Two-degree-of-freedom helicopter predefined time preset performance tracking control method

Abstract

This invention discloses a predefined time-based performance tracking control method for a two-degree-of-freedom helicopter, relating to the field of helicopter control technology. The method includes: first, constructing a helicopter dynamics model and designing a learning observer incorporating fuzzy logic to reconstruct unmeasurable states and approximate unknown nonlinear terms; second, introducing a predefined performance function and an error transformation mechanism to map constrained errors into unconstrained equivalent errors, ensuring that the tracking error converges within a predetermined time and satisfies quasi-steady-state constraints; subsequently, integrating a predefined time-based command filter into the backstepping control framework to avoid computational bloat; further, employing Actor-Critic reinforcement learning to approximate the optimal control law online, achieving adaptive optimization of the control strategy; and finally, introducing an event-triggered mechanism based on a switching threshold to update the control input. This invention ensures predefined time convergence of system signals, effectively reducing communication burden and control energy consumption while significantly improving the quasi-steady-state response quality of the helicopter.

Description

Technical Field

[0001] This invention relates to the field of two-degree-of-freedom helicopter control technology, specifically to a two-degree-of-freedom helicopter predefined time preset performance tracking control method based on a learning observer. Background Technology

[0002] In recent years, unmanned helicopters have been widely used in transportation, marine surveillance, and geological exploration due to their unique advantages such as vertical takeoff and landing, maneuverability, and hovering. In these scenarios, achieving high-precision tracking control of a two-degree-of-freedom helicopter along a desired trajectory is crucial for completing complex tasks. However, a two-degree-of-freedom helicopter system is inherently a multi-input multi-output nonlinear system, characterized by strong coupling, parameter uncertainty, and susceptibility to external disturbances, posing significant challenges to controller design. Furthermore, the system's transient performance (such as overshoot and convergence speed) and steady-state error directly affect flight safety and mission execution effectiveness; therefore, control design must effectively constrain tracking errors. Several patents have proposed improvement solutions to address these issues. For example, patent application number CN118732509A discloses a two-degree-of-freedom helicopter predefined time tracking control method, but does not consider the online optimality problem in the control process, and does not address the impact of unmeasurable state on system performance; patent application number CN114740716A proposes an adaptive neural network control method for helicopter systems based on specified performance constraints, but does not consider the predefined time convergence characteristics, the online optimality of the control strategy, and does not handle the unmeasurable state problem; patent application number CN120195981A proposes an optimal tracking control method based on disturbance observation, but does not introduce a preset performance constraint mechanism, nor does it consider the unmeasurable state problem.

[0003] In summary, the existing technology has at least the following shortcomings:

[0004] 1) The lack of explicit constraints on the transient performance of tracking error makes it difficult to guarantee the quality of system response;

[0005] 2) The online optimal design of the control process was not achieved, and there is significant room for improvement in control performance;

[0006] 3) Insufficient ability to estimate and compensate for unknown dynamics and unmeasurable states of the system. Summary of the Invention

[0007] The present invention provides a two-degree-of-freedom helicopter predefined time preset performance tracking control method to solve the technical problems in existing helicopter control methods, such as the lack of explicit constraints on the transient performance of tracking error, which makes it difficult to guarantee the system response quality, the failure to achieve online optimal design of the control process, which leads to high control energy consumption, and insufficient estimation and compensation capabilities for unknown dynamics and unmeasurable states of the system.

[0008] To solve the above problems, the technical solution adopted by the present invention is as follows:

[0009] A two-degree-of-freedom helicopter predefined time preset performance tracking control method includes:

[0010] Step S1: Construct a two-degree-of-freedom helicopter dynamics model containing modeling uncertainties and external disturbances;

[0011] Step S2: To address the problem of unmeasurable partial states of the system, a learning observer incorporating a fuzzy logic system is designed to reconstruct the system state and to perform real-time approximation and compensation for the comprehensive unknown nonlinear terms in the two-degree-of-freedom helicopter dynamics model.

[0012] Step S3: Introduce a preset performance function and error transformation mechanism to map the constrained system tracking error into an unconstrained equivalent error, so as to ensure that the system tracking error converges to the preset performance boundary within a predetermined time.

[0013] Step S4: Based on the backstepping control framework, the system is decoupled by coordinate transformation to construct a two-level subsystem, and a predefined time command filter is introduced to obtain the derivative of the virtual control law. At the same time, a dynamic compensation term is constructed in combination with the filtering error.

[0014] Step S5: Construct performance index functions for each level of the decoupled subsystem, use the Actor-Critic reinforcement learning structure to solve the Hamilton-Jacobi-Bellman equation online, and design an adaptive optimal control law and its parameter update rules that satisfy the predefined time convergence characteristics.

[0015] Step S6: Introduce an event triggering mechanism based on switching thresholds, which adaptively switches between different triggering thresholds according to the system error state, and updates the actual control input only when the triggering conditions are met.

[0016] Further, in step S1, the two-degree-of-freedom helicopter dynamics model is specifically as follows:

[0017]

[0018] In the formula: Represents the pitch and yaw angles of a helicopter; Angular velocity representing pitch and yaw angles; For control input, where This represents the voltage of the pitch propeller motor. This represents the voltage of the yaw propeller motor; For system output; External environmental interference; , For unknown smooth nonlinear function vectors; and This is the gain matrix of a two-degree-of-freedom helicopter system model.

[0019] Furthermore, in step S2, the structure of the learning observer is as follows:

[0020]

[0021] In the formula: State variables and The estimated value; ; This is an estimated value output by the system. For fuzzy ideal weight vector The estimated value is used to approximate unknown nonlinear functions in the system online; For fuzzy basis function vectors, The input vector estimate; as well as The positive gain constant of the design; For design parameters; This is a predefined convergence time.

[0022] Further, in step S3, the system tracking error is defined as... ,in The desired trajectory; system tracking error Each element is constrained by and Within the symmetrical performance envelope formed, the preset performance function Defined as:

[0023]

[0024] In the formula: and These are the initial boundary value and the steady-state convergence value of the preset performance function, respectively. This is the preset convergence time; This is a constant used to adjust the convergence rate.

[0025] Furthermore, in step S3, the error conversion mechanism uses a mapping function. Limiting system tracking error The mapping is to an unrestricted equivalent error.

[0026] Furthermore, the coordinate transformation equation described in step S4 is:

[0027]

[0028] in, The output signal of the predefined time command filter is constructed as follows: The predefined time command filter and its parameter adaptive update law are constructed as follows:

[0029]

[0030]

[0031] In the formula: for The time derivative; The input signal to the predefined time command filter is the virtual control law; Represents the error of a predefined time filter; Unknown positive term constant Real-time estimated value; , , and It is the gain coefficient composed of positive definite design parameters; and These are positive definite design parameters related to convergence speed or convergence characteristics in filter design. Adjustable design parameters; These are adjustable parameters used to control the nonlinear characteristics of the convergence rate as a function of time. , All are positive design parameters.

[0032] Furthermore, in step S5, the Actor-Critic reinforcement learning structure includes an execution network and an evaluation network, targeting the first subsystem after decoupling. Level subsystem, performing network weight estimation Update law and evaluation network weight estimate The update laws are as follows:

[0033]

[0034]

[0035] In the formula: A simplified version of the basis function vector ; and These are the parameters to be designed.

[0036] Furthermore, in step S5, the adaptive optimal virtual control law of the first-level subsystem... for:

[0037]

[0038] In the formula: This is a first-level dummy error variable; and The gain coefficient is composed of positive definite design parameters; ; ; These are the parameters to be designed; , which is the basis function input vector of the first-level subsystem.

[0039] Furthermore, in step S5, the adaptive optimal actual control law of the second-level subsystem... for:

[0040]

[0041] In the formula: This is a second-level dummy error variable; For matrix The inverse matrix; These are the parameters to be designed; , which is the basis function input vector of the second-level subsystem.

[0042] Furthermore, in step S6, the event triggering mechanism based on the switching threshold specifically involves: within a time period... Inside, the actual control input remains at Until the moment when the next trigger condition is met, then when At that time, the control input is updated to The triggering conditions are designed as follows:

[0043]

[0044] The intermediate control signal is designed as follows:

[0045]

[0046] In the formula: The moment the event is triggered; This is an intermediate control signal; For triggering error; , , , All are preset trigger parameters; ,in ; These are the parameters to be designed.

[0047] Compared with the prior art, the beneficial effects of the present invention are:

[0048] (1) This invention integrates a learning observer, predefined time preset performance control, and optimal control strategy based on an actor-critic network, and combines them with an event triggering mechanism to achieve high-performance robust tracking control under limited communication bandwidth conditions. This invention not only ensures that all signals of a two-degree-of-freedom helicopter closed-loop system are uniformly and eventually bounded within a predefined time, but also significantly improves the transient and steady-state response quality of the system while minimizing control costs and saving communication and computing resources.

[0049] (2) By designing a learning observer containing a fuzzy logic system, the system can accurately reconstruct the unmeasurable angular velocity state of the helicopter system and perform online approximation and real-time compensation for unknown nonlinear dynamics and external lumped disturbances, which greatly improves the robustness and tracking accuracy of the system under conditions of parameter uncertainty and external interference.

[0050] (3) By pre-setting the performance envelope and error transformation, the constrained physical tracking error is mapped to an unconstrained equivalent error, so that the convergence time of the tracking error is decoupled from the initial conditions and can be pre-set in the design stage. This realizes explicit constraints on the system overshoot, convergence speed and steady-state accuracy, and greatly improves the transient and steady-state response performance of the system.

[0051] (4) Introducing a predefined time instruction filter in the backstepping control architecture to obtain the derivative of the virtual control law and using its nonlinear dynamic evolution process to replace the direct differentiation operation in the traditional backstepping method not only effectively avoids the "computation explosion" problem, but also ensures the control accuracy within the predefined time through dynamic compensation of filtering error.

[0052] (5) For the decoupled subsystem, the Hamilton-Jacobi-Bellman equations are solved online using an execution-evaluation network structure, realizing online adaptive optimization of the control law. This mechanism can generate the optimal control strategy that satisfies the performance constraints within a predetermined time without completely relying on the accurate system model, effectively reducing control energy consumption.

[0053] (6) An event triggering mechanism based on a switching threshold was designed, which adaptively switches between different triggering conditions according to the system error state. While ensuring tracking accuracy, this mechanism effectively reduces the communication update frequency between the controller and the actuator, reduces system bandwidth usage and computational overhead, and avoids the Zeno phenomenon mathematically and mechanically, thus greatly improving engineering feasibility.

[0054] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, embodiments of the present invention are described below in detail with reference to the accompanying drawings. Attached Figure Description

[0055] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0056] Figure 1 This is a schematic diagram of a two-degree-of-freedom helicopter model;

[0057] Figure 2 This is a block diagram of a two-degree-of-freedom helicopter control system.

[0058] Figure 3 This is a tracking trajectory diagram of a two-degree-of-freedom helicopter pitch angle versus desired angle.

[0059] Figure 4 This is a tracking trajectory diagram of a two-degree-of-freedom helicopter's yaw angle relative to the desired angle.

[0060] Figure 5 The figure shows the tracking response curve for the angle error of a two-degree-of-freedom helicopter system.

[0061] Figure 6 The control input curves for a two-degree-of-freedom helicopter system are shown.

[0062] Figure 7 The dynamic evolution diagram of the fuzzy logic weight convergence curve and adaptive parameter update law in the learning observer of a two-degree-of-freedom helicopter system;

[0063] Figure 8 The dynamic evolution trajectory of the fuzzy execution-evaluation weights for a two-degree-of-freedom helicopter during the online optimization process;

[0064] Figure 9 The diagram shows the triggering time interval and dynamic characteristics of the switching threshold event triggering mechanism in a two-degree-of-freedom helicopter system. Detailed Implementation

[0065] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments.

[0066] Please refer to Figure 1 and Figure 2 A two-degree-of-freedom helicopter predefined time preset performance tracking control method based on a learned observer includes the following steps:

[0067] Step 1, according to Figure 1The simplified diagram of the two-degree-of-freedom helicopter system shown is used to construct the following dynamic model:

[0068] (1)

[0069] In the formula: and Let be the equivalent inertial parameter of the system, where , , , , These represent the total mass of the helicopter, the acceleration due to gravity, and the distance from the system's center of mass to the support point, respectively. and These represent pitch and yaw angles, respectively. and These represent the angular velocities of pitch and yaw, respectively. and These represent the angular accelerations for pitch and yaw angles, respectively. and These represent the friction damping coefficients present during pitch and yaw rotations, respectively. and These represent the sine and cosine functions, respectively. and These represent the moments of inertia of the pitch and yaw axes, respectively. and These represent the thrust gain of the pitch propeller acting on the pitch axis and yaw axis, respectively. and These represent the thrust gain of the yaw propeller acting on the pitch and yaw axes, respectively. and These are the control input voltages for the pitch and yaw propeller motors, respectively.

[0070] Detailed parameters of the two-degree-of-freedom helicopter system model are shown in Table 1:

[0071] Table 1: Model Parameters of a Two-Degree-of-Freedom Helicopter System

[0072]

[0073] definition , , , represent Furthermore, by transposing the model, the two-degree-of-freedom helicopter system model can be expressed as:

[0074] (2)

[0075] In the formula: External environmental interference; , For unknown smooth nonlinear function vectors; and The gain matrices for the two-degree-of-freedom helicopter system model are as follows:

[0076]

[0077]

[0078] Step 2: Based on the angular velocity in the dynamic model described in Step 1 It cannot be directly and precisely measured, and the function For problems involving unknown nonlinear characteristics, a fuzzy learning observer is introduced for state reconstruction and dynamic learning, especially for uncertain system terms. According to the universal approximation property of FLS, we can obtain:

[0079] (3)

[0080] in, The input vector;

[0081] The ideal weight vector is defined as follows: ;

[0082] Represents a fuzzy basis function vector. The approximation error is bounded.

[0083] To account for state estimation in control design, the lumped approximation error is defined as... Obviously, It is bounded, satisfying ,in It is a positive integer. Therefore, we can conclude that:

[0084] (4)

[0085] in, express To address the challenge posed by the unpredictability of the system's state, this paper designs a fuzzy learning observer for state estimation. The proposed learning observer structure is as follows:

[0086] (5)

[0087] in ; These are system state variables. and The estimated value; For fuzzy ideal weight vector The estimated value; and This is the positive gain constant for the design.

[0088] Define the observation error vector as and order This represents the weight estimation error. Based on this, the observer's error dynamics can be derived as follows:

[0089] (6)

[0090] in , Due to the matrix All eigenvalues ​​have negative real parts, therefore It is a Hurwitz matrix. Furthermore, there exists a positive definite symmetric matrix. Satisfy the following equation:

[0091] (7)

[0092] in Let be any given positive definite matrix.

[0093] Construct candidate Lyapunov functions as follows .right Taking the time derivative, we get:

[0094] (8)

[0095] By simplifying the inequality, we get:

[0096] (9)

[0097] in: , ,

[0098] Representation matrix The smallest eigenvalue.

[0099] Step 3: Based on the system equations obtained in Step 1, the main objective of the two-degree-of-freedom helicopter tracking control is the output of the system model. The desired trajectory needs to be tracked in real time. This will generate a tracking error. System tracking error Each element is constrained by and Within the symmetrical property envelope:

[0100]

[0101] In the formula: and These are the initial boundary values ​​and steady-state convergence values ​​of the predefined time-preset performance function, used to limit the initial width and final accuracy of the error envelope; The preset convergence time ensures that the system... It strictly reaches a steady state; To adjust the convergence rate.

[0102] Furthermore, to achieve this constraint, a transformation function is employed. The tracking error will be subject to inequality constraints. Converted into unconstrained equivalent error .

[0103] Step 4: Based on the equivalent error obtained in Step 3 Using dynamic surface control techniques, the following coordinate transformations are constructed:

[0104] (10)

[0105] In the formula: The output signal of the predefined time filter is constructed as follows:

[0106] (11)

[0107] In the formula: for The time derivative, whose initial value satisfies , For the input signal of a predefined time filter, for The time derivative of , and satisfies , For an unknown positive constant, For parameters Real-time estimated value; Represents the error of a predefined time filter; and Gain coefficient composed of positive definite design parameters; This is a predefined convergence time. and These are positive definite design parameters related to convergence speed or convergence characteristics in filter design. Adjustable design parameters; These are adjustable parameters used to control the nonlinear characteristics of the convergence rate as a function of time. , All are positive design parameters.

[0108] To enhance the system's adaptability to dynamic changes, an adaptive update law is designed. :

[0109]

[0110] In the formula: and Gain coefficient composed of positive definite design parameters.

[0111] The two-degree-of-freedom helicopter system model is decomposed into two-level subsystems, and the first-level subsystem transformation error variable is introduced. Second-level subsystem transformation error variable .

[0112] Step 5: Based on the coordinate transformation obtained in Step 4, in order to optimize the predefined time-preset performance control and derive the ideal optimal virtual output feedback control law. Construct the first-level optimal performance function for the first-level subsystem. :

[0113] (12)

[0114] In the formula: For including the origin The allowable control set on a compact set, As a discount factor,

[0115] Represents the cost function, This is the optimal virtual controller.

[0116] Based on Bellman optimization principles, the following HJB equations are constructed to solve the optimal control problem:

[0117] (13)

[0118] In the formula: express right The partial derivative, for The derivative with respect to time.

[0119] To achieve the optimal control objective within a predefined time period, an intermittent cost function is constructed. as follows:

[0120] (14)

[0121] In the formula: , , ,

[0122] , These are the parameters to be designed.

[0123] Due to the first-level intermittent cost function For unknown and continuous variables, a fuzzy logic network is introduced to perform an online approximate estimation, i.e.:

[0124] (15)

[0125] In the formula: For the ideal weight matrix,

[0126] Let be the basis function vector, and its input vector be defined as follows: ;

[0127] To approximate the error vector, and satisfy... ,in It is a positive number.

[0128] Due to ideal weights To address the unknown, an execution-evaluation network architecture is introduced for online learning. The HJB equation is approximated using an execution-evaluation fuzzy network, yielding the update law for the execution-evaluation network. and and optimal virtual controller They are respectively:

[0129] (16)

[0130] (17)

[0131] (18)

[0132] In the formula: and for The estimated value, and These are the parameters to be designed.

[0133] Constructing Lyapunov functions for the first-stage subsystem of a two-degree-of-freedom helicopter system model :

[0134] (19)

[0135] In the formula: , , To estimate the error, Represents the trace of a matrix.

[0136] Furthermore, the Lyapunov function Taking the derivative with respect to time, we get:

[0137] (20)

[0138] In the formula: for The time derivative.

[0139] The optimal virtual controller designed Adaptive parameter update law Execution-Comment Network Update Law and Substituting into formula (20), we can simplify using inequalities to obtain:

[0140] (twenty one)

[0141] In the formula:

[0142] .

[0143] During the inequality simplification process, the value of the gain of the virtual controller to be designed in the first-level subsystem is obtained.

[0144] Step 6, the second-stage subsystem of the two-degree-of-freedom helicopter system is

[0145] (twenty two)

[0146] Constructing the first-level optimal performance function for the second-level subsystem :

[0147] (twenty three)

[0148] In the formula: , This is the optimal tracking controller.

[0149] Based on Bellman optimization principles, the following HJB equations are constructed to solve the optimal control problem:

[0150] (twenty four)

[0151] In the formula: express right The partial derivative, for The derivative with respect to time.

[0152] To achieve the optimal control objective within a predefined time period, an intermittent cost function is constructed. as follows: (25)

[0153] In the formula: These are the parameters to be designed.

[0154] Due to the second-level intermittent cost function For unknown and continuous variables, a fuzzy logic network is introduced to perform an online approximate estimation, i.e.:

[0155] (26)

[0156] In the formula: Represents the weight vector of an ideal fuzzy network. For the basis function vector,

[0157] To approximate the error vector, and satisfy... ,in It is a positive number.

[0158] Due to the ideal weight vector To address the unknown issue and obtain the optimal tracking controller in real time, an execution-evaluation network architecture is introduced for online learning. Furthermore, the execution network approximates the optimal control strategy, and the evaluation network approximates the second-order Hamilton-Jacobi-Bellman equations to assess the current strategy performance, thus deriving the execution-evaluation adaptive update law. and Ultimately, an adaptive optimal actual control law that meets the predefined time convergence requirement is obtained. :

[0159] (27)

[0160] (28)

[0161] (29)

[0162] In the formula: and for The estimated value, and These are the parameters to be designed.

[0163] Considering the communication bandwidth limitations and computational resource constraints faced by two-degree-of-freedom helicopters in practical engineering applications, this invention introduces a switching triggering mechanism into the predefined time performance control scheme. This mechanism aims to reduce the communication frequency between the controller and actuators while ensuring the system's control performance. Actual control signals At the moment the event is triggered Update, and at intervals The value remains constant, that is:

[0164] (30)

[0165] The triggering conditions are designed as follows:

[0166] (31)

[0167] in, , , , These are the preset trigger parameters;

[0168] For triggering error; This is an intermediate control signal.

[0169] Actual control input at During the period, it remained as Until the next time the triggering condition is met, that will continue.

[0170] when At that time, the control input is updated to .

[0171] In addition, there exists a time-varying function ,satisfy , so that:

[0172] (32)

[0173] in, .

[0174] Furthermore, the present invention will use intermediate control signals Designed as follows:

[0175] (33)

[0176] In the formula, These are the parameters to be designed.

[0177] Constructing Lyapunov functions for the second-stage subsystem of a two-degree-of-freedom helicopter system model :

[0178] (34)

[0179] In the formula: , .

[0180] Furthermore, differentiating formula (34) with respect to time, we obtain:

[0181] (35)

[0182] The designed adaptive optimal actual control law intermediate control signal Execution-Evaluation Adaptive Update Law and Substituting into inequality (35), we can simplify the equation to obtain:

[0183] (36)

[0184] In the formula:

[0185] During the inequality simplification process, the gain value of the actual controller of the second-level subsystem is calculated.

[0186] Step 7: Verify the results obtained in Step 6, and construct the global Lyapunov function for the two-degree-of-freedom helicopter system model. And by differentiating it with respect to time, we can obtain:

[0187] (37)

[0188] In the formula: .

[0189] By simplifying the inequalities, extracting common factors, and combining like terms, Finally, it simplifies to:

[0190] (38)

[0191] In the formula: , ; , ,

[0192] .

[0193] To further study the region of convergence and convergence time, if Then inequality (38) can be changed to:

[0194] (39)

[0195] According to formula (39), the designed learning observer and optimal virtual controller are used. Adaptive optimal actual control law And the corresponding execution-evaluation network adaptive learning law, this result rigorously proves mathematically that the adaptive optimization control scheme can ensure that all signals of the closed-loop system are actually predefined time consistent and eventually bounded, while satisfying transient and steady-state performance constraints. Specifically, the function At a predefined time The interior is driven to the bounded region. The above proof demonstrates that this control scheme not only minimizes control costs but also ensures that the pitch and yaw tracking errors of the two-degree-of-freedom helicopter remain strictly within the constraints of the preset performance function.

[0196] To illustrate the control effect of the method of the present invention in detail, a simulation experiment will be conducted in MATLAB.

[0197] Reference trajectory set ,

[0198] The system initial conditions are set as follows: .

[0199] The default performance function parameters are selected as follows: , , and Second.

[0200] The selected controller gain is shown in Table 2.

[0201] Table 2: Controller Gain

[0202]

[0203] The control scheme proposed in this invention has been verified using the MATLAB simulation platform. The experimental results and technical effects are analyzed as follows: Figure 3 and Figure 4 As shown, the two-degree-of-freedom helicopter system can achieve high-precision real-time tracking of the desired reference trajectory in both pitch and yaw angles. The system output response is smooth, with no obvious overshoot or oscillation. Figure 5 As shown, under the constraints of the proposed predefined time performance function, the angle tracking errors of the pitch and yaw channels are always strictly limited within the preset dynamic boundaries. Experimental data show that the system not only meets the strict transient performance requirements (such as convergence speed and overshoot), but also achieves the preset steady-state accuracy, verifying the effectiveness of predefined time control in improving the system's dynamic response. Figure 6 The system's control input curves are shown, demonstrating that the control signal is continuous and bounded, with smooth changes and no obvious chattering, thus meeting the actuator's physical constraints. Furthermore, the stability of the system's key adaptive parameters is experimentally verified: the fuzzy network weights of the learning observer and the adaptive parameter update law ( Figure 7 ), Actor-Critic network weights based on reinforcement learning ( Figure 8 All of them achieved fast and smooth stable convergence within the predefined control time. Furthermore, Figure 9The triggering time interval and dynamic characteristics of the event triggering mechanism based on switching thresholds are described. As shown in the figure, the triggering interval exhibits significant non-uniformity and the Zeno phenomenon is absent, demonstrating that the mechanism effectively reduces communication bandwidth usage and computational overhead while maintaining control accuracy. Based on the simulation results, the predefined time preset performance tracking control method proposed in this invention can guarantee stable convergence of the two-degree-of-freedom helicopter closed-loop system within a predefined time. The system tracking error can quickly converge to the preset steady-state error neighborhood within a given time, thereby significantly improving the system's transient response performance and steady-state control accuracy. Furthermore, by reasonably adjusting the predefined time and preset performance function parameters, this method can flexibly adapt to control requirements under different complex operating conditions. Moreover, even under uncertainties such as incomplete state measurement, external disturbances, and intermittent updates of the control signal, the system can still achieve high-precision tracking of the reference trajectory, demonstrating strong robustness and reliability, verifying the effectiveness and superiority of the proposed control strategy.

[0204] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., 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 two-degree-of-freedom helicopter predefined time preset performance tracking control method, characterized in that, include: Step S1: Construct a two-degree-of-freedom helicopter dynamics model containing modeling uncertainties and external disturbances; Step S2: To address the problem of unmeasurable partial states of the system, a learning observer incorporating a fuzzy logic system is designed to reconstruct the system state and to perform real-time approximation and compensation for the comprehensive unknown nonlinear terms in the two-degree-of-freedom helicopter dynamics model. Step S3: Introduce a preset performance function and error transformation mechanism to map the constrained system tracking error into an unconstrained equivalent error, so as to ensure that the system tracking error converges to the preset performance boundary within a predetermined time. Step S4: Based on the backstepping control framework, the system is decoupled by coordinate transformation to construct a two-level subsystem, and a predefined time command filter is introduced to obtain the derivative of the virtual control law. At the same time, a dynamic compensation term is constructed in combination with the filtering error. Step S5: Construct performance index functions for each level of the decoupled subsystem, use the Actor-Critic reinforcement learning structure to solve the Hamilton-Jacobi-Bellman equation online, and design an adaptive optimal control law and its parameter update rules that satisfy the predefined time convergence characteristics. Step S6: Introduce an event triggering mechanism based on switching thresholds, which adaptively switches between different triggering thresholds according to the system error state, and updates the actual control input only when the triggering conditions are met.

2. The two-degree-of-freedom helicopter predefined time preset performance tracking control method according to claim 1, characterized in that, In step S1, the two-degree-of-freedom helicopter dynamics model is specifically as follows: In the formula: Represents the pitch and yaw angles of a helicopter; Angular velocity representing pitch and yaw angles; For control input, where This represents the voltage of the pitch propeller motor. This represents the voltage of the yaw propeller motor; For system output; External environmental interference; , For an unknown smooth nonlinear function vector; and This is the gain matrix of a two-degree-of-freedom helicopter system model.

3. The two-degree-of-freedom helicopter predefined time preset performance tracking control method according to claim 2, characterized in that, In step S2, the structure of the learning observer is as follows: In the formula: State variables and The estimated value; ; This is an estimated value output by the system. For fuzzy ideal weight vector The estimated value is used to approximate unknown nonlinear functions in the system online; For fuzzy basis function vectors, The input vector estimate; as well as The positive gain constant of the design; For design parameters; This is a predefined convergence time.

4. The two-degree-of-freedom helicopter predefined time preset performance tracking control method according to claim 2, characterized in that, In step S3, the system tracking error is defined as ,in The desired trajectory; system tracking error Each element is constrained by and Within the symmetrical performance envelope formed, the preset performance function Defined as: In the formula: and These are the initial boundary value and the steady-state convergence value of the preset performance function, respectively. This is the preset convergence time; This is a constant used to adjust the convergence rate.

5. The two-degree-of-freedom helicopter predefined time preset performance tracking control method according to claim 4, characterized in that, In step S3, the error transformation mechanism uses a mapping function. Limiting system tracking error The mapping is to an unrestricted equivalent error.

6. The two-degree-of-freedom helicopter predefined time preset performance tracking control method according to claim 5, characterized in that, The coordinate transformation equation mentioned in step S4 is: in, The output signal of the predefined time command filter is constructed as follows: The predefined time command filter and its parameter adaptive update law are constructed as follows: In the formula: for The time derivative; The input signal to the predefined time command filter is the virtual control law; Represents the error of a predefined time filter; Unknown positive term constant Real-time estimated value; , , and It is the gain coefficient composed of positive definite design parameters; and These are positive definite design parameters related to convergence speed or convergence characteristics in filter design. Adjustable design parameters; These are adjustable parameters used to control the nonlinear characteristics of the convergence rate as a function of time. , All are positive design parameters.

7. The two-degree-of-freedom helicopter predefined time preset performance tracking control method according to claim 6, characterized in that, In step S5, the Actor-Critic reinforcement learning structure includes an execution network and an evaluation network. For the j-th subsystem in the decoupled two-level subsystem, the execution network estimates the weights. Update law and evaluation network weight estimate The update laws are as follows: In the formula: A simplified version of the basis function vector ; and These are the parameters to be designed.

8. The two-degree-of-freedom helicopter predefined time preset performance tracking control method according to claim 7, characterized in that, In step S5, the adaptive optimal virtual control law of the first-level subsystem... for: In the formula: This is a first-level dummy error variable; and The gain coefficient is composed of positive definite design parameters; ; ; These are the parameters to be designed; is the basis function input vector of the first-level subsystem.

9. The two-degree-of-freedom helicopter predefined time preset performance tracking control method according to claim 8, characterized in that, In step S5, the adaptive optimal actual control law of the second-level subsystem... for: In the formula: This is a second-level dummy error variable; For matrix The inverse matrix; These are the parameters to be designed; , which is the basis function input vector of the second-level subsystem.

10. The two-degree-of-freedom helicopter predefined time preset performance tracking control method according to claim 9, characterized in that, In step S6, the event triggering mechanism based on the switching threshold specifically involves: within a time period Inside, the actual control input remains at Until the moment when the next trigger condition is met, then when At that time, the control input is updated to The triggering conditions are designed as follows: The intermediate control signal is designed as follows: In the formula: The moment the event is triggered; This is an intermediate control signal; For triggering error; , , , All are preset trigger parameters; ,in ; These are the parameters to be designed.

Images