, respectively.

[0108] Table 3 Comparison of Comprehensive Performance Indicators

[0109] Note: The optimal value in each column is highlighted in bold.

[0110] Internal mechanism verification: Figure 3 and Figure 4 This reveals the underlying mechanism of performance differences. Figure 3 (a) shows the ESO of C-ADRC for lumped disturbances. The estimation was biased, verifying the problem of "objective non-equivalence". In contrast, Figure 3 (b) shows that the TO-ESO of the present invention can accurately track complex lumped disturbances. This verifies the effectiveness of its method in solving the problem through internalized reference dynamics. Figure 4 This provides direct experimental evidence for the "target equivalence" principle of this invention. In an ideal ( Figure 4 (a) in the middle and noisy ( Figure 4 In cases (b) above, the tracking error Estimation error of composite lumped disturbance (in The dynamic evolution of the ) is highly consistent, confirming that the dynamic of the closed-loop error (corresponding to formula (18)) is indeed dominated by the observer estimation error. This relationship remains robust under noise, indicating that the intrinsic mechanism of TO-ADRC has not been destroyed, and the noise in the reference signal is successfully attributed to the composite lumped disturbance and actively suppressed by the control law.

[0111] Comprehensive experiments have demonstrated that while feedforward control relying on precise derivatives (F-ADRC) can achieve high accuracy under ideal conditions, this performance is difficult to maintain in noisy engineering practices. The TO-ADRC of this invention, through its innovative "target equivalence" structure, circumvents the difficulty of explicit signal differentiation, thus exhibiting excellent robustness and consistently high-precision tracking performance under various conditions.

[0112] Type III System Characteristic Verification By tracking a constant acceleration trajectory, the TO-ADRC system of this invention provides direct time-domain experimental verification of its Type III system characteristics. The trajectory is tracked on a two-degree-of-freedom robotic arm. An ideal signal, free from external disturbances. For example... Figure 5 As shown, neither controller converged the tracking error to a constant value, instead exhibiting bounded oscillations. Table 4 shows the later-stage average error. The results show that the actual errors of both C-ADRC and TO-ADRC did not reach the theoretical values. This deviation can be attributed to lumped perturbations. The complex characteristics of [the material / structure]. Due to the desired speed... Time-varying, disturbance terms arising from model uncertainties (especially those containing The term) is a complex time-varying signal (such as Figure 6 (As shown). Standard LESO has limited ability to estimate such rapidly changing disturbances, and the resulting residual estimation errors lead to persistent tracking error oscillations.

[0113] Table 4 Comparison of average tracking error in the later stages for robotic arm objects

[0114] Core structure verification under ideal benchmark To isolate the effects of complex disturbances and purely verify the structural characteristics of the controller, this experiment uses an ideal dual integrator object. Tracking reference input signal ,exist Apply a unit step disturbance.

[0115] Figure 7 The results in Table 5 are in high agreement with theoretical predictions. For piecewise constant perturbations, the steady-state error of C-ADRC is... , compared with theoretical value Completely consistent. The error of TO-ADRC converges to zero. Even after a step disturbance, it recovers quickly. This result clearly demonstrates the Type III system structure characteristics of TO-ADRC. In summary, the comparative experiment not only verifies this characteristic but also reveals that the performance of standard LESO is a bottleneck limiting its potential in complex applications, highlighting the necessity of integrating more advanced observers into the TO-ADRC framework.

[0116] Table 5 Comparison of steady-state tracking errors under ideal dual integrator conditions

[0117] Modular Synthesis Framework Performance Verification This experiment aims to verify the potential of TO-ADRC as a modular platform and its comprehensive advantages in improving accuracy and suppressing chatter by combining SMC with C-ADRC and TO-ADRC respectively. Comparisons are made between SMC, C-ADRC-SMC, and TO-ADRC-SMC. The experimental conditions are exactly the same as Scenario 2 (noisy signal) in Section 4.2.1.

[0118] Tracking performance analysis: such as Figure 8 As shown in Table 6, the TO-ADRC-SMC framework exhibits a significant advantage in tracking accuracy. Its IAE and ISE metrics are far superior to SMC and C-ADRC-SMC; for example, its ISE is only 3.9% and 1.5% of the latter two. It is noteworthy that the performance of C-ADRC-SMC is even inferior to the standard SMC, due to the structural defects of C-ADRC: under noisy conditions, the reference acceleration estimated by TD... Introducing noise into the auxiliary control law This noisy signal passes through the model's uncertainty term. The reaction acts on the system, causing the real lumped disturbance to... High-frequency dynamics are introduced. This exceeds the effective tracking range of LESO, leading to estimation errors. (in The increased noise and incorrect compensation ultimately worsen overall performance. In contrast, the TO-ADRC framework structurally avoids this problem. It internalizes the reference dynamics and their noise into the composite perturbation. A unified estimation is performed. The inherent low-pass filtering characteristic of TO-ESO effectively attenuates high-frequency noise during the estimation process, ensuring the accuracy of the perturbation estimation term. and final control law This mechanism cuts off the error amplification path, ensuring the system's robust performance under noisy conditions.

[0119] Table 6 Comparison of Performance Indicators of Modular Frames

[0120] Control output and energy consumption analysis: such as Figure 9 The results show that both ADRC-based hybrid controllers generate smoother control torque compared to the severe chattering of the standard SMC. Looking at the control energy (CE) in Table V, although the TO-ADRC-SMC consumes slightly more energy than the C-ADRC-SMC, it achieves a performance improvement of over 60 times in the ISE metric with only a slight increase in energy consumption, and is far less energy-efficient than the standard SMC.

[0121] In summary, the experimental results validate the effectiveness of TO-ADRC as a modular framework. TO-ADRC-SMC achieves the highest tracking accuracy while successfully suppressing the inherent chattering of SMC and maintaining reasonable control energy consumption, demonstrating significantly better overall performance than the comparative methods.

[0122] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for active disturbance rejection control for dynamic trajectory tracking, characterized in that, It includes the following steps: (1) Calculate the system tracking error between the output signal of the controlled object and the reference trajectory, and establish the error dynamic equation of the system tracking error; (2) The error dynamic equation is reconstructed into the integrator cascade canonical form by the composite lumped disturbance, and the composite lumped disturbance is regarded as an extended state to be estimated of the integrator cascade canonical form; wherein, the composite lumped disturbance includes the total disturbance of the controlled object and the dynamic characteristics of the reference trajectory; (3) For the integrator cascaded standard type, a tracking-oriented extended state observer is designed. The tracking-oriented extended state observer takes the system tracking error and control input signal as input, and performs real-time estimation of an extended state vector containing the system tracking error, its derivative and composite lumped disturbance and outputs the corresponding estimated value. (4) Design a compensation control law based on the obtained estimate to generate the control input signal, and use the control input signal to stabilize the error system corresponding to the integrator cascade standard type; The extended state vector of the tracking-guided extended state observer is defined as follows: ,in The system tracking error, Its i-th derivative, The composite lumped disturbance is described above. The compensation control law includes two functional terms: (a) Disturbance compensation term: actively compensates the composite lumped disturbance using the estimated value of the composite lumped disturbance; (b) Error feedback control term: based on the estimated value of an extended state vector containing the system tracking error, its derivative, and the composite lumped disturbance from the tracking-guided extended state observer, stabilizes the error system described by the cascaded canonical form of the compensated integrator.

2. The active disturbance rejection control method for dynamic trajectory tracking as described in claim 1, characterized in that: The composite lumped disturbance includes the unmodeled dynamics of the controlled object, parameter perturbations, external physical disturbances, and the dynamic characteristics of the reference trajectory signal itself.

3. The active disturbance rejection control method for dynamic trajectory tracking as described in claim 1, characterized in that: For an n-order controlled object, its dynamic representation is as follows: ,in The nth derivative of the output signal. For the total disturbance, For control input; the composite lumped disturbance is specifically defined as: ,in Let be the nth derivative of the reference trajectory signal.

4. The active disturbance rejection control method for dynamic trajectory tracking as described in claim 3, characterized in that: The total disturbance The composition methods include: When a portion of the model of the controlled object is known, the total disturbance is offset by feedback linearization after the known dynamics are canceled. It incorporates model uncertainties, unmodeled dynamics, and external disturbances; When the model of the controlled object is completely unknown, the total disturbance It incorporates all internal dynamics and external disturbances of the controlled object.

5. The active disturbance rejection control method for dynamic trajectory tracking as described in claim 1, characterized in that: The steps for generating the compensation control law are as follows: (a) Based on the estimated values ​​of the system tracking error and its derivative obtained from the tracking-guided extended state observer, determine an error feedback control term. ; (b) The error feedback control item The estimated value of the composite lumped disturbance These are combined to form an intermediate control signal, which is used to counteract the effects of the composite lumped disturbance; (c) The intermediate control signal is transmitted through the nominal control gain of the controlled object. Scaling is performed to generate the final compensated control law. .

6. The active disturbance rejection control method for dynamic trajectory tracking as described in claim 1, characterized in that: The error feedback control term is generated by a feedback controller; the tracking-guided extended state observer adopts an observer structure.

7. A disturbance rejection control system for dynamic trajectory tracking, characterized in that: The system includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it performs the active disturbance rejection control method for dynamic trajectory tracking as described in any one of claims 1-6.

8. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores machine-executable instructions, which, when invoked and executed by a processor, cause the processor to implement the active disturbance rejection control method for dynamic trajectory tracking as described in any one of claims 1-6.

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